RUSSIAN ACADEMY OF SCIENCES
Keldysh Institute of Applied Mathematics
INSTITUTE OF ORIENTAL STUDIES
VOLGOGRAD CENTER FOR SOCIAL RESEARCH
HISTORY & MATHEMATICS
Trends and Cycles
Edited by
Leonid E. Grinin,
and Andrey V. Korotayev
‘Uchitel’
Publishing House
Volgograd
ББК 22.318 60.5
‛History & Mathematics’ Yearbook
Editorial Council: Herbert Barry III (Pittsburgh University), Leonid Borodkin
(Moscow State University; Cliometric Society), Robert Carneiro (American
Museum of Natural History), Christopher Chase-Dunn (University of California,
Riverside), Dmitry Chernavsky (Russian Academy of Sciences), Thessaleno
Devezas (University of Beira Interior), Leonid Grinin (National Research University Higher School of Economics), Antony Harper (New Trier College), Peter
Herrmann (University College of Cork, Ireland), Andrey Korotayev (National
Research University Higher School of Economics), Alexander Logunov (Russian State University for the Humanities), Gregory Malinetsky (Russian Academy of Sciences), Sergey Malkov (Russian Academy of Sciences), Charles
Spencer (American Museum of Natural History), Rein Taagapera (University of
California, Irvine), Arno Tausch (Innsbruck University), William Thompson
(University of Indiana), Peter Turchin (University of Connecticut), Douglas
White (University of California, Irvine), Yasuhide Yamanouchi (University of
Tokyo).
History & Mathematics: Trends and Cycles. Yearbook / Edited by Leonid E. Grinin and Andrey V. Korotayev. – Volgograd: ‘Uchitel’ Publishing House, 2014. –
328 pp.
The present yearbook (which is the fourth in the series) is subtitled Trends & Cycles.
It is devoted to cyclical and trend dynamics in society and nature; special attention is paid
to economic and demographic aspects, in particular to the mathematical modeling of the
Malthusian and post-Malthusian traps' dynamics.
An increasingly important role is played by new directions in historical research that
study long-term dynamic processes and quantitative changes. This kind of history can hardly
develop without the application of mathematical methods. There is a tendency to study history
as a system of various processes, within which one can detect waves and cycles of different
lengths – from a few years to several centuries, or even millennia. The contributions to this
yearbook present a qualitative and quantitative analysis of global historical, political, economic and demographic processes, as well as their mathematical models.
This issue of the yearbook consists of three main sections: (I) Long-Term Trends in
Nature and Society; (II) Cyclical Processes in Pre-industrial Societies; (III) Contemporary
History and Processes.
We hope that this issue of the yearbook will be interesting and useful both for historians and mathematicians, as well as for all those dealing with various social and natural
sciences.
The present research has been carried out in the framework of the project of the National
Research University Higher School of Economics.
‛Uchitel’ Publishing House
143 Kirova St.,
400079 Volgograd,
Russia
ISBN 978-5-7057-4223-3
Volgograd 2014
© ‘Uchitel’ Publishing House, 2014
Contents
Leonid E. Grinin and
Andrey V. Korotayev
Introduction. Modeling and Measuring Cycles,
Processes, and Trends . . . . . . . . . . . .
5
I. Long-Term Trends in Nature and Society
Mathematical Modeling of Biological and Social
Leonid E. Grinin,
Alexander V. Markov, Evolutionary Macrotrends . . . . . . . . . .
and Andrey V. Korotayev
Tony Harper
William R. Thompson
and Kentaro Sakuwa
9
The World System Trajectory: The Reality of
Constraints and the Potential for Prediction . . . . .
49
Another, Simpler Look: Was Wealth Really Determined
in 8000 BCE, 1000 BCE, 0 CE, or Even 1500 CE? . .
108
II. Cyclical Processes in Pre-industrial Societies
Cycling in the Complexity of Early Societies . . . . 136
Sergey Gavrilets,
David G. Anderson, and
Peter Turchin
David C. Baker
Sergey A. Nefedov
Demographic-Structural Theory and the Roman
Dominate . . . . . . . . . . . . . . . .
159
Modeling Malthusian Dynamics in Pre-industrial
Societies: Mathematical Modeling . . . . . . . . 190
Сontents
4
III. Contemporary History and Processes
A Trap at the Escape from the Trap? Some Demographic
Andrey V. Korotayev,
Sergey Yu. Malkov, and Structural Factors of Political Instability in Modernizing
Social Systems . . . . . . . . . . . . . .
Leonid E. Grinin
201
Arno Tausch and
Almas Heshmati
Labour Migration and ‘Smart Public Health’ . . . .
268
Anthony Howell
Is Geography ‘Dead’ or ‘Destiny’ in a Globalizing World?
A Network Analysis and Latent Space Modeling Approach
of the World Trade Network . . . . . . . . . . 281
Kent R. Crawford and
Nicholas W. Mitiukov
The British-Italian Performance in the Mediterranean
from the Artillery Perspective . . . . . . . . . 300
The Shield of Islam? Islamic Factor of HIV Prevalence in
Alisa R. Shishkina,
Africa . . . . . . . . . . . . . . . . . 314
Leonid M. Issaev,
Konstantin M. Truevtsev,
and Andrey V. Korotayev
Contributors . . . . . . . . . . . . . . . . . . . . . . . 322
Guidelines for Contributors . . . . . . . . . . . . . . . . . . 328
Introduction
Modeling and Measuring Cycles,
Processes, and Trends
Leonid E. Grinin and Andrey V. Korotayev
The present Yearbook (which is the fourth in the series) is subtitled Trends &
Cycles. Already ancient historians (see, e.g., the second Chapter of Book VI of
Polybius' Histories) described rather well the cyclical component of historical
dynamics, whereas new interesting analyses of such dynamics also appeared in
the Medieval and Early Modern periods (see, e.g., Ibn Khaldūn 1958 [1377], or
Machiavelli 1996 [1531] 1). This is not surprising as the cyclical dynamics was
dominant in the agrarian social systems. With modernization, the trend dynamics became much more pronounced and these are trends to which the students
of modern societies pay more attention. Note that the term trend – as regards its
contents and application – is tightly connected with a formal mathematical
analysis. Trends may be described by various equations – linear, exponential,
power-law, etc. On the other hand, the cliodynamic research has demonstrated
that the cyclical historical dynamics can be also modeled mathematically in
a rather effective way (see, e.g., Usher 1989; Chu and Lee 1994; Turchin 2003,
2005a, 2005b; Turchin and Korotayev 2006; Turchin and Nefedov 2009; Nefedov 2004; Korotayev and Komarova 2004; Korotayev, Malkov, and Khaltourina 2006; Korotayev and Khaltourina 2006; Korotayev 2007; Grinin 2007),
whereas the trend and cycle components of historical dynamics turn out to be
of equal importance.
It is obvious that the qualitative innovative motion toward new, unknown
forms, levels, and volumes, etc. cannot continue endlessly, linearly and smoothly.
It always has limitations, accompanied by the emergence of imbalances, increasing resistance to environmental constraints, competition for resources, etc. These
endless attempts to overcome the resistance of the environment created conditions
for a more or less noticeable advance in societies. However, relatively short periods of rapid growth (which could be expressed as a linear, exponential or hyperbolic trend) tended to be followed by stagnation, different types of crises and setbacks, which created complex patterns of historical dynamics, within which trend
and cyclical components were usually interwoven in rather intricate ways (see,
e.g., Grinin and Korotayev 2009; Grinin, Korotayev, and Malkov 2010).
1
For interpretations of their theories (in terms of cliodynamics, cyclical dynamics etc.) see, e.g.,
Turchin 2003; Korotayev and Khaltourina 2006; Grinin 2012a.
History & Mathematics: Trends and Cycles 2014 5 –8
5
6
Introduction. Cycles, Processes, and Trends
Hence, in history we had a constant interaction of cyclical and trend dynamics, including some very long-term trends that are analyzed in Section I of
the present Yearbook which includes contributions by Leonid E. Grinin,
Alexander V. Markov, and Andrey V. Korotayev (‘Mathematical Modeling
of Biological and Social Evolutionary Macrotrends’), Tony Harper
(‘The World System Trajectory: The Reality of Constraints and the Potential
for Prediction’) and William R. Thompson and Kentaro Sakuwa (‘Another,
Simpler Look: Was Wealth Really Determined in 8000 BCE, 1000 BCE, 0 CE,
or Even 1500 CE?’).
If in a number of societies and for quite a long time we observe regular
repetition of a cycle of the same type ending with grave crises and significant
setbacks, this means that at a given level of development we confront such
rigid and strong systemic and environmental constraints which the given society is unable to overcome.
Thus, the notion of cycle is closely related to the concept of the trap. In the
language of nonlinear dynamics the concept of traps will more or less correspond to the term ‘attractor’. Continuing the comparison with nonlinear dynamics, we should say that a steady escape from the trap will largely correspond to the concept of a phase transition.
In this Yearbook particular attention is paid, of course, to the Malthusian
trap. The escape from the Malthusian trap in historical retrospect was incredibly difficult (see, e.g., Korotayev et al. 2011; Grinin 2012b). Periodically, attempts were made to get out of this trap. However, for many millennia no societies managed to achieve a final steady escape from it, but those attempts in
the long run led to a systematic increase in the level of technological development of the World System.
The problems of the mathematical modeling of the Malthusian trap dynamics are analyzed in the article by Sergey A. Nefedov (‘Modeling Malthusian
Dynamics in Pre-Industrial Societies: Mathematical Modeling’) in Section II of
the present issue of the Yearbook. This section also includes the article by Sergey Gavrilets, David G. Anderson, and Peter Turchin (‘Cycling in the Complexity of Early Societies’), as well as the one by David C. Baker (‘Demographic-Structural Theory and the Roman Dominate’). These articles deal with
various cycles in the historical dynamics of pre-Modern social systems that
are rather tightly connected with demographic macroprocesses. The first article of the next section also deals with the problems of the escape from the
Malthusian trap.
Section III deals with Modern history and contemporary processes and includes the contribution by Andrey V. Korotayev, Sergey Yu. Malkov, and
Leonid E. Grinin (‘A Trap at the Escape from the Trap? Some Demographic
Structural Factors of Political Instability in Modernizing Social Systems’) continuing the discussion on the issues of the Malthusian and post-Malthusian
traps. This issue is also touched upon in the contributions by Arno Tausch
Leonid E. Grinin and Andrey V. Korotayev
7
and Almas Heshmati (‘Labour Migration and “Smart Public Health”’), Anthony Howell (‘Is Geography “Dead” or “Destiny” in a Globalizing World?
A Network Analysis and Latent Space Modeling Approach of the
World Trade Network’), Kent R. Crawford and Nicholas W. Mitiukov
(‘The British-Italian Performance in the Mediterranean from the Artillery
Perspective’), as well as Alisa R. Shishkina, Leonid M. Issaev, Konstantin M. Truevtsev, and Andrey V. Korotayev (‘The Shield of Islam? Islamic
Factor of HIV Prevalence in Africa’).
Articles in this section are devoted to some rather interesting aspects and
events from the Second World War to the prospects for change of the age composition of the Earth's population in the coming decades. What appears valuable is that the contributors have managed to somehow formalize these processes, and to apply various mathematical techniques to the analysis of the recent historical processes.
References
Chu C. Y. C., and Lee R. D. 1994. Famine, Revolt, and the Dynastic Cycle: Population
Dynamics in Historic China. Journal of Population Economics 7: 351–378.
Grinin L. E. 2007. The Correlation between the Size of Society and Evolutionary Type of
Polity. History and Mathematics: The Analysis and Modeling of Socio-historical Processes / Ed. by A. V. Korotayev, S. Yu. Malkov, and L. E. Grinin, pp. 263–303. Moscow: KomKniga/URSS. In Russian ( ри и
. Е. За и и
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и
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Grinin L. E. 2012a. From Confucius to Comte. Formation of the Theory, Methodology
and Philosophy of History / ed. by A. V. Korotayev. Moscow: LIBROKOM. In Russian ( ри и . . Е. О К ф я
К
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, е
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. р . А. . К р а . .: ИБ ОКО ).
Grinin L. E. 2012b. State and Socio-Political Crises in the Process of Modernization.
Cliodynamics 3: 124–157.
Grinin L. E., and Korotayev A. V. 2009. Social Macroevolution: Growth of the World
System Integrity and a System of Phase Transitions. World Futures 65(7): 477–
506.
Grinin L., Korotayev A., and Malkov S. 2010. A Mathematical Model of Juglar Cycles and the Current Global Crisis. History & Mathematics. Processes and Models
of Global Dynamics / Ed. by L. Grinin, P. Herrmann, A. Korotayev, and A. Tausch,
pp. 138–187. Volgograd: Uchitel.
Ibn Khaldūn `Abd al-Rahman. 1958 [1377]. The Muqaddimah: An Introduction to History. New York, NY: Pantheon Books (Bollingen Series, 43).
Korotayev A. 2007. Secular Cycles and Millennial Trends: A Mathematical Model.
Mathematical Modeling of Social and Economic Dynamics / Ed. by M. G. Dmitriev,
A. P. Petrov, and N. P. Tretyakov, pp. 118–125. Moscow: RUDN.
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Introduction. Cycles, Processes, and Trends
Korotayev A., and Khaltourina D. 2006. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends in Africa. Moscow: KomKniga/URSS.
Korotayev A., and Komarova N. 2004. A New Mathematical Model of Pre-Industrial
Demographic Cycle. Mathematical Modeling of Social and Economic Dynamics /
Ed. by M. G. Dmitriev, and A. P. Petrov, pp. 157–163. Moscow: Russian State Social
University.
Korotayev A., Malkov A., and Khaltourina D. 2006. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends. Moscow: KomKniga/URSS.
Korotayev A., Zinkina J., Kobzeva S., Bogevolnov J., Khaltourina D., Malkov A.,
and Malkov S. 2011. A Trap at the Escape from the Trap? Demographic-Structural
Factors of Political Instability in Modern Africa and West Asia. Cliodynamics:
The Journal of Theoretical and Mathematical History 2(2): 276–303.
Machiavelli N. 1996 [1531]. Discourses on Livy. Chicago, IL: University of Chicago
Press.
Nefedov S. A. 2004. A Model of Demographic Cycles in Traditional Societies:
The Case of Ancient China. Social Evolution & History 3(1): 69–80.
Turchin P. 2003. Historical Dynamics: Why States Rise and Fall. Princeton, NJ:
Princeton University Press.
Turchin P. 2005a. Dynamical Feedbacks between Population Growth and Sociopolitical Instability in Agrarian States. Structure and Dynamics 1: 1–19.
Turchin P. 2005b. War and Peace and War: Life Cycles of Imperial Nations. New
York: Pi Press.
Turchin P., and Korotayev А. 2006. Population Density and Warfare: A Reconsideration. Social Evolution & History 5(2): 121–158.
Turchin P., and Nefedov S. 2009. Secular Cycles. Princeton, NJ: Princeton University
Press.
Usher D. 1989. The Dynastic Cycle and the Stationary State. The American Economic
Review 79: 1031–1044.
I. LONG-TERM TRENDS
IN NATURE AND SOCIETY
1
Mathematical Modeling of Biological and
Social Evolutionary Macrotrends*
Leonid E. Grinin, Alexander V. Markov,
and Andrey V. Korotayev
Abstract
In the first part of this article we survey general similarities and differences
between biological and social macroevolution. In the second (and main) part,
we consider a concrete mathematical model capable of describing important
features of both biological and social macroevolution. In mathematical models
of historical macrodynamics, a hyperbolic pattern of world population growth
arises from non-linear, second-order positive feedback between demographic
growth and technological development. Based on diverse paleontological data
and an analogy with macrosociological models, we suggest that the hyperbolic
character of biodiversity growth can be similarly accounted for by non-linear,
second-order positive feedback between diversity growth and the complexity of
community structure. We discuss how such positive feedback mechanisms can
be modelled mathematically.
Keywords: social evolution, biological evolution, mathematical model, bio-
diversity, population growth, positive feedback, hyperbolic growth.
Introduction
The present article represents an attempt to move further in our research on the
similarities and differences between social and biological evolution (see Grinin,
Markov et al. 2008, 2009a, 2009b, 2011, 2012). We have endeavored to make
a systematic comparison between biological and social evolution at different
levels of analysis and in various aspects. We have formulated a considerable
number of general principles and rules of evolution, and worked to develop
a common terminology to describe some key processes in biological and social
evolution. In particular, we have introduced the notion of ‘social aromorphosis’
*
This research has been supported by the Russian Science Foundation (Project No 14-11-00634).
History & Mathematics: Trends and Cycles 2014 9–48
9
10
Modeling of Biological and Social Macrotrends
to describe the process of widely diffused social innovation that enhances the
complexity, adaptability, integrity, and interconnectedness of a society or social
system (Grinin, Markov et al. 2008, 2009a, 2009b). This work has convinced
us that it might be possible to find mathematical models that can describe important features of both biological and social macroevolution. In the first part of
this article we survey general similarities and differences between the two types
of macroevolution. In the second (and main) part, we consider a concrete mathematical model that we deem capable of describing important features of both
biological and social macroevolution.
The comparison of biological and social evolution is an important but (unfortunately) understudied subject. Students of culture still vigorously debate the
applicability of Darwinian evolutionary theory to social/cultural evolution. Unfortunately, the result is largely a polarization of views. On the one hand, there
is a total rejection of Darwin's theory of social evolution (see, e.g., Hallpike
1986). On the other hand, there are arguments that cultural evolution demonstrates all of the key characteristics of Darwinian evolution (Mesoudi et al.
2006).
We believe that, instead of following the outdated objectivist principle of
‘either – or’, we should concentrate on the search for methods that could allow
us to apply the achievements of evolutionary biology to understanding social
evolution and vice versa. In other words, we should search for productive generalizations and analogies for the analysis of evolutionary mechanisms in both
contexts. The Universal Evolution approach aims for the inclusion of all megaevolution within a single paradigm (discussed in Grinin, Carneiro, et al. 2011).
Thus, this approach provides an effective means by which to address the abovementioned task.
It is not only systems that evolve, but also mechanisms of evolution (see
Grinin, Markov, and Korotayev 2008). Each sequential phase of macroevolution is accompanied by the emergence of new evolutionary mechanisms. Certain prerequisites and preadaptations can, therefore, be detected within the previous phase, and the development of new mechanisms does not invalidate the
evolutionary mechanisms that were active during earlier phases. As a result, one
can observe the emergence of a complex system of interaction composed of the
forces and mechanisms that work together to shape the evolution of new forms.
Biological organisms operate in the framework of certain physical, chemical and geological laws. Likewise, the behaviors of social systems and people
have certain biological limitations (naturally, in addition to various socialstructural, historical, and infrastructural limitations). From the standpoint of
Universal Evolution, new forms of evolution that determine phase transitions
may result from activities going in different directions. Some forms that are
similar in principle may emerge at breakthrough points, but may also result in
evolutionary dead-ends. For example, social forms of life emerged among
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 11
many biological phyla and classes, including bacteria, insects, birds, and
mammals. Among insects, in particular, one finds rather highly developed
forms of socialization (see, e.g., Robson and Traniello 2002; Ryabko and Reznikova 2009; Reznikova 2011). Yet, despite the seemingly common trajectory
and interrelation of social behaviors among these various life forms, the impacts that each have had on the Earth are remarkably different.
Further, regarding information transmission mechanisms, it appears possible to speak about certain ‘evolutionary freaks’. Some of these mechanisms
were relatively widespread in the biological evolution of simple organisms, but
later became less so. Consider, for example, the horizontal exchange of genetic
information (genes) among microorganisms, which makes many useful genetic
‘inventions’ available in a sort of ‘commons’ for microbe communities. Among
bacteria, the horizontal transmission of genes contributes to the rapid development of antibiotic resistance (e.g., Markov and Naymark 2009). By contrast,
this mechanism of information transmission became obsolete or was transformed into highly specialized mechanisms (e.g., sexual reproduction) in the
evolution of more complex organisms. Today, horizontal transmission is mostly
confined to the simplest forms of life.
These examples suggest that an analysis of the similarities and differences
between the mechanisms of biological and social evolution may help us to understand the general principles of megaevolution1 in a much fuller way. These
similarities and differences may also reveal the driving forces and supra-phase
mechanisms (i.e., mechanisms that operate in two or more phases) of megaevolution. One of our previous articles was devoted to the analysis of one such
mechanism: aromorphosis, the process of widely diffused social innovation that
enhances the complexity, adaptability, integrity, and interconnectedness of a society or social system (Grinin, Markov, and Korotayev 2011; see also Grinin and
Korotayev 2008, 2009a, 2009b; Grinin, Markov, and Korotayev 2009a, 2009b).
It is important to carefully compare the two types of macroevolution (i.e.,
biological and social) at various levels and in various aspects. This is necessary
because such comparisons often tend to be incomplete and deformed by conceptual extremes. These limitations are evident, for example, in the abovereferenced paper by Mesoudi et al. (2006), which attempts to apply a Darwinian method to the study of social evolution. Unfortunately, a failure to recognize or accept important differences between biological and social evolution
reduces the overall value of the method that these authors propose. Christopher
Hallpike's rather thorough monograph, Principles of Social Evolution (1986),
provides another illustration of these limitations. Here, Hallpike offers a fairly
complete analysis of the similarities and differences between social and bio1
We denote as megaevolution all the process of evolution throughout the whole of Big History,
whereas we denote as macroevolution the process of evolution during one of its particular phases.
12
Modeling of Biological and Social Macrotrends
logical organisms, but does not provide a clear and systematic comparison between social and biological evolution. In what follows, we hope to avoid similar pitfalls.
Biological and Social Evolution: A Comparison at Various
Levels
There are a few important differences between biological and social macroevolution. Nonetheless, it is possible to identify a number of fundamental similarities, including at least three basic sets of shared factors. First, we are discussing
very complex, non-equilibrium, but stable systems whose function and evolution can be described by General Systems Theory, as well as by a number of
cybernetic principles and laws. Second, we are not dealing with isolated systems, but with the complex interactions between organisms and their external
environments. As a result, the reactions of systems to ‘external’ challenges can
be described in terms of general principles that express themselves within
a biological reality and a social reality. Third (and finally), a direct ‘genetic’
link exists between the two types of macroevolution and their mutual influence.
We believe that the laws and forces driving the biological and social phases of Big History can be comprehended more effectively if we apply the concept of biological and social aromorphosis (Grinin, Markov, and Korotayev
2011). There are some important similarities between the evolutionary algorithms of biological and social aromorphoses. Thus, it has been noticed that
the basis of biological aromorphosis
is usually formed by some partial evolutionary change that... creates significant advantages for an organism, puts it in more favorable conditions
for reproduction, multiplies its numbers and its changeability..., thus accelerating the speed of its further evolution. In those favorable conditions, the total restructurization of the whole organization takes place afterwards (Shmal'gauzen 1969: 410; see also Severtsov 1987: 64–76).
During the course of adaptive radiation, such changes in organization diffuse more or less widely (frequently with significant variations).
A similar pattern is observed within social macroevolution. An example is
the invention and diffusion of iron metallurgy. Iron production was practiced
sporadically in the 3rd millennium BCE, but regular production of low-grade
steel did not begin until the mid-2nd millennium BCE in Asia Minor (see, e.g.,
Chubarov 1991: 109). At this point, the Hittite kingdom guarded its monopoly
over the new technology. The diffusion of iron technology led to revolutionary
changes in different spheres of life, including a significant advancement in
plough agriculture and, consequently, in the agrarian system as a whole (Grinin
and Korotayev 2006); an intensive development of crafts; an increase in urban-
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 13
ism; the formation of new types of militaries, armed with relatively cheap but
effective iron weapons; and the emergence of significantly more developed
systems of taxation, as well as information collection and processing systems,
that were necessary to support these armies (e.g., Grinin and Korotayev 2007a,
2007b). Ironically, by introducing cheaply made weapons and other tools into
the hands of people who might resist the Hittite state, this aromorphosis not
only supported the growth of that kingdom, it also laid the groundwork for historical phase shifts.
Considering such cases through the lens of aromorphosis has helped us to
detect a number of regularities and rules that appear to be common to biological
and social evolution (Grinin, Markov, and Korotayev 2011). Such rules and
regularities (e.g., payment for arogenic progress, special conditions for the
emergence of aromorphosis, etc.) are similar for both biological and social
macroevolution. It is important to emphasize, however, that similarity between
the two types of macroevolution does not imply commonality. Rather, significant similarities are frequently accompanied by enormous differences. For example, the genomes of chimpanzees and the humans are 98 per cent similar, yet
there are enormous intellectual and social differences between chimpanzees and
humans that arise from the apparently ‘insignificant’ variations between the
two genomes (see Markov and Naymark 2009).
Despite its aforementioned limitations, it appears reasonable to continue
the comparison between the two types of macroevolution following the analysis
offered by Hallpike (1986). Therefore, it may prove useful to revisit the pertinent observations of this analysis here. Table 1 summarizes the similarities and
differences that Hallpike (1986: 33–34) finds between social and biological
organisms.
While we do not entirely agree with all of his observations – for example,
the establishment of colonies could be seen as a kind of social reproduction
akin to organic reproduction – we do feel that Hallpike comes to a sound conclusion: that similarities between social and biological organisms are, in general, determined by similarities in organization and structure (we would say
similarities between different types of systems). As a result, Hallpike believes
that one can use certain analogies in which institutions are similar to some organs. In this way, cells may be regarded as similar to individuals, central government similar to the brain, and so on. Examples of this kind of thinking can
be found in the classic texts of social theory (see, e.g., Spencer 1898 and Durkheim 1991 [1893]), as well as in more recent work (see, e.g., Heylighen 2011).
14
Modeling of Biological and Social Macrotrends
Table 1. Similarities and differences between social and biological
organisms, as described by Hallpike (1986)
Similarities
Differences
Social institutions are interrelated in a man- Individual societies do not have clear
ner analogous to the organs of the body. boundaries. For example, two societies
may be distinct politically, but not culturally or religiously.
Despite changes in membership, social Unlike organic cells, the individuals
institutions maintain continuity, as do within a society have agency and are
biological organs when individual cells capable of learning from experience.
are replaced.
The social division of labor is analogous Social structure and function are far less
to the specialization of organic functions. closely related than in organic structure
and function.
Self-maintenance and feedback processes Societies do not reproduce. Cultural
characterize both kinds of system.
transmission between generations cannot be distinguished from the processes
of system maintenance.
Adaptive responses to the physical envi- Societies are more mutable than organronment characterize both kinds of sys- isms, displaying a capacity for metatem.
morphosis only seen in organic phylogeny.
The trade, communication, and other Societies are not physical entities, rather
transmission processes that characterize their individual members are linked by
social systems are analogous to the proc- information bonds.
esses that transmit matter, energy, and
information in biological organisms.
When comparing biological species and societies, Hallpike (1986: 34) singles out the following similarities:
(1) that, like societies, species do not reproduce,
(2) that both have phylogenies reflecting change over time, and
(3) that both are made up of individuals who compete against one another.
Importantly, he also indicates the following difference: ‘[S]ocieties are organized systems, whereas species are simply collections of individual organisms’ (Hallpike 1986: 34).
Hallpike tries to demonstrate that, because of the differences between biological and social organisms, the very idea of natural selection does not appear
to apply to social evolution. However, we do not find his proofs very convincing on this account, although they do make sense in certain respects. Further,
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 15
his analysis is confined mainly to the level of the individual organism and the
individual society. He rarely considers interactions at the supra-organism level
(though he does, of course, discuss the evolution of species). His desire to demonstrate the sterility of Darwinian theory to discussions of social evolution notwithstanding, it seems that Hallpike involuntarily highlights the similarity between biological and social evolution. As he, himself, admits, the analogy
between the biological organism and society is quite noteworthy.
Just as he fails to discuss interactions and developments at the level of the
supra-organism in great detail, Hallpike does not take into account the point in
social evolution where new supra-societal developments emerge (up to the level of the emergence of the World System [e.g., Korotayev 2005, 2007, 2008,
2012; Grinin and Korotayev 2009b]). We contend that it is very important to
consider not only evolution at the level of a society but also at the level above
individual societies, as well as the point at which both levels are interconnected.
The supra-organism level is very important to understanding biological evolution,
though the differences between organisms and societies make the importance of
this supra-level to understanding social evolution unclear. Thus, it might be more
productive to compare societies with ecosystems rather than with organisms or
species. However, this would demand the development of special methods, as it
would be necessary to consider the society not as a social organism, but as a part
of a wider system, which includes the natural and social environment (cf., Lekevičius 2009, 2011).
In our own analysis, we seek to build on the observations of Hallpike
while, at the same time, providing a bit more nuance and different scales of
analysis. Viewing each as a process involving selection (natural, social, or
both), we identify the differences between social and biological evolution at the
level of the individual biological organism and individual society, as well as at
the supra-organismic and supra-societal level.
Natural and Social Selection
Biological evolution is more additive (cumulative) than substitutive. Put another way: the new is added to the old. By contrast, social evolution (especially
over the two recent centuries) is more substitutive than additive: the new replaces the old (Grinin, Markov et al. 2008, 2011).
Further, the mechanisms that control the emergence, fixation, and diffusion
of evolutionary breakthroughs (aromorphoses) differ between biological and
social evolution. These differences lead to long-term restructuring in the size
and complexity of social organisms. Unlike biological evolution, where some
growth of complexity is also observed, social reorganization becomes continuous. In recent decades, societies that do not experience a constant and significant evolution look inadequate and risk extinction.
16
Modeling of Biological and Social Macrotrends
In addition, the size of societies (and systems of societies) tends to grow
constantly through more and more tightly integrative links (this trend has become especially salient in recent millennia), whereas the trend towards increase
in the size of biological organisms in nature is rather limited and far from general. At another level of analysis, one can observe the formation of special suprasocietal systems that also tend to grow in size. This is one of the results of
social evolution and serves as a method of aromorphosis fixation and diffusion.
The Individual Biological Organism and the Individual Society
It is very important to note that, although biological and social organisms are
significantly (actually ‘systemically’) similar, they are radically different in
their capacities to evolve. For example, as indicated by Hallpike (see above),
societies are capable of rapid evolutionary metamorphoses that were not observed in the pre-human organic world. In biological evolution, the characteristics acquired by an individual are not inherited by its offspring; thus, they do
not influence the very slow process of change.
There are critical differences in how biological and social information are
transmitted during the process of evolution. Social systems are not only capable
of rapid transformation, they are also able to borrow innovations and new elements from other societies. Social systems may also be transformed consciously and with a certain purpose. Such characteristics are absent in natural
biological evolution.
The biological organism does not evolve by itself: evolution may only take
place at a higher level (e.g., population, species, etc.). By contrast, social evolution can often be traced at the level of the individual social organism (i.e., society). Moreover, it is frequently possible to trace the evolution of particular institutions and subsystems within a social organism. In the process of social evolution the same social organism or institution may experience radical transformation more than once.
The Supra-organic and Supra-societal Level
Given the above-mentioned differences, within the process of social evolution
we observe the formation of two types of special supra-societal entity:
(1) amalgamations of societies with varieties of complexity that have analogues
in biological evolution, and (2) elements and systems that do not belong to any
particular society and lack many analogues in biological evolution.
The first type of amalgamation is rather typical, not only in social but also
in biological evolution. There is, however, a major difference between the two
kinds of evolution. Any large society usually consists of a whole hierarchy of
social systems. For example, a typical agrarian empire might include nuclear
families, extended families, clan communities, village communities, primary
districts, secondary districts, and provinces, each operating with their own rules
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 17
of interaction but at the same time interconnected. This kind of supra-societal
amalgamation can hardly be compared with a single biological organism
(though both systems can still be compared functionally, as is correctly noted
by Hallpike [1986]). Within biological evolution, amalgamations of organisms
with more than one level of organization (as found in a pack or herd) are usually very unstable and are especially unstable among highly organized animals.
Of course, analogues do exist within the communities of some social animals
(e.g., social insects, primates). Neither should we forget that scale is important:
while we might compare a society with an individual biological organism, we
must also consider groups of organisms bound by cooperative relationships
(see, e.g., Boyd and Richerson 1996; Reeve and Hölldobler 2007). Such groups
are quite common among bacteria and even among viruses. These caveats
aside, it remains the case that within social evolution, one observes the emergence of more and more levels: from groups of small sociums to humankind as
a whole.
The multiplication of these levels rapidly produces the second kind of
amalgamation. It is clear that the level of analysis is very important for comparison of biological and social evolution. Which systems should be compared?
Analogues appear to be more frequent when a society (a social organism) is
compared to a biological organism or species. However, in many cases, it may
turn out to be more productive to compare societies with other levels of the
biota's systemic organization. This might entail comparisons with populations,
ecosystems and communities; with particular structural elements or blocks of
communities (e.g., with particular fragments of trophic networks or with particular symbiotic complexes); with colonies; or with groups of highly organized
animals (e.g., cetaceans, primates, and other social mammals or termites, ants,
bees and other social insects).
Thus, here we confront a rather complex and rarely studied methodological
problem: which levels of biological and social process are most congruent?
What are the levels whose comparison could produce the most interesting results? In general, it seems clear that such an approach should not be a mechanical equation of ‘social organism = biological organism’ at all times and in every
situation. The comparisons should be operational and instrumental. This means
that we should choose the scale and level of social and biological phenomena,
forms, and processes that are adequate for and appropriate to our intended
comparisons.
Again, it is sometimes more appropriate to compare a society with an individual biological organism, whereas in other cases it could well be more appropriate to compare the society with a community, a colony, a population, or
a species. At yet another scale, as we will see below, in some cases it appears
rather fruitful to compare the evolution of the biosphere with the evolution of
the anthroposphere.
18
Modeling of Biological and Social Macrotrends
Mathematical Modeling of Biological and
Social Macroevolution
The authors of this article met for the first time in 2005, in the town of Dubna
(near Moscow), at what seems to have been the first ever international conference
dedicated specifically to Big History studies. Without advance knowledge of one
another, we found ourselves in a single session. During the course of the session,
we presented two different diagrams. One illustrated population dynamics in
China between 700 BCE and 1851 CE, the other illustrated the dynamics of marine Phanerozoic biodiversity over the past 542 million years (Fig. 1).
Fig. 1. Similarity between the long-term population dynamics of China (top: millions of people, following Korotayev, Malkov, et al.
2006b: 47–88) and the dynamics of Phanerozoic marine biodiversity (bottom: number of genera, N, following Markov and
Korotayev 2007)
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 19
The similarity between the two diagrams was striking. This, despite the fact
that they depicted the development of very different systems (human population vs. biota) at different time scales (hundreds of years vs. millions of years),
and had been generated using the methods of different sciences (historical demography vs. paleontology) with different sources (demographic estimates vs.
paleontological data). What could have caused similarity of developmental dynamics in very different systems?
* * *
In 1960, von Foerster et al. published a striking discovery in the journal
Science. They showed that between 1 and 1958 CE, the world's population (N)
dynamics could be described in an extremely accurate way with an astonishingly simple equation:2
C
,
(Eq. 1)
Nt
( t0 t )
where Nt is the world population at time t, and C and t0 are constants, with t0
corresponding to an absolute limit (‘singularity’ point) at which N would become infinite. Parameter t0 was estimated by von Foerster and his colleagues as
2026.87, which corresponds to November 13, 2026; this made it possible for
them to supply their article with a title that was a public-relations masterpiece:
‘Doomsday: Friday, 13 November, A.D. 2026’.
Of course, von Foerster and his colleagues did not imply that the world
population on that day could actually become infinite. The real implication was
that the world population growth pattern that operated for many centuries prior
to 1960 was about to end and be transformed into a radically different pattern.
This prediction began to be fulfilled only a few years after the ‘Doomsday’
paper was published as World System growth (and world population growth in
particular) began to diverge more and more from the previous blow-up regime.
Now no longer hyperbolic, the world population growth pattern is closer to
a logistic one (see, e.g., Korotayev, Malkov et al. 2006a; Korotayev 2009).
Fig. 2 presents the overall correlation between the curve generated by von
Foerster et al.'s equation and the most detailed series of empirical estimates of
world population (McEvedy and Jones 1978, for the period 1000–1950; U.S.
Bureau of the Census 2013, for 1950–1970). The formal characteristics are:
R = 0.998; R2 = 0.996; p = 9.4 × 10–17 ≈ 1 × 10–16. For readers unfamiliar with
mathematical statistics: R2 can be regarded as a measure of the fit between
2
To be exact, the equation proposed by von Foerster and his colleagues looked as follows:
Nt
C
(t0 t)0.99
simplified as
. However, as von Hoerner (1975) and Kapitza (1999) showed, it can be
Nt
C
t0 t
.
20
Modeling of Biological and Social Macrotrends
the dynamics generated by a mathematical model and the empirically observed
situation, and can be interpreted as the proportion of the variation accounted for
by the respective equation. Note that 0.996 also can be expressed as 99.6 %.3
Thus, von Foerster et al.'s equation accounts for an astonishing 99.6 % of all
the macrovariation in world population, from 1000 CE through 1970, as estimated by McEvedy and Jones (1978) and the U.S. Bureau of the Census
(2013).4 Note also that the empirical estimates of world population find themselves aligned in an extremely neat way along the hyperbolic curve, which convincingly justifies the designation of the pre-1970s world population growth
pattern as ‘hyperbolic’.
Fig. 2. Correlation between empirical estimates of world population
(black, in millions of people, 1000–1970) and the curve generated by von Foerster et al.'s equation (grey)
3
The second characteristic (p, standing for ‘probability’) is a measure of the correlation's statistical
significance. A bit counter-intuitively, the lower the value of p, the higher the statistical significance of the respective correlation. This is because p indicates the probability that the observed
correlation could be accounted solely by chance. Thus, p = 0.99 indicates an extremely low statistical significance, as it means that there are 99 chances out of 100 that the observed correlation is
the result of a coincidence, and, thus, we can be quite confident that there is no systematic relationship (at least, of the kind that we study) between the two respective variables. On the other
hand, p = 1 × 10–16 indicates an extremely high statistical significance for the correlation, as it
means that there is only one chance out of 10,000,000,000,000,000 that the observed correlation
is the result of pure coincidence (a correlation is usually considered statistically significant once
p < 0.05).
4
In fact, with slightly different parameters (С = 164890.45; t0 = 2014) the fit (R2) between the
dynamics generated by von Foerster's equation and the macrovariation of world population for
1000–1970 CE as estimated by McEvedy and Jones (1978) and the U.S. Bureau of the Census
(2013) reaches 0.9992 (99.92 %); for 500 BCE – 1970 CE this fit increases to 0.9993 (99.93 %)
with the following parameters: С = 171042.78; t0 = 2016.
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 21
The von Foerster et al.'s equation, N t C
t0 t
, is the solution for the fol-
lowing differential equation (see, e.g., Korotayev, Malkov et al. 2006a: 119–
120):
(Eq. 2)
dN
N2
.
dt
C
This equation can be also written as:
(Eq. 3)
dN
aN 2 ,
dt
where a
1
.
C
What is the meaning of this mathematical expression? In our context, dN/dt
denotes the absolute population growth rate at a certain moment in time. Hence,
this equation states that the absolute population growth rate at any moment in
time should be proportional to the square of world population at this moment.
This significantly demystifies the problem of hyperbolic growth. To explain
this hyperbolic growth, one need only explain why for many millennia the
world population's absolute growth rate tended to be proportional to the square
of the population.
The main mathematical models of hyperbolic growth in the world population (Taagapera 1976, 1979; Kremer 1993; Cohen 1995; Podlazov 2004; Tsirel
2004; Korotayev 2005, 2007, 2008, 2009, 2012; Korotayev, Malkov et al.
2006a: 21–36; Golosovsky 2010; Korotayev and Malkov 2012) are based on
the following two assumptions:
(1) ‘the Malthusian (Malthus 1978 [1798]) assumption that population is
limited by the available technology, so that the growth rate of population
is proportional to the growth rate of technology’ (Kremer 1993: 681–
682),5 and
(2) the idea that ‘[h]igh population spurs technological change because it
increases the number of potential inventors… In a larger population there
will be proportionally more people lucky or smart enough to come up with
new ideas’, thus, ‘the growth rate of technology is proportional to total
population’(Kremer 1993: 685).6
Here Kremer uses the main assumption of Endogenous Technological
Growth theory (see, e.g., Kuznets 1960; Grossman and Helpman 1991; Aghion
5
6
In addition to this, the absolute growth rate is proportional to the population itself. With a given
relative growth rate, a larger population will increase more in absolute number than a smaller one.
Note that ‘the growth rate of technology’ here means the relative growth rate (i.e., the level to
which technology will grow in a given unit of time in proportion to the level observed at the beginning of this period).
22
Modeling of Biological and Social Macrotrends
and Howitt 1998; Simon 1977, 2000; Komlos and Nefedov 2002; Jones 1995,
2005).
The first assumption looks quite convincing. Indeed, throughout most of
human history the world population was limited by the technologically determined ceiling of the carrying capacity of land. For example, with foraging subsistence technologies the Earth could not support more than 8 million people
because the amount of naturally available useful biomass on this planet is limited. The world population could only grow over this limit when people started
to apply various means to artificially increase the amount of available biomass
that is with the transition from foraging to food production. Extensive agriculture is also limited in terms of the number of people that it can support. Thus,
further growth of the world population only became possible with the intensification of agriculture and other technological improvements (see, e.g., Turchin
2003; Korotayev, Malkov et al. 2006a, 2006b; Korotayev and Khaltourina
2006). However, as is well known, the technological level is not constant, but
variable (see, e.g., Grinin 2007a, 2007b, 2012), and in order to describe its dynamics the second basic assumption is employed.
As this second supposition was, to our knowledge, first proposed by Simon
Kuznets (1960), we shall denote the corresponding type of dynamics as ‘Kuznetsian’. (The systems in which the Kuznetsian population-technological dynamics are combined with Malthusian demographic dynamics will be denoted
as ‘Malthusian-Kuznetsian’.) In general, we find this assumption rather plausible – in fact, it is quite probable that, other things being equal, within a given
period of time, five million people will make approximately five times more
inventions than one million people.
This assumption was expressed mathematically by Kremer in the following
way:
dT
kNT .
dt
(Eq. 4)
This equation simply says that the absolute technological growth rate at
a given moment in time (dT/dt) is proportional to the technological level (T)
observed at this moment (the wider the technological base, the higher the number of inventions that can be made on its basis). On the other hand, this growth
rate is also proportional to the population (N): the larger the population, the
larger the number of potential inventors.7
When united in one system, Malthusian and Kuznetsian equations account
quite well for the hyperbolic growth of the world population observed before
the early 1990s (see, e.g., Korotayev 2005, 2007, 2008, 2012; Korotayev,
Malkov, et al. 2006a). The resultant models provide a rather convincing expla7
Kremer did not test this hypothesis empirically in a direct way. Note, however, that our own empirical test of this hypothesis has supported it (see Korotayev, Malkov et al. 2006b: 141–146).
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 23
nation of why, throughout most of human history, the world population followed the hyperbolic pattern with the absolute population growth rate tending
to be proportional to N2. For example, why would the growth of population
from, say, 10 million to 100 million, result in the growth of dN/dt 100 times?
The above mentioned models explain this rather convincingly. The point is that
the growth of world population from 10 to 100 million implies that human subsistence technologies also grew approximately 10 times (given that it will have
proven, after all, to be able to support a population ten times larger). On the
other hand, the tenfold population growth also implies a tenfold growth in the
number of potential inventors, and, hence, a tenfold increase in the relative
technological growth rate. Thus, the absolute technological growth rate would
expand 10 × 10 = 100 times as, in accordance with Eq. 4, an order of magnitude
higher number of people having at their disposal an order of magnitude wider
technological base would tend to make two orders of magnitude more inventions. If, as throughout the Malthusian epoch, the world population (N) tended
toward the technologically determined carrying capacity of the Earth, we have
good reason to expect that dN/dt should also grow just by about 100 times.
In fact, it can be shown (see, e.g., Korotayev, Malkov et al. 2006a, 2006b;
Korotayev and Khaltourina 2006) that the hyperbolic pattern of the world's population growth could be accounted for by a nonlinear second-order positive feedback mechanism that was long ago shown to generate just the hyperbolic growth,
also known as the ‘blow-up regime’ (see, e.g., Kurdyumov 1999). In our case,
this nonlinear second-order positive feedback looks as follows: more people –
more potential inventors – faster technological growth – faster growth of the
Earth's carrying capacity – faster population growth – more people allow for
more potential inventors – faster technological growth, and so on (see Fig. 3).
Fig. 3. Cognitive scheme of the nonlinear second order positive feedback between technological development and demographic
growth
Note that the relationship between technological development and demographic
growth cannot be analyzed through any simple cause-and-effect model, as we
24
Modeling of Biological and Social Macrotrends
observe a true dynamic relationship between these two processes – each of
them is both the cause and the effect of the other.
The feedback system described here should be identified with the process
of ‘collective learning’ described, principally, by Christian (2005: 146–148).
The mathematical models of World System development discussed in this article can be interpreted as models of the influence that collective learning has on
global social evolution (i.e., the evolution of the World System). Thus, the rather peculiar hyperbolic shape of accelerated global development prior to the
early 1970s may be regarded as a product of global collective learning. We
have also shown (Korotayev, Malkov et al. 2006a: 34–66) that, for the period
prior to the 1970s, World System economic and demographic macrodynamics,
driven by the above-mentioned positive feedback loops, can simply and accurately be described with the following model:
dN
aSN ,
dt
dS
bNS .
dt
(Eq. 5)
(Eq. 6)
The world GDP (G) can be calculated using the following equation:
G = mN + SN,
(Eq. 7)
where G is the world GDP, N is population, and S is the produced surplus per
capita, over the subsistence amount (m) that is minimally necessary to reproduce the population with a zero growth rate in a Malthusian system (thus,
S = g – m, where g denotes per capita GDP); a and b are parameters.
The mathematical analysis of the basic model (not described here) suggests
that up to the 1970s, the amount of S should be proportional, in the long run, to
the World System's population: S = kN. Our statistical analysis of available
empirical data has confirmed this theoretical proportionality (Korotayev,
Malkov et al. 2006a: 49–50). Thus, in the right-hand side of Eq. 6, S can be
replaced with kN, resulting in the following equation:
dN
kaN 2 .
dt
Recall that the solution of this type of differential equations is:
N
t
C
(t0 t )
,
which produces a simple hyperbolic curve.
As, according to our model, S can be approximated as kN, its long-term
dynamics can be approximated with the following equation:
S
kC
.
t0 t
(Eq. 8)
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 25
Thus, the long-term dynamics of the most dynamic component of the
world GDP, SN, the ‘world surplus product’, can be approximated as follows:
SN
t 0 t 2
kC 2
.
(Eq. 9)
This suggests that the long-term world GDP dynamics up to the early
1970s must be approximated better by a quadratic hyperbola, rather than by
a simple one. As shown in Fig. 4, this approximation works very effectively
indeed.
18000
16000
14000
12000
10000
8000
6000
4000
2000
predicted
0
observed
0
250
500
750
1000
1250
1500
1750
2000
Fig. 4. The fit between predictions of a quadratic-hyperbolic model
and observed world GDP dynamics, 1–1973 CE (in billions of
1990 international dollars, PPP)
Note: R = .9993, R2 = .9986, p << .0001. The black markers correspond to Maddison's
(2001) estimates (Maddison's estimates of the world per capita GDP for 1000 CE
has been corrected on the basis of [Meliantsev 2004]). The grey solid line has
been generated by the following equation:
17749573.1 .
G
( 2006 t ) 2
Thus, up to the 1970s the hyperbolic growth of the world population was accompanied by the quadratic-hyperbolic growth of the world GDP, as suggested
by our model. Note that the hyperbolic growth of the world population and the
quadratic-hyperbolic growth of the world GDP are very tightly connected processes, actually two sides of the same coin, two dimensions of one process propelled by nonlinear second-order positive feedback loops between the technological development and demographic growth (see Fig. 5).
26
Modeling of Biological and Social Macrotrends
Fig. 5. Cognitive scheme of the world economic growth generated by
nonlinear second-order positive feedback between technological development and demographic growth
We have also demonstrated (Korotayev, Malkov et al. 2006a: 67–80) that the
World System population's literacy (l) dynamics are rather accurately described
by the following differential equation:
dl
aSl (1 l ),
dt
(Eq. 10)
where l is the proportion of the population that is literate, S is per capita surplus, and a is a constant. In fact, this is a version of the autocatalytic model.
Literacy growth is proportional to the fraction of the population that is literate,
l (potential teachers), to the fraction of the population that is illiterate, (1 – l)
(potential pupils), and to the amount of per capita surplus S, since it can be used
to support educational programs. (Additionally, S reflects the technological
level T that implies, among other things, the level of development of educational technologies.) From a mathematical point of view, Eq. 9 can be regarded
as logistic where saturation is reached at literacy level l = 1. S is responsible for
the speed with which this level is being approached.
It is important to stress that with low values of l (which correspond to
most of human history, with recent decades being the exception), the rate of
increase in world literacy generated by this model (against the background
of hyperbolic growth of S) can be approximated rather accurately as hyperbolic (see Fig. 6).
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 27
70
observed
60
predicted
50
40
30
20
10
0
0
500
1000
1500
2000
Fig. 6. The fit between predictions of the hyperbolic model and observed world literacy dynamics, 1–1980 CE (%%)
Note: R = 0.997, R2 = 0.994, p << 0.0001. Black dots correspond to World Bank (2013)
estimates for the period since 1970, and to Meliantsev's (2004) estimates for the
earlier period. The grey solid line has been generated by the following equation:
3769.264
lt
.
( 2040 t ) 2
The best-fit values of parameters С (3769.264) and t0 (2040) have been calculated
with the least squares method.
The overall number of literate people is proportional both to the literacy level
and to the overall population. As both of these variables experienced hyperbolic
growth until the 1960s/1970s, one has sufficient grounds to expect that until
recently the overall number of literate people in the world (L)8 was growing not
just hyperbolically, but rather in a quadratic-hyperbolic way (as was world
GDP). Our empirical test has confirmed this – the quadratic-hyperbolic model
describes the growth of the literate population of this planet with an extremely
good fit indeed (see Fig. 7).
8
Since literacy appeared, almost all of the Earth's literate population has lived within the World
System; hence, the literate population of the Earth and the literate population of the World System
have been almost perfectly synonymous.
28
Modeling of Biological and Social Macrotrends
1800
1600
observed
1400
predicted
1200
1000
800
600
400
200
0
0
500
1000
1500
2000
Fig. 7. The fit between predictions of the quadratic-hyperbolic model
and observed world literate population dynamics, 1–1980 CE
(L, millions)
Note: R = 0.9997, R2 = 0.9994, p << 0.0001. The black dots correspond to
UNESCO/World Bank (2014) estimates for the period since 1970, and to Meliantsev's (2004) estimates for the earlier period; we have also taken into account
the changes of age structure on the basis of UN Population Division (2014) data.
The grey solid line has been generated by the following equation:
4958551 .
L
t
( 2033 t ) 2
The best-fit values of parameters С (4958551) and t0 (2033) have been calculated
with the least squares method.
Similar processes are observed with respect to world urbanization, the macrodynamics of which appear to be described by the differential equation:
du
bSu ( u lim u ) ,
(Eq. 11)
dt
where u is the proportion of the population that is urban, S is per capita surplus
produced with the given level of the World System's technological development, b is a constant, and ulim is the maximum possible proportion of the population that can be urban. Note that this model implies that during the Malthusian-Kuznetsian era of the blow-up regime, the hyperbolic growth of world
urbanization must have been accompanied by a quadratic-hyperbolic growth
of the urban population of the world, as supported by our empirical tests (see
Figs 8–9).
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 29
Fig. 8. The fit between predictions of the hyperbolic model and empirical estimates of world megaurbanization dynamics (% of
the world population living in cities with > 250,000 inhabitants), 10,000 BCE – 1960 CE
Note: R = 0.987, R2 = 0.974, p << 0.0001. The black dots correspond to Chandler's
(1987) estimates, UN Population Division (2014), Modelski (2003), and Gruebler
(2006). The grey solid line has been generated by the following equation:
403.012 .
u
t
(1990 t )
The best-fit values of parameters С (403.012) and t0 (1990) have been calculated
with the least squares method. For comparison, the best fit (R2) obtained here for
the exponential model is 0.492.
30
Modeling of Biological and Social Macrotrends
Fig. 9. The fit between predictions of the quadratic-hyperbolic model
and the observed dynamics of world urban population living in
cities with > 250,000 inhabitants (millions), 10,000 BCE –
1960 CE
Note: R = 0.998, R2 = 0.996, p << 0.0001. The black markers correspond to estimates of
Chandler (1987) and UN Population Division (2014). The grey solid line has been
generated by the following equation:
912057.9 .
U
t
( 2008 t ) 2
The best-fit values of parameters С (912057.9) and t0 (2008) have been calculated
with the least squares method. For comparison, the best fit (R2) obtained here for
the exponential model is 0.637.
Within this context it is hardly surprising to find that the general macrodynamics of largest settlements within the World System are also quadratichyperbolic (see Fig. 10).
As has been demonstrated by socio-cultural anthropologists working across
cultures (see, e.g., Naroll and Divale 1976; Levinson and Malone 1980: 34), for
pre-agrarian, agrarian, and early industrial cultures the size of the largest settlement is a rather effective indicator of the general sociocultural complexity of
a social system. This, of course, suggests that the World System's general sociocultural complexity also grew, in the Malthusian-Kuznetsian era, in a generally quadratic-hyperbolic way.
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 31
Fig. 10. The fit between predictions of the quadratic-hyperbolic model
and the observed dynamics of size of the largest settlement of
the world (thousands of inhabitants), 10,000 BCE – 1950 CE
Note: R = 0.992, R2 = 0.984, p << 0.0001. The black markers correspond to estimates of
Modelski (2003) and Chandler (1987). The grey solid line has been generated by
the following equation:
104020618. 573 .
U max t
( 2040 t ) 2
The best-fit values of parameters С (104020618.5) and t0 (2040) have been calculated with the least squares method. For comparison, the best fit (R2) obtained here
for the exponential model is 0.747.
Turning to a more concrete case study, as suggested at the beginning of this
section, the hyperbolic model is particularly effective for describing the longterm population dynamics of China, the country with the best-known demographic history. The Chinese population curve reflects not only a hyperbolic
trend, but also cyclical and stochastic dynamics. These components of longterm population dynamics in China, as well as in other complex agrarian societies, have been discussed extensively (see, e.g., Braudel 1973; Abel 1980; Usher 1989; Goldstone 1991; Chu and Lee 1994; Komlos and Nefedov 2002; Turchin 2003, 2005a, 2005b; Nefedov 2004; Korotayev 2006; Korotayev and
Khaltourina 2006; Korotayev, Malkov et al. 2006b; Turchin and Korotayev
2006; Korotayev, Komarova et al. 2007; Grinin, Korotayev et al. 2008; Grinin,
Malkov et al. 2009; Turchin and Nefedov 2009; van Kessel-Hagesteijn 2009;
Korotayev, Khaltourina, Malkov et al. 2010; Korotayev, Khaltourina et al.
2010; Grinin and Korotayev 2012).
As we have observed with respect to world population dynamics, even
before the start of its intensive modernization, the population dynamics of
China were characterized by a pronounced hyperbolic trend (Figs 11 and 12).
32
Modeling of Biological and Social Macrotrends
The hyperbolic model describes traditional Chinese population dynamics much
more accurately than either linear or exponential models.
500
400
300
200
Observed
100
Linear
0
Exponential
0
200
100
400
300
600
500
800
700
1000
900
1200
1100
1400
1300
1600
1500
1800
1700
1900
YEAR
Fig. 11. Population dynamics of China (million people, following Korotayev, Malkov et al. 2006b: 47–88), 57–1851 CE. Fit with
Linear and Exponential Models
Note: Linear model: R2 = 0.469. Exponential model: R2 = 0.600.
450
400
350
300
250
200
150
100
50
observed
predicted
0
50
250
450
650
850
1050
1250
1450
1650
1850
Fig. 12. Fit between a hyperbolic model and observed population dynamics of China (million people), 57–1851 CE
Note: R2 = 0.884. The grey solid line has been generated by the following equation:
Nt
33431 .
1915 t
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 33
The hyperbolic model describes the population dynamics of China in an especially accurate way if we take the modern period into account (Fig. 13).
1400
1200
1000
800
600
400
200
predicted
0
observed
0
300
600
900
1200
1500
1800
2100
t, years
Fig. 13. Fit between a hyperbolic model and observed population dynamics of China (million people, following Korotayev, Malkov
et al. 2006b: 47–88), 57–2003 CE
Note: R2 = 0.968. The grey solid line has been generated by the following equation:
63150 .
Nt
2050 t
It is curious that, as we noted above, the dynamics of marine biodiversity are
strikingly similar to the population dynamics of China. The similarity probably
derives from the fact that both curves are produced by the interference of the
same three components (the general hyperbolic trend, as well as cyclical and
stochastic dynamics). In fact, there is a lot of evidence that some aspects of
biodiversity dynamics are stochastic (Raup et al. 1973; Sepkoski 1994; Markov
2001; Cornette and Lieberman 2004), while others are periodic (Raup and Sepkoski 1984; Rohde and Muller 2005). In any event, the hyperbolic model describes marine biodiversity (measured by number of genera) through the Phanerozoic much more accurately than an exponential model (Fig. 14).
When measured by number of species, the fit between the empirically observed marine biodiversity dynamics and the hyperbolic model becomes even
better (Fig. 15).
34
Modeling of Biological and Social Macrotrends
Fig. 14. Global change in marine biodiversity (number of genera, N)
through the Phanerozoic (following Markov and Korotayev 2007)
Note: Exponential model: R2 = 0.463. Hyperbolic model: R2 = 0.854. The hyperbolic
line has been generated by the following equation:
Nt
183320 .
37 t
Fig. 15. Global change in marine biodiversity (number of species, N)
through the Phanerozoic (following Markov and Korotayev 2008)
Note: Exponential model: R2 = 0.51. Hyperbolic model: R2 = 0.91. The hyperbolic line
has been generated by the following equation:
Nt
892874 .
35 t
Likewise, the hyperbolic model describes continental biodiversity in an especially accurate way (Fig. 16).
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 35
Fig. 16. Global change in continental biodiversity (number of genera,
N) through the Phanerozoic (following Markov and Korotayev
2008)
Note: Exponential model: R2 = 0.86. Hyperbolic model: R2 = 0.94. The hyperbolic line
has been generated by the following equation:
Nt
272095 .
29 t
However, the best fit between the hyperbolic model and the empirical data is
observed when the hyperbolic model is used to describe the dynamics of total
(marine and continental) global biodiversity (Fig. 17).
Fig. 17. Global change in total biodiversity (number of genera, N) through
the Phanerozoic (following Markov and Korotayev 2008)
Note: Exponential model: R2 = 0.67. Hyperbolic model: R2 = 0.95. The hyperbolic line
has been generated by the following equation:
Nt
434635 .
30 t
36
Modeling of Biological and Social Macrotrends
The hyperbolic dynamics are most prominent when both marine and continental biotas are considered together. This fact can be interpreted as a proof of the
integrated nature of the biosphere. But why, throughout the Phanerozoic, did
global biodiversity tend to follow a hyperbolic trend similar to that which we
observed for the World System in general and China in particular?
As we have noted above, in sociological models of macrohistorical dynamics, the hyperbolic pattern of world population growth arises from non-linear
second-order positive feedback (more or less identical with the mechanism of
collective learning) between demographic growth and technological development. Based on analogy with these sociological models and diverse paleontological data, we suggest that the hyperbolic character of biodiversity growth
can be similarly accounted for by non-linear second-order positive feedback
between diversity growth and the complexity of community structure: more
genera – higher alpha diversity – enhanced stability and ‘buffering’ of communities – lengthening of average life span of genera, accompanied by a decrease
in the extinction rate – faster diversity growth – more genera – higher alpha
diversity, and so on. Indeed, this begins to appear as a (rather imperfect) analogue of the collective learning mechanism active in social macroevolution.
The growth of genus richness throughout the Phanerozoic was mainly due
to an increase in the average longevity of genera and a gradual accumulation of
long-lived (stable) genera in the biota. This pattern reveals itself in a decrease
in the extinction rate. Interestingly, in both biota and humanity, growth was
facilitated by a decrease in mortality rather than by an increase in the birth rate.
The longevity of newly arising genera was growing in a stepwise manner.
The most short-lived genera appeared during the Cambrian; more long-lived
genera appeared in Ordovician to Permian; the next two stages correspond to
the Mesozoic and Cenozoic (Markov 2001, 2002). We suggest that diversity
growth can facilitate the increase in genus longevity via progressive stepwise
changes in the structure of communities.
Most authors agree that three major biotic changes resulted in the fundamental reorganization of community structure during the Phanerozoic: Ordovician radiation, end-Permian extinction, and end-Cretaceous extinction (Bambach 1977; Sepkoski et al. 1981; Sepkoski 1988, 1992; Markov 2001; Bambach
et al. 2002). Generally, after each major crisis, the communities became more
complex, diverse, and stable. The stepwise increase of alpha diversity (i.e., the
average number of species or genera in a community) through the Phanerozoic
was demonstrated by Bambach (1977) and Sepkoski (1988). Although Powell
and Kowalewski (2002) have argued that the observed increase in alpha diversity might be an artifact caused by several specific biases that influenced the
taxonomic richness of different parts of the fossil record, there is evidence that
these biases largely compensated for one another so that the observed increase
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 37
in alpha diversity was probably underestimated rather than overestimated (Bush
and Bambach 2004).
Another important symptom of progressive development of communities is
an increase in the evenness of species (or genus) abundance distribution. In
primitive, pioneer, or suppressed communities, this distribution is strongly uneven: the community is overwhelmingly dominated by a few very abundant
species. In more advanced, climax, or flourishing communities, this distribution
is more even (Magurran 1988). The former type of community is generally
more vulnerable. The evenness of species richness distribution in communities
increased substantially during the Phanerozoic (Powell and Kowalewski 2002;
Bush and Bambach 2004). It is most likely there was also an increase in habitat
utilization, total biomass, and the rate of trophic flow in biota through the
Phanerozoic (Powell and Kowalewski 2002).
The more complex the community, the more stable it is due to the development of effective interspecies interactions and homeostatic mechanisms
based on the negative feedback principle. In a complex community, when the
abundance of a species decreases, many factors arise that facilitate its recovery
(e.g., food resources rebound while predator populations decline). Even if the
species becomes extinct, its vacant niche may ‘recruit’ another species, most
probably a related one that may acquire morphological similarity with its predecessor and thus will be assigned to the same genus by taxonomists. So
a complex community can facilitate the stability (and longevity) of its components, such as niches, taxa and morphotypes. This effect reveals itself in the
phenomenon of ‘coordinated stasis’. The fossil record contains many examples
in which particular communities persist for million years while the rates of extinction and taxonomic turnover are minimized (Brett et al. 1996, 2007).
Selective extinction leads to the accumulation of ‘extinction-tolerant’ taxa
in the biota (Sepkoski 1991b). Although there is evidence that mass extinctions
can be nonselective in some aspects (Jablonski 2005), they are obviously highly
selective with respect to the ability of taxa to endure unpredictable environmental changes. This can be seen, for instance, in the selectivity of the endCretaceous mass extinction with respect to the time of the first occurrence of
genera. In younger cohorts, the extinction level was higher than that of the older cohorts (see Markov and Korotayev 2007: fig. 2). The same pattern can be
observed during the periods of ‘background’ extinction as well. This means that
genera differ in their ability to survive extinction events, and that extinctiontolerant genera accumulate in each cohort over the course of time. Thus, taxa
generally become more stable and long-lived through the course of evolution,
apart from the effects of communities. The communities composed of more
stable taxa would be, in turn, more stable themselves, thus creating positive
feedback.
38
Modeling of Biological and Social Macrotrends
The stepwise change of dominant taxa plays a major role in biotic evolution. This pattern is maintained not only by the selectivity of extinction (discussed above), but also by the selectivity of the recovery after crises (Bambach
et al. 2002). The taxonomic structure of the Phanerozoic biota was changing in
a stepwise way, as demonstrated by the concept of three sequential ‘evolutionary faunas’ (Sepkoski 1992). There were also stepwise changes in the proportion of major groups of animals with different ecological and physiological
parameters. There was stepwise growth in the proportion of motile genera to
non-motile, ‘physiologically buffered’ genera to ‘unbuffered’, and predators to
prey (Bambach et al. 2002). All these trends should have facilitated the stability
of communities. For example, the diversification of predators implies that they
became more specialized. A specialized predator regulates its prey's abundance
more effectively than a non-specialized predator.
There is also another possible mechanism of second-order positive feedback between diversity and its growth rate. Recent research has demonstrated
a shift in typical relative-abundance distributions in paleocommunities after the
Paleozoic (Wagner et al. 2006). One possible interpretation of this shift is that
community structure and the interactions between species in the communities
became more complex. In post-Paleozoic communities, new species probably
increased ecospace more efficiently, either by facilitating opportunities for additional species or by niche construction (Wagner et al. 2006; Solé et al. 2002;
Laland et al. 1999). This possibility makes the mechanisms underlying the hyperbolic growth of biodiversity and human population even more similar, because the total ecospace of the biota is analogous to the ‘carrying capacity of
the Earth’ in demography. As far as new species can increase ecospace and
facilitate opportunities for additional species entering the community, they are
analogous to the ‘inventors’ of the demographic models whose inventions increase the carrying capacity of the Earth.
Exponential and logistic models of biodiversity imply several possible
ways in which the rates of origination and extinction may change through time
(Sepkoski 1991a). For instance, exponential growth can be derived from constant per-taxon extinction and origination rates, the latter being higher than the
former. However, actual paleontological data suggest that origination and extinction rates did not follow any distinct trend through the Phanerozoic, and
their changes through time look very much like chaotic fluctuations (Cornette
and Lieberman 2004). Therefore, it is more difficult to find a simple mathematical approximation for the origination and extinction rates than for the total
diversity. In fact, the only critical requirement of the exponential model is that
the difference between the origination and extinction through time should be
proportional to the current diversity level:
(No −Ne)/Δt ≈ kN,
(Eq. 12)
Leonid E. Grinin, Alexander V. Markov, and Andrey V. Korotayev 39
where No and Ne are the numbers of genera with, respectively, first and last
occurrences within the time interval Δt, and N is the mean diversity level during
the interval. The same is true for the hyperbolic model. It does not predict the
exact way in which origination and extinction should change, but it does predict
that their difference should be roughly proportional to the square of the current
diversity level:
(No −Ne)/Δt ≈ kN2.
(Eq. 13)
In the demographic models discussed above, the hyperbolic growth of the
world population was not decomposed into separate trends of birth and death
rates. The main driving force of this growth was presumably an increase in the
carrying capacity of the Earth. The way in which this capacity was realized –
either by decreasing death rate or by increasing birth rate, or both – depended
upon many factors and may varied from time to time.
The same is probably true for biodiversity. The overall shape of the diversity curve depends mostly on the differences in the mean rates of diversity
growth in the Paleozoic (low), Mesozoic (moderate), and Cenozoic (high).
The Mesozoic increase was mainly due to a lower extinction rate (compared to
the Paleozoic), while the Cenozoic increase was largely due to a higher origination rate (compared to the Mesozoic) (see Markov and Korotayev 2007: 316,
fig. 3a and b). This probably means that the acceleration of diversity growth
during the last two eras was driven by different mechanisms of positive feedback between diversity and its growth rate. Generally, the increment rate
((No −Ne)/Δt) was changing in a more regular way than the origination rate
No/Δt and extinction rate Ne/Δt. The large-scale changes in the increment
rate correlate better with N2 than with N (see Markov and Korotayev 2007: 316,
fig. 3c and d), thus supporting the hyperbolic rather than the exponential model.
Conclusion
In mathematical models of historical macrodynamics, a hyperbolic pattern of
world population growth arises from non-linear second-order positive feedback
between the demographic growth and technological development. Based on the
analogy with macrosociological models and diverse paleontological data, we
suggest that the hyperbolic character of biodiversity growth can be similarly
accounted for by non-linear second-order positive feedback between the diversity growth and the complexity of community structure. This hints at the presence, within the biosphere, of a certain analogue to the collective learning
mechanism. The feedback can work via two parallel mechanisms: (1) a decreasing extinction rate (more surviving taxa – higher alpha diversity – communities become more complex and stable – extinction rate decreases – more
taxa, and so on), and (2) an increasing origination rate (new taxa – niche construction – newly formed niches occupied by the next ‘generation’ of taxa –
new taxa, and so on). The latter possibility makes the mechanisms underlying
40
Modeling of Biological and Social Macrotrends
the hyperbolic growth of biodiversity and human population even more similar,
because the total ecospace of the biota is analogous to the ‘carrying capacity of
the Earth’ in demography. As far as new species can increase ecospace and
facilitate opportunities for additional species entering the community, they are
analogous to the ‘inventors’ of the demographic models whose inventions increase the carrying capacity of the Earth.
The hyperbolic growth of Phanerozoic biodiversity suggests that ‘cooperative’ interactions between taxa can play an important role in evolution, along
with generally accepted competitive interactions. Due to this ‘cooperation’
(which may be roughly analogous to ‘collective learning’), the evolution of
biodiversity acquires some features of a self-accelerating process. The same is
naturally true of cooperation/collective learning in global social evolution. This
analysis suggests that we can trace rather similar macropatterns within both the
biological and social phases of Big History. These macropatterns can be represented by relatively similar curves and described accurately with very simple
mathematical models.
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2
The World System Trajectory:
The Reality of Constraints
and the Potential for Prediction
Tony Harper
Abstract
This paper discusses a number of constraints imposed on the trajectory of the
World-System. Chief among these are the overall trend of the trajectory of
the world system, the existence of lines of equal maximum urban area, that is
iso-urban lines, constraints revealed by converting the trajectory to polar coordinates, periodic relationships within that representation, and the use of the
ratio of observed maximum urban area to idealized maximum urban area to
establish significant similarity with regard to two separate phases of urbanization including similarity in fractal dimensions of each phase. Beyond recognizing this suite of constraints, their potential for prediction of the state or position of the world system is discussed.
Keywords: de-urbanization, fractal dimension, iso-urban lines, optimum
urban area, parametric equation.
In the employing of mathematical methods,
however, biological facts must be reduced to
a mere abstract of their real complexity. It is important to understand that this simplification is
recognized for what it is: a working method. It
does not mean to ignore the complexity and totality of biological relationships. These clearly
remain the foundation upon which any mathematical model may be built.
C. C. Li, 1955
Acknowledgements
I wish to thank the following people for their comments and constructive criticisms: Andrey Korotayev, Sergey Tsirel, and Alexey Fomin. However, any
errors or misinterpretations within the text of this paper are mine and mine
alone. I wish to thank Kseniya Ukhova for her expert editorial hand.
History & Mathematics: Trends and Cycles 2014 49–107
49
50
The World System Trajectory
Dedication: I wish to dedicate this paper to four scholars who have helped
shape my thinking: the late Dr. Richard V. Bovbjerg, Dr. Robert DeMar,
Dr. Elliott Speiss, and Dr. Dennis Bramble.
Introduction
Constraints on living systems are ubiquitous, and, if anything, the WorldSystem should certainly be consider a living system. Constraints at the population level of biological organization have been documented formally for over
200 years à la Malthus, and mathematical formalism has been used to represent
those constraints for almost as long. Verhulst in 1838 (as noted in Hutchinson
1978) proposed the logistic equation,
dN/dt = rN(1 – N/K),
(Eq. 1)
as a reasonable model of population growth occurring within limits, that is within
constraints, the constraint being represented by K, the carrying capacity. Further, although K was considered a constant by Verhulst and by many to follow
who applied this equation to a variety of problems in population biology (for
a review of the utility of this equation see Hutchinson 1978), the constraint itself
can be seen to change, and in his insightful book, How Many People Can the
Earth Support, Joel Cohen presents this extended model of population growth,
dN/dt = rN(1 – N/K) and dK/dt = [L/N]dN/dt,
(Eq. 2)
where L is some threshold below which K grows by a factor greater than 1 and
above which K grows by a factor less than one. Note that the growth of K does
decrease continuously from N < L through N > L. In this more complicated
model L represents then a second constraint.
The World System, at its most fundamental level, is a system of populations and is therefore it should be expected that the World System would be
subject to the constraints imposed on population growth. In this light Korotayev, Malkov, and Khaltourina (2006a, 2006b, and 2006c) use a system of
equations with the core of the system dependent on logistic-like constraints.
Specifically, their system of equations,
dN/dt = aS(1 – L)N,
(Eq. 3a)
dS/dt = bSN, and
(Eq. 3b)
dL/dt = cS(1 – L)L,
(Eq. 3c)
and the coefficients a, b, and c can also be seen as constraints on the system.
The end result of applying this system is that as the World System grows it will
reach an equilibrium established by L = 1. How rapidly the system reaches
equilibrium will be determined by initial conditions and by the values of the
three coefficients mentioned above. A further paper by Grinin and Korotayev
(2006) demonstrated that the process of mega-urbanization exhibits similar
constrained behavior. See their Diagrams 1, 3, 4, 7, and 10 which clearly suggest a strong and constraining relationship between the process of (mega-) urbanization, state formation, and associated territory and in fact show logistic-
Tony Harper
51
like behavior with the existence of plateaus punctuating periods of rapid, hyperbolic growth. Inspection of Diagrams 3, 4, 7, and 10 reveal not only logisticlike behavior but also more complex behavior than might otherwise be expected. (Also see papers by Korotayev [2010] and by Grinin and Korotayev
[2006] for similar analyses.) Such complexities are in all probability emergent,
that is in the manner of Anderson (1972) and of Mayr (1988), in that they are
characteristic of the level of organization of the world system and not of its
component parts.
It is on this level of organization of the World System, highly complex and
urbanized, that this paper will be focused. The pattern of the trajectory of the
World System, previously reported on by Harper (2010a, 2010b), exhibits both
general trends and more complex finer structure, both levels of which exhibit
constrained behavior. It will be the intent of this paper first to investigate these
constraints and then to consider their potential for predicting the behavior of the
system. Constraints will be considered from three different perspectives, that of
the morphology of the graph in Fig. 1, that of a modified polar representation
of the same data, and that of a comparison of observed maximum urban area
and idealized maximum urban area. Once these different sets of constraints
have been analysed, then the information that these constraints contribute to
predicting the behavior of the system will be considered.
Finally, the research that this paper is based on was done in the spirit of the
lead quotation from C. C. Li (1955). It is important for the reader, particularly
those with little or no serious mathematical training, to understand that the simplifications used to make the Mathematics even somewhat tractable do not in
any way devalue the detailed knowledge of the historian, but at once are both
a consequence of that detailed work and also a context in which it is hoped the
work of the historian and social scientist can be give new perspective. There is
one more thing: mathematical reasoning may in many instances be the only
way in which the emergent properties of complex systems can be revealed and
understood.
The Organization of the Trajectory of the World System
This section will show that the organization of the world system trajectory as
first described in Harper (2010a, 2010b) exhibits both gross structural trends
and finer trends, all explainable in terms of urbanization, de-urbanization, and
the constraint that maximum urban area places on the trajectory. There are clear
trends at both the macro-level of organization of the trajectory and at finer
scales that all suggest constraint and, as previously suggested, ultimately the
potential for prediction.
Fig. 1 is a rotated version of Fig. 7 in Harper (2010b) in which the variable,
γ, has been rotated to the y-axis and the variable, lnT, that is the natural log
transform of the global population of the world system, has then obviously been
rotated to the x-axis. This was done so that certain trends and characteristics of
this trajectory would become more obvious than in the way these variables
52
The World System Trajectory
were originally displayed. In particular, some of the fine(r) scale characteristics
are easier to understand, and this graphical representation also displays a nonobvious relationship between the two variables graphed and the natural log of
maximum urban area size.
Fig. 1. lnT on the X-axis is graphed against γ on the y-axis
Fig. 2. The graph above is as in Fig. 1 but with a linear regression
imposed on the data. A linear regression of the data yields,
γ = –.0465lnT + 2.2607, representing an inverse relationship
between γ and lnT. R2 = .5225
It can be seen by inspection of Fig. 1 that there is an inverse relationship between γ and lnT, since over the full range of lnT γ decreases from an initial
value of 1.4851 to a final value of 1.2099, a difference of .2752 or a decrease of
18.53 % of the initial value of γ. Further, the largest values of γ occur with low
values of lnT, for example, when γ = 1.5674, its largest value, the value of lnT
Tony Harper
53
is 17.1731, which is an increase of 4.37 % over the initial value of lnT, while
the largest value of lnT, 22.5478, is an increase of 37.03 % of the initial value
of lnT. Perhaps, an easier and more general method of demonstrating this trend
of decreasing γ with respect to lnT would be to generate a linear regression of
this data. This is done in Fig. 2, yielding the regression equation,
γ = 2.23 – .0449lnT,
(Eq. 4)
and the fit of this equation is quite good with r = –.708 and the RMSE = .0593.
The fact that this equation has a negative slope clearly shows that the overall
trend of the world system is one of decreasing γ with increasing lnT. What does
this general trend imply?
Decreasing γ implies increasing urbanization. By establishing a fixed value
of C, that is Ca, with respect to Cmax, a defined section of the triangular area
bounded by the natural log transform of the equation,
F = αC–γ
(Eq. 5)
can be arbitrarily defined as a boundary between urbanized and non-urbanized
regions of the world system at a given time. By then holding A, the area bounded by
lnF = lnα – γlnC,
(Eq. 6)
constant and reducing γ it can be shown that the subsection of A bounded by Ca
is greater than the subsection bounded by the original value of γ, and consequently represents an increase in urbanization. Note, that for any given time it
can be shown that the ratio of urbanized to non-urbanized portions of the world
system is given by:
U = (lnCm + x – lnCc)2/(lnCm + x)2.
(Eq. 7)
As γ decreases with increasing lnT as represented by Eq. 4, it then follows
that urbanization increases with increasing lnT. Modelski (2003) and Korotayev and Grinin (2006) have shown that urbanization has increased over time
with the increase being punctuated by plateau-like phases and these phases appear to be synchronized with a similar pattern in global population, here labeled
as T. It is a contention of this paper that the increasing population of the world
system is dependent on increasing urbanization and would not occur without
the process of urbanization and in turn its attendant process of technological
progress.
Within this broad trend of decreasing gamma, increasing lnT and therefore
T, and increasing urbanization are micro-trends only the average of which is
reflected by these broad trends. While a detailed analysis, on a century by century basis, will not be entered into here, two significant micro-trends will be
mentioned, the period from 400 BCE to 700 CE, essentially the formation, florescence, and demise of Rome, of the Han Empires and the mosaic of empires
to follow the Han through to the establishment of the Tang Empire, and the
origination of the Islamic Caliphates, and then the 12th to the 14th centuries CE.
These two periods of time are significant, because they represent periods of
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The World System Trajectory
rapid urbanization followed by rapid de-urbanization. Both are also associated
with significant pandemics, with epidemic warfare, and with a variety of technological changes, for example, aqueducts in the West and the Grand Canal in
the East to name two.
From 400 BCE to 100 BCE both East and West experienced very rapid urbanization, and if changes in gamma can be taken as an indicator of this trend,
then over that period gamma decreased by .1460, or per century, .0487. These
numbers may seem insignificant, but they are associated with a three-fold
change in maximum urban area size from 320,000 in 400 BCE to approximately one million in 100 BCE. The reverse trend, increasing gamma over
time, began in 200 CE with γ = 1.2699 and ended in 500 CE with γ = 1.3793,
a change of .1097 or .0565 per century. With respect to change in maximum
urban area size the decrease was from 1.2 million to approximately one-half
million, or slightly less than a three-fold decrease. In the case of the 12th to the
13th century the changes in both gamma and maximum urban area size were
less in absolute terms, but per century the change in gamma was .0486 accompanied by an increase in maximum urban area size of approximately one-half
million, and the following century there was an increase of .0461 with a concomitant decrease in maximum urban area size of one-half million, almost exactly reversing the trend of the century before. What occurred over six hundred
years in the period of Rome, Han et al. occurred in this second episode within
a period of two hundred years, that is from 1200 CE to 1400 CE. (Note that the
period from 100 BCE to 200 CE was not included, because it involved relatively small changes in gamma and urbanization and the detail at present of
these changes does not add to understanding of the overall process of urbanization and de-urbanization.)
What also is significant is the fact that both sets of changes occurred during
periods of relatively small change, sometimes negative, in the world-system
population as a whole. From 400 BCE to 100 BCE there was a net loss of two
million people from the global population, that is from 162E6 to 160E6, and from
200 CE to 500 CE there was no change in the population of the world system.
While from 1200 CE to 1300 CE there was also no change in population, but in
the succeeding century there was a loss of ten million to the total population.
This all seems to imply that the rapid changes in urbanization followed by rapid
de-urbanization, are directly associated with a static or negatively growing total
population. To demonstrate this point using
(Eq. 8)
Cmaxγ – Cmax – (γ – 1)T = 0,
observed values of Cmax from 400 BCE through 100 BCE were used with held
constantat 1.4239 to compute T, the total population of the world system for
each century. These values are given in Table 1 below. As can be seen the observed values of T remain relatively constant, while the expected values for T
as dictated by the pattern of urbanization constrained by γ = 1.4239 increase
significantly. This implies that support of the pattern of urbanization with in-
55
Tony Harper
creasing maximum urban area size required much greater world system population size.
Table 1. Maximum urban area and gamma with respect to both observed and expected population sizes
Century
400 BCE
300 BCE
200 BCE
100 BCE
Cmax
32.E5
5.0E5
6.0E5
1.0E6
γ
1.4239
“
“
“
TEXP
162E6
306E6
397E6
822E6
TOBS
162E6
156E6
150E6
160E6
A further implication of this difference between the observed and expected values of T then would be that the initial level of urbanization was somehow adjusted or adapted to an initial level or threshold of population, but when the
process of urbanization continued but was not underwritten by continued total
population growth, then after a time delay exceeding that threshold was followed by a process of de-urbanization that occurred until a reasonable steady
state was re-established with respect to the total population.
Constraints Imposed on the Trajectory
of the World System by Maximum Urban Area Size
Visual inspection of Fig. 1 will reveal that certain sets of points appear to be
arranged linearly. As an example of a linear array a high-lighted region of the
graph in Fig. 1 is depicted in Fig. 3.
Fig. 3. LnT v. γ. Note the section of the graph indicated with an arrow. This section represents four data points as an example
of a linear array of points
This linear array of points shares the same maximum urban area size, and it can
be shown that other less obvious linear arrays embedded within this graph also
56
The World System Trajectory
share unique maximum urban areas; in other words, the arrangement of points
in this graph is determined by and limited by associated maximum urban area
sizes. Fig. 4 below shows three such sets, each with a line drawn through the
set having an equation of the form,
γ = mlnT + b.
(Eq. 9)
Table 1 gives the set of all slopes and y-intercept values for each maximum
urban area size, however, in several instances a specific point has a unique
maximum urban area value, and for those cases a linear regression of all empirically determined slopes and of all empirically determine y-intercepts was
used to determine the specific values of the slope and y-intercept for these
unique maximum urban area sizes.
Fig. 4. This graph is similar to that of Fig. 1 but with iso-urban lines
representing all positions of the world system with respect to
γ and lnT for three specified maximum urban area sizes. All
three lines have similar but not identical parameters for their
characteristic equations
Table 2
Maximum urban area
size
1
4E4
5E4
6E4
7E4
8E4
1E5
1.2E5
1.25E5
Slope
(m)
2
.115
.1120
.1110
.1090
.1100
.1060
.1055
.1037
Y-intercept
(b)
3
–.400
–.3940
–.4090
–.4410
–.4410
–.4110
–.4227
–.3986
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Tony Harper
1
2E5
3.2E5
4E5
5E5
6E5
7E5
8E5
9E5
1E6
1.1E6
1.2E6
1.5E6
6.5E6
35E6
2
.1006
.0980
.0967
.0948
.0946
.0938
.0944
.0927
.0910
.0918
.0926
.0906
.0858
.0828
3
–.4104
–.4393
–.4440
–.4532
–.4532
–.4560
–.4801
–.4614
–.4430
–.4614
–.4946
–.4723
–.5037
–.5308
Note: Numbers in bold face type were produced by linear regression of empirically determined slopes and y-intercepts. All slope and intercept values can be substituted
into an equation of the form, γ = mlnT + b.
There are several consequences of this finding. First, it is entirely possible to
determine the position of an ordered pair of values of lnT and γ as the position
of that point must lie on the appropriate linear array, here referred to as an isourban line, as determined by specific maximum urban area size. Second, the set
of all linear arrays falls on a complex curved surface as determined by the
range of values of both slope and y-intercept. Third, this surface must be undulatory as slope and y-intercept values change with respect to maximum urban
area size, while slope appears to decrease with respect to maximum urban area
size, y-intercept values fluctuate, for example, the sequence from 4E4 through
2E5 exhibits continually decreasing slope values but decreasing then increasing
then decreasing values of b. Fourth, the distance over which the world system
moves is directly determined by maximum urban area. Fifth, since change in
position of the world system from century to century can be represented by
angular change with respect to a given iso-urban line and the actual distance
moved, the world system trajectory can be represented by polar coordinates.
This last aspect will investigated in the next section.
A Polar Plot Representation of the World System Trajectory
As was previously mentioned iso-urban lines can be used to generate a polarplot of the world system trajectory. This was done in the following way. Local
distance, defined as the distance from one point representing the position of the
world system to a consecutive point was determined by the formula
(Eq. 10)
d = [(γ1 – γ0 )2 + (lnT1 – lnT0)2].5.
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The World System Trajectory
The continuous summation of d is represented by S = Σd. The angle of the
distance vector, θ, was determined by finding the cosine of the angle between
the local distance and the vertical distance from the previous iso-urban line to
the following iso-urban line as determined be the value of the maximum urban
area. Once this was done, the ratio of the vertical distance divided by the local
distance is then used to determine the arc cosine. This angle, θ, is then summed
continuously and is represented by
Σθ= Ψ.
(Eq. 11)
These parameters, S and Ψ, are then used in the parametric equations:
X = ScosΨ,
(Eq. 12a)
Y = SsinΨ,
(Eq. 12b)
to determine the polar coordinates for each position of the world system.
Using the above procedure a polar plot of the world system was generated
and represented in Fig. 5 below.
Fig. 5. A polar plot of the World System Trajectory. X = ScosΨ. Y =
= SsinΨ. This graph extends from 3000 BCE at the center
most position to 2000 CE at the far right
Clearly, the overall form of the plot is that of a spiral with the initiation of the
system at the origin which then spirals outward in a counter-clockwise fashion.
Changes in the distance of the outwardly spiraling plot are a consequence of
both changes in Ψ and in S, however, there are instances in which the magnitude of the change in one of these parameters over-rides the change in the other,
that is where there is greater change in either Ψ or more likely, S, which would
imply an increase or decrease in urbanization. It should also be noted that the
distances from individual position (of the world-system) to individual position
vary and are a consequence of the relative changes in both Ψ and S, and it is
these positions collectively that bring about changes in Ψ and S. Further,
change in Ψ represents change in lnT, and change in S represents change in the
Tony Harper
59
distribution of urban area sizes as represented by γ. It should also be quite apparent that the spiral plot is not a smooth one but is punctuated by a number of
segments which unquestionably represent a shifting forward of the entire position of the spiral and, further, the changes in segment length cause the spiral at
times to fold over on itself. From the perspective of Fig. 5 the trajectory of
more recent spirals falls beneath the point on a previous spiral. This is due primarily to the paucity of data and the specific perspective of Fig. 5.
If the data used to produce the previous graph are supplemented with
a time axis, that is the x-axis represents time, the y-axis represents X = ScosΨ,
and the z-axis represents Y = SsinΨ, then a three dimensional polar plot of the
world system trajectory can be created. Such a graph is represented immediately below and consists of a slight rotation of the graph in Fig. 5 to give the
impression of depth.
Z Axis
Fig. 6. This graph gives a 3D representation of the polar plot of the
world system trajectory over the last 5000 years. The graph
has been rotated to give the perception of depth with
3000 BCE being represented in the upper left of the graph and
2000 CE being represented on the far right hand side of the
graph
There are three aspects of the graph in Fig. 6 that are immediately striking, the
regularity of the spirals, the expansion of each spiral over the previous one, and
the extended position of the last point, that of 2000 CE. As previously mentioned, however, further inspection of this graph will reveal that there are any
number of instances in which the trajectory does not spiral but moves directly
forward, for example, the sharp spike immediately to the left of the 2000 CE
position. These periods of forward movement (in time) without rotation are best
represented by rotation of this graph so that the y-axis is minimized as in Fig. 7
below.
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The World System Trajectory
Fig. 7. The z-axis has been converted to a y-axis and plotted against
time. This is equivalent to rotating the graph in Fig. 6 so that
the y-axis has been eliminated. The regions of the graph in
which there is no rotation but only forward movement in time
are represented by the (near) parallel setions to the x-axis
As is clearly apparent, the maximum and minimum y-axis values appear to be
approximately linearly distributed, and, as to be expected, expand with time,
since S is a summation of each movement, and there is clear regularity or periodicity exhibited by the maxima and minima. In turn, if the z-axis in Fig. 6 is
eliminated so that Y = SsinΨ is represented on the y-axis, the graph is Fig. 8
is produced, which differs little in over-all form from that in Fig. 7. It exhibits
the periodically spaced maxima and minima exhibited by Fig. 7, all of which
appear to be approximately linearly ordered with the exception one point, the
last maximum, which is unquestionably positioned beyond any reasonable linear extension of the previous points. In other words, the current position of the
world system with respect to its previous linear expansion is much greater than
would otherwise be expected.
The regularity of the graphs in Figs 7 and 8 can be further investigated by
considering the periodicity exhibited by these curves. The magnitudes of the
maxima and minima of each are represented in Table 3 on the following page
and their periodicities are represented in Table 4. It is quite clear from an inspection of the data in Table 3 that the maximum values for ScosΨ and SsinΨ
are offset by either 200 or 300 years (av. = 240 years), while the periodicities in
Table 4 range from 700 to 900 years (av. = 833.3 years) and 800 to 900 years
(820 years) respectively.
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Tony Harper
Fig. 8. Time v. Y = SsinΨ. Those regions of the trajectory without
rotation are less apparent. However, the periodicity of the
trajectory is quite obvious, as is the linearity of maximum
and minimum y-axis values. Of significance is the extended
position of the last point on the graph
Table 3
Time
3000
BCE
2200
BCE
1300
BCE
500
BCE
200 CE
1100
CE
2000
CE
ScosΨ
Max
.0671
.6504
1.3846
2.3495
3.1995
3.4538
7.1432
Time
2600
BCE
1800
BCE
1000
BCE
100
BCE
700 CE
1800
CE
X
ScosΨ
Min
–.2488
–1.0405
–1.6646
–3.1177
–3.5077
–4.3881
X
Time
2800
BCE
1900
BCE
1100
BCE
300
BCE
500 CE
1300
CE
X
SsinΨ
Max
.1577
Time
SsinΨ
Min
–.4392
2.9417
2400
BCE
1500
BCE
800
BCE
1 CE
–2.8417
3.4192
900 CE
–3.6111
4.1896
1900
CE
X
–5.4817
.8303
1.5547
X
–1.2398
–1.9387
X
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The World System Trajectory
Table 4
ΔTime
800
900
800
700
900
900
ΔScosΨ
Max
.5833
.7342
.9649
.8500
.2545
3.6894
ΔTime
800
800
900
800
1100
X
ΔScosΨ
Min
.7917
.6241
1.4531
.39
.8804
X
ΔTime
900
800
800
800
800
X
ΔSsinΨ
Max
.6726
.7244
1.3870
.4775
.7704
X
ΔTime
900
700
800
900
1000
X
ΔSsinΨ
Min
.8006
.6989
.903
.7694
1.8706
X
Considering the crudeness of the data, these respective periodicities are approximately the same. Further, both the periodicities and the regularity of pattern of polar trajectory of the world system contribute to the support of the notion that the world system trajectory is highly constrained.
The data represented in Tables 3 and 4 can be visualized by putting both
plots, those of Figs 7 and 8 on the same axes as in Fig. 9. In this graph it can be
seen that the maxima of the solid curve that is X = ScosΨ, precedes the maxima
of the dotted curve, Y = SsinΨ, by approximately 200 years.
Fig. 9. Time on the x-axis and both X = ScosΨ, solid curve, and Y =
= SsinΨ, dotted curve, on the y-axis. While these oscillations
are offset by approximately one-fourth of a period, they are
not analogous to predator-prey oscillations, as both curves
reach approximately the same maxima and minima per period, whereas the prey species would maintain a population
level far below the prey species population, that is approximately one-tenth of the prey species population. The expanding oscillations imply that the world system as it is represented here is a non-equilibrium system
Tony Harper
63
It is also apparent that the spacing of minima is more variable as noted in Table 4. If the overall pattern in Fig. 9 is compared with that of Fig. 5 it can be
seen that the amplitude of the spiral in each graph increases over time and can
be expected to continue increasing over time, the single and momentary exception of increase in S without increase in Ψ which will be addressed shortly.
Given that in general the amplitude of the world system will continue to increase with some regularity, it can be accepted that this is supporting evidence
for the world system being a non-equilibrium system.
If we now return to the graph in Fig. 9 and the data in Tables 3 and 4 and
focus only on the maxima and minima in that graph and those tables, it becomes quite apparent that the maxima and minima occur periodically. What is
the relationship over time of these maxima and minima? The periodicity of
these maxima and minima is plotted against time in Fig. 10 below.
Fig. 10. Time is represented on the x-axis, and the magnitude of the
maxima of both X = ScosΨ and Y = SsinΨ is represented on
the y-axis. The periodicity of the maxima of both X and Y is
apparent. This graph was created with the use of spline interpolation
Clearly, with the exceptions of the first and last point, the maxima for both
X = ScosΨ and Y = SsinΨ occur periodically as is visually represented below
and noted in Tables 3 and 4. It is also interesting, and it is understood that extrapolation is a far riskier business than interpolation, that if this periodicity holds,
then the second point beyond the one representing the maximum of 2000 CE,
that is 50 on the x-axis below, will occur some 200 years into the future, and if
one observes the overall pattern of the graph and notes that we have now entered a demographic transition, perhaps a comparison can be made between the
current position of the world system and its position at 500 BCE, that is point
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The World System Trajectory
25 on the x-axis of Fig. 10. If this is a valid comparison, then it can be expected
that some 200 years into the future the world system will be approaching a demographic plateau. It is noted here that this speculation goes counter to the
thinking of a number of scholars, for example, von Forester et al. (1960), that
plateau will be achieved this century.
If attention is now turned to the pattern of minima as represented in
Fig. 11, it is again clear that these pairs of minima occur periodically and therefore predictably. The fact that there are six complete pairs of minima, as opposed to the five pairs of maxima and two singleton points is simply a function
of the range of the data and the domain of the respective maxima and minima
with respect to the current position of the world system. It is quite clear that
while the most recent pair of minima will be succeeded by the next pair some
200 years into the future, there is no way to associate the most recent data directly with any demographic transition, as all minima are paired and as the
most recent have no previously corresponding position for comparison.
Fig. 11. Time is represented on the x-axis, and the magnitude of
minima for both X = ScosΨ and Y = SsinΨ is represented
on the y-axis. This graph was created with the use of spline
interpolation
The overall regularity of both polar plots can also be visualized by considering
a plot of S v. Ψ, as is represented in Fig. 12.
Tony Harper
65
Fig. 12. Ψ is graphed on the x-axis, and S is graphed on the y-axis.
Note the near linearity of this graph with a linear regression
yielding, Ψ = .0026S – .3128. R2 = .9521. Each vertical
segment of the graph, and there are seven of them, represents a period of time when there was no change in Ψ but
only in S
It can be seen that this plot, as represented by
Ψ = .0026S – .3128,
(Eq. 13)
is relatively linear, R2 = .9521. However, there are pronounced non-linear aspects
to this graph, and this amount to considerable positive changes in S with respect
to Ψ, most probably phase changes in the system itself. Further, these phase
changes occur in a two-step process, and there are three such two-step phase
changes, 2000 BCE – 1700 BCE, 900 BCE – 300 BCE, and 900 CE – 2000 CE,
this last amounting to 1100 years of change and the total amount of time associated with these changes is 2300 or approximately 46 % of the total time of
recorded history. It should be noted that a single step change occurred from
2500 BCE – 2200 BCE and is the earliest example of such change.
If the axes in Fig. 12 are rotated so that S is represented on the x-axis, as in
Fig. 13, an interesting pattern is revealed which is not apparent in the previous
figure. Here it is quite apparent that periods of heightened increase in Ψ alternate with periods of increase in S. Specifically, from 3000 BCE to 900 BCE
and from 400 BCE to 1400 CE, Ψ changes rapidly, but S changes moderately,
while from 900 BCE to 400 BCE and from 1400 CE to 2000 CE represents
periods of relatively rapid change in S, again with only moderate change in Ψ.
These data are represented numerically in Table 5.
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The World System Trajectory
Fig. 13. S is represented on the x-axis, and Ψ is represented on the
y-axis. Of note in this graph is the fact that periods of rapid
change in S alternate with periods of rapid change in Ψ
In this table the per cent rates of change for both Ψ and S over their respective
periods of change. For the first 2100 years of world system history the rate of
change in Ψ is almost twice that of S, while in the next 500 years are reversed
with S having twice the rate of change per century that Ψ does, and, again, for
the next 1000 years the rate of change for Ψ is now approximately twice that of
S. Finally, for the last 600 years the rate of S becomes three times that of Ψ.
Of significant interest is the fact that the two time periods for rapid change in
each variable are approximately the same, that is both periods of rapid change for
Ψ are approximately a millennium in length, while both periods of change for S
are approximately one-half a millennium in length. Of some significance is the
fact that if increased changes in S occur over a period of one-half a millennium,
then the world system should be entering another period of rapid change in Ψ
which should last approximately 1000 years.1
Table 5
Time Period
1
3000 BCE –
900 BCE
900 BCE–
400 BCE
1
% ΔΨ/Time
2
2.1511
% ΔS/Time
3
1.2335
1.5251
2.9833
The data set on which this last statement is made is not exceptionally large, and, consequently,
making a statement such as this last one comes at some risk. My salvation is that none of us will
be here 1000 years from now, however, hopefully the world system will be!
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Tony Harper
1
400 BCE–
1400 CE
1400 CE–
2000 CE
2
2.0104
3
1.0351
1.8356
6.7747
The focus of this paper will now be turned to the abstract distance traveled
from point to point on the polar representation of the world system trajectory.
These changes in spiral distance with respect to time are represented in Fig. 14.
Segment length was determined by Pythagorean Theorem as in Eq. 8, where
the parametric equations were used to determine X and Y values.
Fig. 14. Time is represented on the x-axis and spiral segment length
as determined by the Pythagorean Theorem is represented
on the y-axis. Note that the maximum size of segment
length increases slightly with time. Also note that there are
a number of instances in which segment length almost drops
to zero. In fact, this is an artifact of the data and will be
explained in the text
As can be seen below, there is a slight increase in average size of individual
spiral segments over the 5000 years of world system history, and a wide range
of values from almost zero to almost 90 is apparent.2 Given that these near zero
instances of spiral segment length exist, what is implied by their existence? Are
they unique in world system history or simply artifacts of the data themselves?
The idiosyncrasies of the graph in Fig. 14 are to some extent an artifact of the
procedure to create the graph as opposed to the data themselves. Due to the fact
that the data for S range from approximately .02 to 1.40, while the data for Ψ
2
The reader should be aware that the data in Fig. 14 have not been normalized.
68
The World System Trajectory
range from approximately 6.00 to almost 90.00, the procedure for computing
segment length results in heavily weighting the values for Ψ over those of
S. Even so, the question must be asked, to what extent does the graph reflect
reality? In order to address this question both sets of data, those of Ψ and those
of S, were normalized by their largest value. Using this normalized data the
graph in Fig. 12 was produced. In fact, this graph exhibits the same general
characteristics of the graph in Fig. 11, that is as light increase in average segment length over time and periods in which the size of segment length decreases precipitously. It should be noted that these minima represent instances
in which there is no change from century to century in maximum urban area
size, and as a result the component, S, is the only component to contribute to
the summative process producing successive new positions of the world system. Returning to the comparison of the graphs in Figs 11 and 12, both graphs
reveal the same general pattern.
Fig. 15. Time is represented on the x-axis, and segment length is
represented on the y-axis. The average size of the largest
segment lengths remains relatively stable across time with
a slight increaseover that same period of time. The instances
of minimal segment length are pronounced as they are in
Fig. 14
Considering only the component, S, the summation of the distance component
in the polar plot of the world system trajectory, and plot it against time a near
linear graph is produced as can be seen in Fig. 15. This graph shows clearly that
on average S grows incrementally in a regular fashion, but with two pronounced exceptions where the slope of the graph changes abruptly. These are the
period of time from 500 BCE to 400 BCE and also from 1800 CE to 2000 CE.
Tony Harper
69
In both instances the slope of the graph becomes markedly more positive, that
is the rate of change of S increases. With regard to the most recent instance this
change can be associated with the industrial revolution, however, with regard to
the first instance of increased slope, one can only guess at a variety of technological changes of the time, a time when the Roman Empire was in its formative stage and shortly before the genesis and development of the Han Empire in
China. If the slopes of the four respective periods, 5000 BCE – 500 BCE,
500 BCE – 400 BCE, 400 BCE – 1800 CE, and 1800 CE – 2000 CE, they are
respectively: .0938, .4828, .0956, and 1.0261.
Fig. 16. Time is represented on the x-axis, and S is represented on
the y-axis
This plot is effectively linear with the exception of the last 200 years of world
system history, that is points 49 and 50. Even so, linear regression of this data
gives:
S = .1102t – .2654
(Eq. 14)
with R2 = .9568.
Interestingly, the slopes of the two extended periods are approximately the
same, while the slopes of the two transition periods are both significantly greater than the slopes of the extended periods, by a factor of 5.1471 for the phase change from 500 BCE to 400 BCE and by a factor of 10.7333 for the phase
change from 1800 CE to 2000 CE, a period of change that may not yet be over.
One further comment here, if the phase change is in fact over, do these data
imply that the change in S will return to a more stately ~.09?
When a similar analysis is performed on Ψ, the summation of θ, the individual angles normal to specific iso-urban lines. Fig. 16 represents the graph of
70
The World System Trajectory
this data, and, most remarkably, the plot is effectively linear yielding the equation,
Ψ = 42.6751t + 22.3262,
(Eq. 15)
with R2 = .9968. This graph is quite different from that of Fig. 15, in that it has
a closer linear fit and that while there are divergences from linearity there are
no significant instances of what have been labeled as phase changes but rather
the divergences from linearity are distributed throughout the range of the graph.
Appropriately, the next step in analysis is to compare the differences between
observed and expected values of both S and Ψ, the latter as predicted by linear
regression.
Fig. 17. Time is represented on the x-axis and Ψ is represented
on the y-axis. Linear regression gives: Ψ = 42.6751t +
+ 22.3263, R2 = .9968
If the differences are taken between the observed values for both S and Ψ based
on their respective linear regressions and plotted against time, the following
two graphs reveal a periodic character to both plots. These graphs are represented in Figs 18 and 19. The first of these two graphs representing the difference between observed and expected for the variable, S, shows approximate
periodicity with peaks at 100 BCE and (apparently) at 2000 CE. Both of these
peaks represent times of rapid urbanization, the first matching the urban area
growth approximating 1,000,000 succeeding the previous maximum of 600,000
one century prior and the second representing the incredible growth from
6,500,000 in 1900 CE to an approximately 35,000,000 in 2000 CE. Both of
these instances represent events in which the maximum urban area size increases by approximately an order of magnitude, with the second maximum
urban area increase associated with the change from the industrial to the postindustrial world system. The pattern of the graph in Fig. 18, that of the difference between observed and expected in the variable, Ψ, is more problematic
Tony Harper
71
with nine clear maxima with values greater than zero but excluding both the
first and last points, 3000 BCE and 2000 CE.
Fig. 18. Time is represented on the x-axis and the difference betweeh
the observed value for S and the regressed value for S is
represented on the y-axis
These maxima correspond to 2600 BCE, 2100 BCE, 1000 BCE, 800 BCE,
500 BCE, 100 CE, 600 CE, 900 CE, and 1200 CE. With the exception of
2100 BCE, which represents a new maxima for urban area size in the world system of the time, no other times represent unique maxima, although the maxima at
both 800 BCE and 500 BCE represent instances of sequential new maxima, that
is instances when the new maxima was maintained over a period of 100 years.
Fig. 19. Time is represented on the x-axis, and the differences
between the observed values for Ψ and the regressed
values for Ψ are represented on the y-axis
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The World System Trajectory
There is another unique characteristic of this particular graph, the minima at
1700 CE, which is the smallest minima, that is the greatest negative difference
exhibited over the entire 5000 year history of the world system. This minima
also precedes the greatest increase in maximum urban area size over the entire
history of the world system.
In summary, this section has demonstrated the value of restructuring the
world system data on time, log-transformed total population, and log-transformed
maximum urban area population for a polar plot representation. First, the polar
plot with time eliminated yields a counterclockwise outwardly spiraling graph
that reveals the magnitude of contribution to the world system at any time
throughout its history. When this graph is rotated appropriately its threedimensional nature can be observed, and, on further rotation, the contribution and
periodicity of each polar component can be evaluated. In turn, the periodicity of
these components, S and Ψ, can be represented for both their maxima and minima. Then if S and Ψ are plotted against one another, both with S on the x-axis
and Ψ on the axis, it can be seen that the last 5000 years of world system history
have alternated periods in which change in Ψ and change in S were greater, usually on the order of a 2X factor, with the exception of this last period in which S
was greater than Ψ by a factor of 3X. Differences between observed and expected
values of both S and Ψ were calculated revealing peaks in ΔS corresponding to
about a 2500 year periodicity. The record for Δ Ψ is less clear.
Optimal Urban Area Size аnd Observed Maximum Urban
Area
In previous work there was no standard of comparison of observed maximum
urban area other than the context of the temporal sequence that each maximum urban area was part of. In this section a standard of comparison will be
established, which will then be the basis of comparison per time step for each
maximum urban area. In turn, any relationships revealed by comparative research will be analysed.
The theoretical maximum urban area size, here called the optimum urban
area size, can be determined by recognizing that the natural log-transform of
the equation, F = αC–γ (Eq. 5), represents the hypotenuse of a right triangle in
log-space (see Fig. 14). Consequently, the area of this triangle is given by
(Eq. 16)
A = .5γlnCmax2.
Further, the relationship between the sides of this triangle is an inverse one, that
is if one side is increased by an amount, x, then the other is decreased by the
same amount. Eq. 11 may then be rewritten as:
A = (γ – x)(1 + x).5lnCmax2,
(Eq. 17a)
or
(Eq. 17b)
[γ + (γ – 1)x – x2].5lnCmax2.
Tony Harper
73
Fig. 20. This is a graph of the log-transformation of F = αC–γ, that is
LnF = lnα – γlnC, for the specific values, C = 6E5, and
γ = 1.3606
The graph of this last equation (see Fig. 15) is a parabola, concave down, and
area is maximized at the peak of the parabola by the appropriate value of x.
It should be noted that for any given set of data the observed maximum urban area remains constant, so then finding the optimum urban area becomes
a maximization problem in which the partial derivative of A with respect to x is
set equal to zero, and then x is solved for. This gives the very simple formula,
x = (γ – 1)/2,
(Eq. 18)
and on substituting into both (γ – x) and (1 + x) it is found that both of these
terms are equal to (γ + 1)/2 (Eqs 18a and 18b). In other words, maximization
with respect to x requires that both sides of the triangle be equal, and this implies that the optimal urban area is determined graphically (and analytically) by
[(γ + 1)/2]lnCmax, the anti-log of which is Cmax(γ + 1)/2, the importance of this relationship will become clear shortly.
Given that the optimum urban area can be determined from readily available data (Harper 2010a, 2010b), the observed maximum urban area magnitude
can then be compared with the optimum urban area magnitude. This will be
done by generating the ratio, Cmax/Cmax(γ + 1)/2, for each point of the world system
trajectory as it is represented by γ, lnCmax, and ln T. This graph is given in
Fig. 3. The graph clearly exhibits two distinct phases, each about 2500 years
in length separated by a brief period of transition.
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The World System Trajectory
Fig. 21. The above is a graph of Eq. 2 using the specific values of γ =
= 1.3606 and Cmax = 6E5 or lnCmax = 13.3047
Note: the x-axis is for the range of x, while the y-axis represents A in Eq. 2. Further
note, as long as the values of γ and Cmax are those determined by observation for
a specific time, any (of those) values may be used (see Harper 2010a).
It is also apparent that the latter phase on average has a higher position than the
former. This is a clear indication that the level of urbanization over the last
2500 years or so is greater than in the former period and implies a greater level
of technology to support the greater degree of urbanization.
The graph in Fig. 16 may be divided into two equal segments, one from
3000 BCE to 500 BCE, and the other from 500 BCE to 2000 CE (see Figs 17
and 18). These separate graphs share some common characteristics. They
both begin with a trend of increasing urbanization as defined by the ratio,
Cmax/Cmax(γ + 1)/2, they both end with slight decreases in urbanization, and they
both exhibit considerable oscillations between their initiation and termination.
However, to give the reader perspective, the y-axis has been scaled to the same
interval as the x-axis, and, as revealed in Figs 6 and 7, at this scaling the graphs
are effectively linear.
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75
Fig. 22. The above graph represents the ratio of Cmax/Cmax(γ + 1)/2 over
the last 5000 years of world system history. Very clearly
there are two distinct phases, each about 2500 years in
length, with a short transition period in between each
The graph in Fig. 16 may be divided into two equal segments, one from
3000 BCE to 500 BCE, and the other from 500 BCE to 2000 CE (see Figs 17
and 18). These separate graphs share some common characteristics. They both
begin with a trend of increasing urbanization as defined by the ratio,
Cmax/Cmax(γ + 1)/2, they both end with slight decreases in urbanization, and they
both exhibit considerable oscillations between their initiation and termination.
However, to give the reader perspective, the y-axis has been scaled to the same
interval as the x-axis, and, as revealed in Figs 6 and 7, at this scaling the graphs
are effectively linear.
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The World System Trajectory
Fig. 23. This graph represents the first 2500 years of the time span represented in Fig. 3 and with an imposed trend line. The slope of
the line is slightly negative, –.00111, and implies a decreasing
ratio of Cmax/Cmax(γ + 1)/2 over that period of time
Fig. 24. This graph represents the second 2500 years of the graph
in Fig. 3, again with an imposed trend line, also with
a negative slope, –.00118, which implies decreasing
Cmax/Cmax(γ + 1)/2 over this latter time period
Tony Harper
77
This point is being emphasized so that the reader will keep in perspective the
actual magnitude of change represented by these graphs over their respective
time periods of 2500 years.
Fig. 25. This graph represents the same data as in Fig. 17 but with
the y-axis adjusted to the same scale as the x-axis. The intent is to give context to the actual magnitude of change of
world system urbanization as represented by the ratio,
Cmax/Cmax(γ + 1)/2
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The World System Trajectory
Fig. 26. This graph is of the data represented in Fig. 18 but adjusted so
that both the x and y-axes are scaled the same as in Fig. 19
If linear regression is applied to both sets of data, that is data from both the first
and second 2500 year periods, the respective linear equations,
(Eq. 19)
CR = .0869 – .00111t,
and
(Eq. 20),
CR = .148 – .00118t,
where CR represents the ratio, Cmax/Cmax(γ + 1)/2, and t is time. The slopes of these
regression equations are effectively the same, differing by only .00008, implying
similar rates of average change with respect to the changing magnitude of
Cmax/Cmax(γ + 1)/2 over the two respective 2500 year periods. This can be more
emphatically demonstrated by looking at a composite graph in Fig. 27 of both
regression lines. In this graph the lower solid line represents the average change
in the ratio, Cmax/Cmax(γ + 1)/2, for the first 2500 years of world system history, and
the higher solid line represents the same for the second 2500 years of world
system history. Both lines have been extrapolated by a dashed line to represent
the full extent of the trend had the trend been extended over the full 5000 years.
79
CR
Tony Harper
Fig. 27. This is a composite graph of the linear regressions in which
the x-axis is time and the y-axis is CR, and in which the
trend averages for the first and second halves of world system history as represented individually in Figs 17 and 18 are
combined. Emphasized is the fact that the change from the
trajectory of the first half to the second half, the solid lines
of the graph, occurred relatively quickly and represents
a significant change in the position of the world system
While the trend lines give the average direction of change, it is quite clear that the
observed data are very different and exhibit change, as mentioned previously, that
oscillates about each trend line. A two sample T-test was performed on the y-axis
data of each set to see if there was any similarity in trend and the P-value for
pooled data is 1.9926E-5, implying that the two sets of data are significantly
different. This evidence is of course at odds with a visual comparison. For
instance as mentioned previously but here more explicitly, such a comparison
reveals that there is a 500 year decrease in Cmax/Cmax(γ + 1)/2 prior to an upturn at
the end of each time period, and there are other similarities. These patterns need
to be investigated more thoroughly in future research.
A remark here needs to be made about both Grinin and Korotayev's research
(2006), the research of Korotayev and Grinin (2013, and that of George Modelski
(2003) with respect to world system phases, periodicities, and trends.
The previous graph represents a single and quite rapid phase change from that of
the Ancient World to the Modern World we now live in, and it suggests that
regarding urbanization the data here imply that the Modern World began
2500 years ago. I would argue that that is the case only with respect to the ratio,
Cmax/Cmax(γ + 1)/2, however, it does also suggest that our modern world has very
deep roots, and that Arrighi's The Long Twentieth Century and other research on
historical trends by a variety of authors (see above) are clearly prescient. Mention
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The World System Trajectory
should also be made of L. S. Stavrianos' The Promise of the Coming Dark Age as
a work of deep historical insight in the same vein as Arrighi's but with focus on
the future.
Given that there is evidence for both dissimilarity and similarity of the data
over each 2500 year subset, a very simple fractal analysis was performed to see if
the fractal dimension of each sub pattern shared any similarity. This was done by
determining the total distance in theoretical space of the world system trajectory
for each subset, determining the length of the line segment of the regression
equation for each respective time period of 2500 years, that is the lengths of the
solid lines in Fig. 21, taking the natural log-transform of each, and dividing the
log-transformed distance of the actual trajectory by the log-transformed
regression distance. This gives the fractal dimension, here labeled D, or more
explicitly,
D = lnΣCo/lnCR.
(Eq. 21)
C will be used to represent ΣCo to simplify the symbolism. The anti-log of
Eq. 18 is C = CRD (Eq. 19). When the dimension, D, was calculated for each
subset of data, these values were respectively, D = 1.4853 for the first 2500 years,
and D = 1.4870 for the second 2500 years. The difference between these two
values is .0017 or approximately two one-thousands, quite slight.
Unquestionably, these are important results, as they imply fractal similarity over
different time periods of the same magnitude but with different histories, which
further implies significant constraints on the trajectory of the world system.
As an extension of the metric used previously to represent world system
trends, that is Cmax/Cmax(γ + 1)/2, this section will investigate the relationship between the theoretical area determined by the actual values of lnCmax and lnα and
the maximum possible area determined by [(γ + 1)/2]2lnCmax2. This involves
producing a ratio of {(γlnCmax)2/[(γ + 1)2/4) lnCmax2 )]}, which simplifies to
Cmax^[(2γ – γ2 – 1)/2] in the following way: Since (γlnCmax)2 simplifies
to Cmax2γ, and since [(γ+1)/2]2lnCmax2 simplifies to Cmax^(γ2 + 2γ + 1)/2, then
Cmax2γ/Cmax^(γ2 + 2γ + 1)/2 = Cmax^2γ – (γ2 + 2γ + 1)/2 which in turn equals
Cmax^(2γ – γ2 – 1)/2. Calculated values for this new metric were graphed on the
y-axis against time in increments of 100 years over the past 5000 years of
world system history to give Fig. 22 below. This graph represents two periods
of fluctuation about a mean separated by a transition phase or phase change.
This period of phase change has been included within the bounds of both
portions of the graph for convenience, but should be considered to span the
time period, 700 BCE to 100 BCE, including what Karl Jaspers referred to as
the Axial Age. If a linear regression is fitted to these graphed data the results
are as represented in Fig. 23 below. It should be noted that the slope of the regression equation is quite small, m = .00450, in fact almost horizontal, and also
that the actual fit of the data is quite good.
Tony Harper
81
Fig. 28. Time in increments of 100 years for the 5000 years of world
system history is represented on the x-axis, while values of
Cmax^(2γ – γ2 – 1)/2are represented on the y-axis. Note that
this graph effectively has two portions, one from 3000 BCE to
500 BCE and the other from 500 BCE to 2000 CE. These
portions or segments of the graph will be analysed separately later in this section
Fig. 29.
In this graph the data of the previous graph have been linearly regressed to produce the equation,
L = .00450t + .264,
(Eq. 22)
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The World System Trajectory
having r = .564, and having an RMSE = .0971, where L represents the expression, Cmax^(2γ – γ2 – 1)/2. The implications of this graph are that, while the
correlation is acceptable but not strong, the RMSE, indicting goodness of fit is
quite good. Further, there appear to be two distinct periods of activity of the
world system, each spanning about 2500 years.
Fig. 30. This graph shows the relatively linear trend exhibited by the
data represented in the previous graph and also the relatively close fit of the data to the regression line
To place the graph in a different and more appropriate context to show its linearity, the y-axis values have been expanded to –2, 2 in Fig. 30 above. This figure shows both the linear trend of the data plotted in Figs 22 and 23 and the
closeness of fit of the data to the regression line. However, the representation of
the distinct phases of world system activity separated by a phase change is
blurred. What the above graph does reveal is the clear liner trend of world system history over the last 5000 years, which is, again, an indication of constraints operating on the system.
What is also interesting is that the graph of the entire world system history
of the relationship represented by the term, Cmax^(2γ – γ2 – 1)/2 does not require
natural log transformation, so that changes in early world system history, say,
during the first 1000 years or so, can be compared directly with any other portion of the data plot. With this in mind, it should be noted that the system
change in the phase change noted previously represents an overlapping of system activity in that the greatest y-values of the first 2500 years are greater that
the smallest y-values of the second 2500 years. What this may imply is that the
second phase change may represent a similar overlap and can be predicted to
extend to a y-value of approximately .85, which indicates that the world system
has reached a level of activity which is 85 % of its theoretical maximum, no
small consequence to contemplate.
Turning now to a representation of the individual periods, the first
2500 years of world system activity are represented in Fig. 25 and including the
regression line, show a slightly negative slope, m = –.00227, with a weak r =
= –.244, but a significant RMSE = .0677. The second 2500 years of world sys-
Tony Harper
83
tem activity are represented in Fig. 26 with a slope, m = –2.22E-4, that is
an order of magnitude less negative than that of the first and an RMSE = .0916
which is not significantly different from the RMSE of the first, that is RMSE =
= .0971, representing a difference of .0055 between the RMSE's of the two regressions.
What is significantly different between the two regressions are the y-intercept
values, the first being .264 and the second being .470. Clearly, while the slopes
of both regressions are almost horizontal, the intercepts are quite different and
can be represented in the composite graph in Fig. 27. This is not unlike the
graph in Fig. 21, however the difference in the current y-intercept values is
.206, while that in Fig. 21 is .0611, and the difference in the differences is unquestionably a function of the analysis in Fig. 21 being done at a single dimension, while that in Fig. 27 involves a two-dimensional analysis.
Fig. 31. This graph is of Cmax^(2γ – γ2 – 1)/2 plotted over the first
2500 years of world system history.The important aspects
of this graph are that the slope of the linear regression is
almost zero and that the RMSE is quite small
Х
Further, the composite graph in Fig. 27 affirms the assertion made regarding
the graph in Fig. 21, that of a distinctly different level of world system activity
for the last 2500 years of world system history and also that the world system is
in all probability in a phase transition to a new level of activity. This last assertion is based on the change in world system position for the last two positions
represented in Fig. 26 which show a remarkable increase from 1800 CE,
that is point 48 on the x-axis, to the year 2000 and also the assumption that
84
The World System Trajectory
phase changes occur approximately every 2500 years with respect to the metric,
Cmax^(2γ – γ2 – 1)/2.
Fig. 32. This graph represents Cmax^(2γ – γ2 – 1)/2 plotted over the
second 2500 years of world system history, and, as in Fig. 27
has a very acceptable RMSE value and a slope approaching
zero
Further, the composite graph in Fig. 27 affirms the assertion made regarding
the graph in Fig. 21, that of a distinctly different level of world system activity
for the last 2500 years of world system history and also that the world system is
in all probability in a phase transition to a new level of activity. This last assertion is based on the change in world system position for the last two positions
represented in Fig. 26 which show a remarkable increase from 1800 CE,
that is point 48 on the x-axis, to the year 2000 and also the assumption that
phase changes occur approximately every 2500 years with respect to the metric,
Cmax^(2γ – γ2 – 1)/2.
Of further importance is the considerable change in position of the world
system at the 2500 year point. As it is represented in Fig. 27, it appears as
a discontinuity in history, however, the reality is that continuous change, much
of it over the Axial Age, brought about the new mode (and tempo) for the
world system. One has only to take a look at Fig. 23 to see the nature of this
phase transition, which is quite rapid, occurring over a period of 600 years, but
hardly instantaneous! Exactly how this phase transition was brought about from
a cliodynamic perspective should be the focus of future research.
85
2
Cmax^(2γ – γ – 1)/2
Tony Harper
Fig. 33. This graph represents the trends of Cmax^(2γ – γ2 – 1)/2 for
both the first and second portions of world system history,
both 2500 years in extent. Of note is the significant change
in both position and slope of the second 2500 years
A rudimentary fractal analysis was done for the trends of Cmax/Cmax(γ + 1)/2 over
all of world system history, and the same will be done for the metric Cmax^(2γ –
– γ2 – 1)/2 over the same period of time using the same symbolism, see Eq. 19.
When D, the fractal dimension, was calculated for both the first and second
2500 year periods and also for the entire extent of world system history the
values computed were all approximately the same and did not vary significantly
from linearity, that is D ~ 1. More specifically, D1 = 1.0029, D2 = 1.0036, and
D3 = 1.0059. These values are effectively linear and suggest that the trajectory
of the world system as represented by the regressions,
(Eq. 23)
R1 = .318 – .0027t,
R2 = .470 – 2.22E-4, and
R = .00450t + .264,
(Eq. 24)
Of Cmax^(2γ – γ2 – 1)/2 over world system history, is dimension-limited and
therefore a considerable constraint on the future course of that trajectory.
The Relationship between Maximum Urban Area and
World System Population over the Last 5000 Years
The graph of lnT against lnCmax is given in Fig. 34 on the following page. There
is a clear positive trend to the plot of this graph, albeit with some dispersion of
points. It should be noted that the actual space occupied by this graph is quite
restricted with respect to the phase space that it resides in. In Fig. 35, the same
graph but with a best fit line, the aspect of linearity is more clearly defined, and
the equation for this line is:
(Eq. 25)
lnCmax = 1.0521lnT – 6.8404
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The World System Trajectory
with an R2 = .9171, in other words, the fit of this line is quite good. It is hardly
earth-shattering that there is a positive relationship between increased urbanization and the increased magnitude of the world system population over time, but
the ability to give an explicit description to this relationship has some considerable utility. Even though the trend of this natural log plot is unquestionably
linear, there are some significant departures from linearity, and there are also
other characteristics of this graph that bear commenting on.
For the sake of communication it will be best to consider the graphs in
Figs 34 and 35 to be divided into three regions, the first from 16.45 to 1nT =
= 18.42, the second from lnT = 18.42 to lnT = 20.52, and the third from
lnT = 20.52 to the right-most extension of the graph, 22.55. In Region 1 there
are clear early (and tight) oscillations having periods on the order of 100 years
that give way to more extended oscillations. The significance of these oscillations is that an increase above the mean position of the trajectory, as defined by
the regression line, implies increasing urbanization, while a downward trend
implies decreasing urbanization.
Fig. 34. X-axis is lnT, and Y-axis is lnCmax. The trend is linear with
some dispersion of points
It could be argued that the relationship is only with maximum urban area, however, there is a clearly defined relationship between T and Cmax as represented
by the equation: Cmaxγ – Cmax – (γ – 1)T = 0 (Eq. 2). So, a change in the magnitude of Cmax also implies a change in the pattern of urbanization as reflected in
the variable, γ.
Tony Harper
87
Fig. 35. Axes same as in Fig. 1. The regressed line is represented by
the equation: lnCmax = 1.0521lnT – 6.8404. R2 = .9171
Considering the first segment of the world system trajectory from 16.45 to
18.42, which spans the time from 3000 BCE to 500 BCE, the key characteristic
of this segment is the oscillatory nature of the trajectory and, in particular, the
relatively width of the oscillations and their frequency. It could be argued here,
especially through ~17.2, the world system was equilibrating from the emergence of the first empires. The trajectory rises quite rapidly through 17.6,
a point on the graph representing the end of the Late Bronze Age, which is
followed by a significant down turn, a mild rise and plateau, another slight
down turn and then a rise to the end of this period. What characterizes this
first half of the trajectory with respect to time, that is 2500 years, is apparent
rapid urbanization which appears to overshoot the carrying capacity for that
degree of urbanization and is consequently followed by decline. This segment
is followed by a segment representing the next 2300 years of world system
history.
The second segment of the world system trajectory is punctuated by two
prominent events. The first of these begins with a very rapid phase of urbanization accompanied by stable or slightly decreasing world system population figures and begins in Figs 1 and 2 around lnT ~ 19.0. A maximum is reached after
300 years, followed by a slight decline and then a second maximum, which
spans 300 years from 100 BCE to 200 CE. After this a second period of relative
world system population stasis accompanies a decline in urbanization, spanning
some 500 years. The total time period from the beginning of increased urbanization to the end of decreasing urbanization amounts to 1100 years. The second, although a temporally briefer event, represents a total excursion of
200 years from 1200 CE to 1400 CE, during which the maximum urban area
population swung from 1.0 million to 1.5 million and then back again to
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The World System Trajectory
1.0 million with a slight decrease with world system population from 360 million at 1300 CE to 350 million at 1400 CE, due in large part to the ravages of
pandemic plague.
The third segment extending from lnT = 20.52 at 1800 CE to 22.55 at 2000 CE
represents similar change in the magnitude of the world system population but
over a much shorter period of time, only 200 years. This massive excursion
over a much shorter time period is unquestionably a product of the industrial
revolution but more deeply a consequence of hyperbolic population growth
(Korotayev et al. 2006a), which is itself a result of cooperative human interaction. If the ratio, ΔlnT/Δt, for each period, the values tell an interesting story.
The values for the first two periods are respectively, 7.88E-4 and 9.22E-4, both
within the same order of magnitude. However, the value for the third period is,
ΔlnT/Δt = 1E-2, two orders of magnitude greater than either of the two previous periods and represents a rate of change of the world system that is unique in
world system history. Further, during this period of rapid change there are no
significant oscillations, no evidence of overshoot soon to be followed by rapid
deurbanization. A caveat here, this present analysis documents change but does
not ascribe a cost, either environmentally or economically, to that change, consequently, the footprint of the last two centuries, either in carbon or some energy unit, is not apparent. In perusing the Fig. 34, there is only one portion of
that plot that bears any resemblance to this third segment and that is the portion
from lnT = 18.42 to 18.90, that is from 400 BCE to 100 BCE, which was succeeded by a period of very rapid urbanization.
If attention is now turned to Eq. 1, it will be seen that the fit is quite good
with respect to correlation, R2 = .9171, and the world system as reflected in
a graph of lnCmax v. lnT has a clear primary direction that is both linear and
positive. What are the implications of this positive linearity? First, it appears
that each variable depends strongly on the other. It is important to emphasize
that a large world system population is not simply a result of a large urban area
population, just as it is important to avoid stating the opposite, that a large urban area is not a consequence of a large world system population. Both are interdependent on the other, and the fact that lnT is represented on the y-axis and
not the x-axis is a result of choice by the author to emphasize the rapid changes
in urbanization apparent in the second section of the graph. Second, the positive
trend of the trajectory suggests that the near future state of the trajectory will in
a general way continue to be positive. If the previous pattern of this trend is
considered, specifically with respect to relatively significant positive change in
lnT, then the section of the graph immediately prior to lnT = 18.90, that is at
400 BCE when T ~ 162E6, may be considered a reasonable analogue of the last
200 years of the World System trajectory. Following this period of increased
lnT, was, as described previously, a period of rapid urbanization, followed by
a period of relative stasis, and then rapid deurbanization. May the same be ex-
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89
pected in the near future, that is relative stasis of lnT but a rapid increase in
urbanization as characterized both by increasing lnCmax and decreasing magnitude of γ. From my perspective, this is a distinct possibility, as the rate at which
the world system population is growing has been declining since the early
1960's, which mirrors the relative stasis of the population between 400 BCE
and 100 BCE.
A Comparison of the Time Series of Both the Natural Log
Transform of World System Population (lnT) and the
Natural Log Transform of Maximum Urban Area (lnCmax)
When the plot of points represented in both Figs 34 and 35 is decomposed into
two time series plotted on the same axes (see Fig. 3), a shared characteristic of
both plots becomes apparent. They are approximately parallel to each other
separated by an approximately constant distance. However, the upper plot, that
of lnT, is far smoother with an almost linear component over the first
2500 years of world system history, a slight increase immediately after
500 BCE followed by another relatively linear component ending about
1000 years ago, which was in turn followed by slight oscillations over the next
800 years, and terminated by an abrupt upturn representing the consequences of
the industrial and post-industrial eras. When these data are plotted on rectangular axes, the classic hyperbolic growth curve as noted by von Forester et al.
(1960) and by Korotayev et al. (2006a) is produced. Without the advent of the
Industrial Revolution the trajectory of the world system would be almost linear,
reflecting exponential growth. Second, the positive linearity of these two variables suggests that the system as a whole will continue to move in a positive
direction, which of course suggests constraint on the direction of the trajectory
and also suggests the potential for prediction of the future position of the trajectory.
Linear regressions of each plot give respectively,
lnT = 16.2 – .0868t
(Eq. 26)
and
(Eq. 27)
lnCmax = 10.3 – .0904t
As can be seen by comparing values at t = 0, the equivalent of 3000 BCE
and t = 2000 CE, the difference in regressed values at t = 0 is 5.9 and that at
t = 50 is 6.08, so, as a general trend the difference has diverged over time.
The implication being that a larger portion of the world system population lives
outside the largest urban area, and in fact it could be restated as the largest urban areas, if the observed difference matches the expected difference. This,
however, is not the case. The observed value of ln[T/Cmax] is 5.6000, which of
course implies that a greater proportion of the world system population than
expected due to regressed values resides in large urban areas.
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The World System Trajectory
Fig. 36. Time is represented on the x-axis as a multiple of 100 years.
The natural log transform of population size is represented
on the y-axis with the top plot being that of lnT, the total
population of the world system through the last 5000 years
and the bottom plot being the plot of the natural log transform of maximum urban size, lnCmax, over the same period
of time. The essentially parallel trajectories of both plots
should be quite apparent, suggesting a very clear relationship between the two.
Fig. 37. The axes are the same as in Fig. 3, however each trajectory
has been fitted by linear regression. The equation for the top
regression is, lnT = .0826t + 16.1681, and that of the lower
regression is, lnCmax = .0904t + 10.2681, where lower case
‘t’ = time, again in units times 100 years. The parallels nature of both plots is even more apparent in Fig. 4
Tony Harper
91
If the values of γ are compared at each of the times, 1.4851 at t = 0 and 1.2490
at t = 50, it can be seen that a larger proportion of the total population would be
expected to reside in (relatively) large urban areas.
A Model of the Difference between lnT and lnСmax
This parallel trend is relatively easy to model mathematically. Inspection of
Figs 3 and 4 will show that lnT – lnCmax ~ 5.9, or more explicitly, lnT – lnCmax=
= 5.9 – .0078t, where t = time. The anti-log transform of this equation is
(Eq. 28)
T/Cmax = e5.9 – .0078t
or by rearrangement,
(Eq. 29)
T = Cmaxe5.9 – .0078t.
While this is an empirically based model, an analytical model can also be
derived. Recall Eq. 2, Cmaxγ – Cmax – (γ – 1)T = 0. It is not too difficult to show
that
(Eq. 30)
T/Cmax = (Cmaxγ– 1 – 1)/(γ – 1)
(see Mathematical Appendix) and therefore,
(Eq. 31)
lnT – lnCmax = ln(Cmaxγ– 1 – 1)/(γ – 1).
If the natural log-transformed right hand sides of Eqs 5 and 6 are equated,
we have,
(Eq. 32)
5.9 – .0078t = ln[(Cmaxγ–1 – 1)/(γ – 1)],
and the left and right hand sides of this last equation, representing observed and
expected values of the world system, can be regressed against one another (see
Fig. 40).
Fig. 38. Observed v. Expected re: ln[T/Cmax] = ln[Cmaxγ–1 – 1]/[γ –
– 1], where the left-hand side of the equation represents the
observed, which is calculated from data on both T and Cmax,
while the right-hand side of the equation is used to predict
the left-hand side
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The World System Trajectory
It should be noted here that the above relationship is not unexpected, as Eq. 2
was used to generate values of γ with observed values of both lnT and lnCmax.
However, it should also be noted that the left-hand side of Eq. 32 represents
an alternative way of finding ln[T/Cmax], one in which the fit is quite good.
Interestingly, the essentially parallel trend of lnT and lnCmax over the last
5000 years suggests that there is a clear link between urbanization and total
population growth. This in one sense is unsurprising, however, the contention
here and in previous research is that link is in fact γ, the exponent characterizing the distribution of urban size given maximum urban size and total world
system population.
The Potential for Prediction
The previous four sections of this paper have addressed the notion of constraints imposed on the trajectory, the historical trajectory, of the world system
over the last 5000 years. A clear general trend with respect to the relationship
between γ and lnT has been demonstrated, one that shows a decrease in γ and
therefore an increase in the total distribution of the urban population, here defined as N ≥ 100, as the natural logarithm of the world system population and
therefore the population itself increases. It has been shown that there are specific instances of change in the world system position in reaction to previous
system change, e.g., the rapid urbanization of the world system from 400 BCE
to 100 BCE followed by a rapid de-urbanization from 200 CE to 500 CE, that
suggest that the system is being returned to some steady-state level. The existence of iso-urban lines has been established, lines of similar maximum urban
area magnitude with respect to both γ and lnT, and the polar plot of the world
system trajectory, the rather tight linearity between H and Ψ, H and time and Ψ
and time, the periodicity between the observed and expected of the last two
linear relationships, and the ratio of the observed maximum urban area value
and the idealized one determined by maximizing Eq. 12a, A = (γ – x)(1 + x).
5lnCmax2, which reveals that the urbanization of the world system appears to
have occurred in two specific regimes, each with a similar rate of occurrence
but with differing points of initiation, and which also demonstrates a fractal
relationship for the two regimes that is effectively identical. All of these instances suggest that the world system is highly constrained, and, in turn, if this
is in fact the case, that the behavior of the system, at least at the level of organization implied by the equation, Cmaxγ – Cmax – (γ – 1)T = 0 (Harper 2010b), is
(potentially) predictable.
Each of the above constraints will now be given more detailed analysis and
explanation and then some discussion will follow with respect to the potential
for prediction both in the past, that is retroactively, and for the system as a whole.
To begin, the fact that the linear relationship between γ and lnT has a negative slope suggests in general that for any given position of the world system
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Tony Harper
future positions from that point on will involve both a decrease in γ and an increase in lnT, and over an extended period of time this is unquestionably the
case. For example, the position of the world system in 200 CE is one in which
the value of γ has decreased as lnT has increased with respect to the world system position of, say, 2000 BCE. However, if the position of the world system
from 200 CE to 300 CE is considered, this is not the case, as there the change
involves an increase in γ with no attendant decrease in lnT. In Table 6 below
are documented all the changes in both γ and lnT and what this data reveals is
that while two relationships predominate, there are several other arrangements
between γ and lnT.
Table 6
γ/lnT
Number
+/+
22
+/0
3
+/–
1
–/–
2
–/0
1
–/+
21
As is represented above on a century by century basis then depending where
one starts the actual trend of change in γ with respect to lnT may fall into one of
six categories.
What is to be made then of the negative slope of the equation
γ = 2.23 – .0449lnT?
(Eq. 33)
This unquestionably has to be an emergent property of the system itself
and as such is only of general predictive value. Of more importance is the fact
that the dispersion of points about the trend line is that the greatest variance is
approximated by ~.1γ. This fact along with the negative slope have some predictive worth in that bounds are placed on future changes in position of the
world system from any previous point. A note of caution here: There are at
least two instances in which lnT, and therefore T, the population itself, decrease, the first during the period of intense urbanization from 300 BCE to
200 BCE and the second from 1300 CE to 1400 CE, the (calamitous) 14th century, and these population deficits were quite small.
It is to these two specific instances, the period of rapid urbanization at the
end of the first millennium BCE and the 14th century and the periods of adjustment that followed them, that attention will now be given. Both of these periods
of time share the same pattern of development and response, that is both represent periods of intense urbanization directly associated with little or no negative
change in total population followed by rapid de-urbanization, in the case of the
first period, punctuated by a brief period of de-urbanization followed by a short
period of urbanization. It appears then that rapid urbanization constrained by
zero world system population growth results in equally rapid de-urbanization,
either directly or followed by some relatively short period of time.
To give a numerical explanation for the above phenomenon Eq. 23 from
Harper (2010b) was used to calculate the ratio of urbanized population to that
of the rural population for the total population. The data are given in Table 7
below.
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The World System Trajectory
Table 7
γ
1.1
1.2
1.3
1.4
1.5
1.6
Cmax
2.9E6
1.3E6
5.7E5
2.7E5
1.4E5
7.3E4
Tu/Tr
1.2803
.6197
.3301
.1876
.1110
.0673
Note: The values of Tu/Tr were calculated by Eq. 23 from Harper (2010b): Tu/Tr =
= (a(1 – γ) – 1)/(1 – C0(γ – 1)), where a = Cmax/C0, and C0 = 100.
It can be seen that as γ decreases the proportion of the urbanized population
increases. Note that Cmax had to be computed for each γ, and note also that the
above table is meant to be a numerical example in which γ was varied over its
observed range. This is further represented in Fig. 28 in which γ is plotted
against Tu/Tr shows a rapid decline of the urbanized population with respect to
increasing γ.
However, the reverse of this trend should actually be considered, as the urbanization process is associated with decreasing γ. The non-linearity of this
process implies a very rapid increase in the proportion of the urbanized population as suggested by the power relation,
(Eq. 34)
Tu/Tr = 2.81γ–8.41,
where very rapid urbanization can be expected with smaller and smaller γ. It is
my contention that both instances of rapid urbanization followed shortly by
rapid de-urbanization, that of the latter part of the last millennium BCE and the
300 years represented by the period of time from 200 CE to 500 CE and also
the 13th and 14th centuries CE, are consequences not only of this rapid urbanization but of the consequences of that urbanization process exceeding some as yet
to be defined threshold regarding system wide sustainability. This may well be
the process of overshoot and its consequences referred to in the book of the
same title Overshoot: The Ecological Basis of Revolutionary Change by William R. Catton, Jr.
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95
Fig. 39. The relationship between γ and Tu/Tr is shown to be inverse
and non-linear, the implication being that as urbanization increases it does so at an ever increasing rate with respect to
decreasing γ
Movement of the system, whether as a consequence of over-shoot, as explained
previously, or simply as a result of the more normal processes of world system
development, is associated with the distribution of the urbanized population and
as such can be characterized by maximum urban area, by γ, and by the total
population of the system itself. Further, it was previously shown that the relationship between identical maximum urban areas, γ, and lnT is linear.
In other words, if maximum urban area can be predicted, the position of the
world system can also be predicted as all points for the world system having
a given maximum urban area will fall on the same straight line, an iso-urban
line. This fact then further limits the position of the world system and can be
used as a potential predictor of the position of the system.
Using these iso-urban lines as a base from which to track the movement of
the world system through time allows for a polar representation of the world
system trajectory. When this polar plot is inspected the change in the trajectory
over time is limited to either a counter-clockwise and ever expanding (with
respect to the origin of the plot) new position or a linear change in position without change in Ψ, that is a change in which the plot has the appearance of proceeding out of the plane of the page. These limitations are again another way of
representing imposed constraints on the system, and they represent a means
of prediction of the future state of the system, noting of course that the future
state of the system can be viewed from any previous state of the system, that is
that the future can be in the past.
Associated with the process of representing the world system trajectory in
polar coordinates is the ability to represent the relationship between the pa-
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The World System Trajectory
rameters, H and Ψ themselves, and also to represent the relationship between
these parameters individually over time. In all three cases, the relationships can
be represented by a linear regression of the data, which implies the ability to
predict in relatively specific terms. It is interesting, though, to recognize that
while a linear representation of each of the relationships represents a good deal
of the variability in the data, there are non-linearities, either due to phase
changes of the system or periodic changes in the variables, S and Ψ. While
there are several two-step phase changes represented in Fig. 6, in fact four, one
beginning at 2500 BCE, one at 2000 BCE, one at 1000 BCE, and a final one
beginning at 900 CE, and while the temporal position of these phase changes is
suggestive of an exponential sequence, 500 years separating the first from the
beginning of the trajectory, 500 years to the next, then 1000 years to the next,
and finally 1900 years or almost 2000 years to the beginning of the final phase
change, it is the aforementioned periodicities that will be discussed next.
Finally, the relationship between the observed and idealized values for
maximum urban area size over time will be considered, as will the relationship
between observed and expected theoretical world system space. It was shown
that the graph of this data over the 5000 year history of the world system represented two distinct sets of data on urbanization, distinct in that they gave different linear regressions, but only by y-intercept, not by slope. This would seem
to indicate a similar over-all process of urbanization which was simply shifted to
a higher level on the graph with the beginning of the existence of the Roman Empire and shortly after that of the Han Empire. Also, when the natural logarithm of
the length of the regression segment was divided into the natural logarithm of the
total (abstract) distance traveled by the world system in each 2500 year section of
time, the quotient, in other words the fractal dimension, of each was effectively
the same. This indicates a very strong potential for prediction, since per 2500 year
period the fractal dimension appears to be almost identical.
When a fractal analysis was undertaken for the relationship between observed and expected world system theoretical space, quite different results were
arrived at. First, the relationship between the linear regression of the data for
each 2500 year section of world system history and the entire 5000 years of that
history and the actual distance traveled were considered, all the fractal dimensions were approximately 1. Second, given that this is the case, then the trajectory of the world system as represented by this ratio, that is lnD/lnR, is linear,
which implies that at this scale of inspection the world system trajectory is
highly constrained.
Beyond fractal analysis when the log-transformed parallel trajectory of lnT
and lnCmax is considered, the relationship between these two variables seems
strong and allows for further generalized prediction. First, although the variability of lnT – lnCmax ranges from approximately 5 to approximately 6.5,
Tony Harper
97
the regressed value is approximately 5.9. Using this average value, it is easy to
extrapolate into the future. If regression yields
(Eq. 35)
lnT – lnCmax = 5.9,
then maintaining the 100 year interval that the world system history is divided
by permits prediction from any position on the regressed trajectory to the next
position on the trajectory and also beyond the current last position of the trajectory, 2000 CE (see Fig. 40). This is not a particularly satisfactory predictive
tool however, because, as was mentioned previously, there is variability in the
difference, lnT – lnCmax. However, if the data on lnT and lnCmax are considered
specifically, a better predictive procedure, but one that still yields approximate
results, emerges. This better predictive model, let us call it the ‘abstract square
model’, is represented in Figs 41a and 41b.
Fig. 40. lnT is represented on the x-axis, and lnCmax is represented
on the y-axis. The points used to generate this regression
are sets of lnT, lnCmax in 500 year increments. The regressed equation is: lnCmax= 1.1680lnT – 9.0269 (Eq. 34),
R2 = .9736. If this line is extrapolated over the next
100 years the values of lnT and lnCmax are easily predictable
Note: lnT – lnCmax = Z, or lnCmax = lnT – 5.9, which is clearly an approximated version
of the regression equation. Note that Z = any value between 5.0647 and 6.6846,
the range of observed values of lnT – lnCmax.
Here the linear regression represented in Fig. 40 is combined with the observed
limits of the system. In other words, a rectangle is created with a point representing the position of the world system as a reference. Then the range that the
next generation of lnT values is determined by
(Eq. 36)
lnT = lnCmax + [5 .0646 → 6.6846]
and by
(Eq. 37)
lnCmax = lnT– [6.6846 → 5.0646].
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The World System Trajectory
This gives a square with the dimensions, 1.6199 × 1.6199, in which it is
predicted the next generation's world system position can potentially be found.
Sadly, this square has within an infinite number of points, which is hardly helpful. Can probability be used to reduce the possible number of points? Possibly.
Note that this square can be subdivided into four different sections, and the
sections vary in area suggesting that the probability of the position of the world
system falling in any of the subsections is proportional to the area of the subsection. This is helpful but only in a general way, since each of these rectangular figures has within it an infinite number of points. If the position of the world
system is calculated per century with respect to the context of this square, the
position of the world system is observed to change, and since this change falls
within the zero sum limits of the value, 1.6199, for both axes, then only one
variable is necessary to characterize the position of the world system. Specifically, the reference of a zero sum relationship between the position of the world
system within the boundaries of the square model imply that if the difference
between the position of the world system and the maximum boundary of the
square is known, then the other three differences between the other three
boundaries are explicitly predictable, because all relationships are dependent on
lnT – lnCmax = [6.6846 – 5.0647].
Fig. 41a. This is a simple representation of the general trend of the
world system with respect to lnT on the x-axis and lnCmax
on the y-axis. In broad terms, the predictability of the
future state of the system is simply a matter of following
the trend of the line. However, when the range of values
between lnT and lnCmax are imposed the number of future
positions of the world system becomes more varied as will
be seen in Fig. 41b.
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Tony Harper
*
Fig. 41b. The box in the upper right hand corner of this graph represents the space delimited by the maximum and minimum
values for the difference between lnT and lnCmax of all possible values that the world system position can have in
100 years from the present. Note that the position of the
asterisk, the current position of the world system changes
with respect to the boundaries of the square
Data for the position of lnCmax with respect to the maximum value of lnCmax as
determined by lnCmax = lnT – [6.6846 → 5.0646] were used to construct the
graph in Fig. 42. There are several unique features of this graph. First, the reader should understand that a vertical step representation was chosen so that the
change in the difference of the observed value of lnCmax and its maximum, Z,
could be represented. This plot reveals little change in the domain of Z over
time, that is a linear regression would be expected to give a slope close to zero,
and, in fact, the slope is .0027, very close to zero. Further, although the graph is
punctuated by a number of peaks and troughs, that there is very little visual
regularity to their occurrence. If peaks or maxima are defined as any increase
over a previous minimum of .2 or greater on the y-axis scale of Fig. 42 then
there are thirteen such maxima occurring at 2800 BCE, 2300 BCE, 2100 BCE,
1800 BCE, 1200 BCE, 900 BCE, 600 BCE, 100 BCE, 200 CE, 600 CE,
1000 CE, 1300 CE, and 2000 CE and doing so in a somewhat irregular way.
It is also disconcerting to note that, while increases on the y-axis values are
done incrementally and in a stepwise fashion, the decent from twelve of
the thirteen maxima is done so precipitously; the decent from the thirteenth
maximum has yet to occur and all of these descents may refer to what William
Catton refers to as overshoot, or rather the consequences of overshoot (Catton
1982). Superficially, this data appear not to contribute much to prediction with
the previous statement about overshoot excepted, however, there is some light
at the end of this particular tunnel.
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The World System Trajectory
Fig. 42. Time is represented on the x-axis, and the computation,
[lnCmax + 6.6846 – lnT]/1.6199, is represented on the
y-axis. This computation is proportional to the position of
the world system within the phase space defined by the
maxima and minima of lnT – lnCmax. The regression, having
a slope, m = .003, indicates that over the 5000 years of
world system history investigated here these changes in the
position of the world system with respect to the maximum
value of lnCmax changes and does so episodically
If focus is brought to bear on the changes in y-axis values across time, and, in
fact, their absolute value, a size frequency distribution can be produced as represented in Fig. 43. This distribution and the curve fit to this distribution clearly
represent a pattern of exponential decay, which can be characterized by a power
function with a negative exponent, e.g., y = ax–b, or an exponential function
such as, F = F0 + ae–b. With regard to the specific data used to create the graph
in Fig. 43 and using the actual values for the exponential form of this equation,
the equation becomes,
(Eq. 38)
F = 48.58881e–r/.4609 + 3.6212,
where ‘r’ is the rank of each frequency. The natural log transformation of the
frequency data gives the following linear equation,
lnF = 3.9135 – 1.6999r,
(Eq. 39)
the equation of a straight line as represented in Fig. 44. If the natural log transformed frequency data are plotted against class size, the linear distribution of
points, as represented in Fig. 45, is the result.
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101
Fig. 43. Class size is represented on the x-axis, and frequency is represented on the y-axis. The regression curve is described by
the equation of the form, F = F0 + Ae–x/t, where F0 = 3.6212,
A = 48.5888, and t = .4609.R2 = .9667
These equations and the facts that it has been demonstrated that the world system is a non-equilibrium system and that the world system is a large, complex
system both suggest that the world system exhibits self-organized criticality,
SOC (Bak 2003 and else where). A random distribution of numbers over the
same range was generated and coupled with the data in Fig. 43 was subjected to
a two-sample t-test. The P-value of this test was P = 1.8176E-5. In other words,
the probability of these two data sets being related was approximately 18 in
1,000,000, the implication being that the data showing SOC for the world system are non-random. Further and obviously, if the frequency data for Fig. 43
are natural-log transformed, a linear distribution is produced as represented in
Fig. 44. Here the distribution is unquestionably linear and implies continuity of
change over the range of the data but also implies the consequences of SOC,
which will be discussed briefly in the following paragraph.
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The World System Trajectory
Fig. 44. Class size is represented on the x-axis, and lnF is represented on the y-axis. lnF = 3.9135 – 1.6999r, where r is the
rank of the frequency (Eq. 38). R2 = .9716
The consequences of a system exhibiting SOC are significant. First, periods of
rapid urbanization and de-urbanization are punctuated by periods of relative
stasis. This pattern is also exhibited in the second section of this paper discussing the polar plot representation of the world system, specifically in Figs 12 and
13. Second, the pattern of systems exhibiting SOC can be represented by a simple power function or exponential function as is the case here. Third, this pattern is continuous, as is clearly represented in both Figs 44 and 45, and consequently there is no difference in the factors that cause small events of urbanization and those that cause major events of urbanization. Fourth, the timing of
these events individually is not predictable, either with regard to increased or
decreased urbanization. This was suggested and only suggested by the temporal
distribution of maxima in Fig. 42. While these data then are suggestive of regularity, they are not suggestive of explicit temporal predictability, however, the
inference that the world system exhibits SOC is itself a prediction in terms of
the behavior of the system.
In conclusion, what are the actual implications of this section for predictability? First, the original trajectory of the world system in its natural logtransformed state yields a relatively linear regression with some significant digressions from linearity as have already been mentioned. So, in general, the extension of the regression gives an approximate prediction of the future of the
system, and the same holds true for postdictions. However, if one were making
a prediction for the future of the system in 500 BCE or, say, 1300 CE, in terms
of linearity the prediction would be wildly wrong. In both instances very rapid
urbanization occurs in the face of very little or no increase in lnT, the consequence for the trajectory being that it takes very sharp right turns at both
500 BCE and 1300 BCE, clearly events that do not fit the trend of the linear
model. So, the linear model is of limited use.
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103
A more detailed study of the trajectory reveals that iso-urban lines exist, in
other words, that regarding the graph of γ v. lnT points of identical maximum
urban area magnitude align linearly. This in itself is of course a prediction. If
the current state of the system were to revert to a maximum urban area size of
1,000,000, then the position of the system would fall somewhere on the isourban line with m = .0910 and b = –.4430. Consulting Fig. 4 will allow the
reader to estimate the current position of the world system if this reversion in
maximum urban area size were to occur with no change in lnT. Again, any prediction using iso-urban lines would be far from explicit.
In turn, the iso-urban lines were used as a basis for constructing a polar
plot of the world system trajectory, an ever expanding spiral subject to the
changes in both X = ScosΨ and Y = SsinΨ, the parametric equations for the plot.
A three dimensional polar plot reveals a relative degree of regularity in the system. Given a couple of two-dimensional perspectives, it is quite clear that a relatively linear increase in maxima occurs, and the same may be stated for minima. Further, when both X and Y are plotted against time their maxima occur in
a predictable fashion and, in general, so do the minima. If S and Ψ are plotted
against one another, a near-linear plot is achieved, however, there are clear
punctuations in this graph in which S changes rapidly while Ψ does not change
at all. This behavior of the world system represents punctuations in change alternating with relative stasis and is characteristic of a number of biological systems. In itself, this characteristic of the world system is predictive of general,
over-all prediction but not explicit prediction.
When maximum urban area size is compared with optimal urban area size
a clear trend is revealed with decreasing γ, in that the two values approach one
another. The ratio of these two values, Cmax/Cmax(γ + 1)/2, when plotted against
time clearly reveals a disjunct graph, one in which the Ancient World is separated by a phase change in maximum urban area magnitude from the Classical
and Modern Worlds. This phase change occurs during a period of time that
roughly coincides with Karl Jasper's Axial Age, but the graph and the data behind the graph do not explain why this phase change occurred when it did. It is
interesting to note here that the world system may be entering another period of
phase change, however, aside from the periodicity of these two events being
approximately 2500 years in length, there is little reliance at present that can be
placed on a data set of only two events. It is interesting, however, that when
a simple fractal analysis is applied to this data that the fractal dimensions of
both are nearly identical. This is, in one sense, intellectually comforting, but
again does not lend itself to explicit prediction.
When the separate trajectories of both lnT and lnCmax are compared they
appear nearly linear and parallel to one another. This is confirmed by calculating the differences between the linear regressions of both trajectories. However,
the observed data vary in the difference of their magnitude by 1.6199, a signifi-
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The World System Trajectory
cant variance when one deals with log-transformed data. While the general relationship between lnT and lnCmax is linear, when the variability between lnT
and lnCmax makes the prediction within that range of variability for both
lnT and lnCmax less possible (see Fig. 41b). Over time the position of the world
system varies with respect to the boundaries of the variability. This variability
opens the door to a new perspective on the behavior of the world system and
the predictability of that behavior.
When this variance in position of the world system with respect to the
boundaries of the variance in the difference between lnT and lnCmax is plotted
against time and is represented as a vertical series of steps, it is quite clear that
the average slope of this graph (Fig. 42.) is nearly zero. But, when a size frequency distribution of the absolute values of the vertical steps is constructed,
the result is a curve exhibiting decay, which can be represented by either a power
function or an exponential function. Given that the world system is a large, complex, non-equilibrium system, this result implies that the world system exhibits
self-organized criticality. There are three important consequences of this implication. First, the factors that both increase and decrease rates of urbanization
are similar for all magnitudes of urbanization. Second, it should be expected
that periods of urbanization are episodic. Third, these periods of episodic urbanization appear not to be temporally predictable.
This research paper closes with two concerns: First, somewhat conflicting
data have been presented with regard to the predictability of the world system
trajectory as it is understood over the last 5000 years of its history. Unquestionably, much more research is required to resolve this disparity, however,
personally my intuition tells me that further study of the potential for the world
system to exhibit SOC, self-organized critically, will be quite productive. Second, Fig. 43 reveals a pattern of change in which increase in urbanization with
respect to the total population of the world system is for the most part done
incrementally. However, change in the opposite direction is not, it occurs precipitously. If these data are correct there are two further consequences, that the
timing of these down turns is episodic and may not be predictable, and that
the magnitudes of the down turns is quite large.
Summary
1. The intent of this paper is to show, first, that the trajectory of the world system is highly constrained, and, second, that these constraints lead to the possibility
of prediction, that is that the position of the world system at any point on its trajectory is potentially predictable based on the nature of the constraints analysed.
2. The organization of the world system was described in terms of the relationship between γ, a parameter that generalizes the distribution of urban areas for
any given maximum urban area and the total population of the system.
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105
3. Several types of constraint on the world system trajectory were recognized. Specifically, the overall trend of the system and the existence of iso-urban
lines were discussed.
4. The trajectory of the world system was reconfigured in polar dimensions,
the morphology of this plot was described, and the changes over time with respect to the polar parameters were noted, and any non-linearities, either of
a punctuated or periodic nature were analysed.
5. A standard, the idealized maximum urban area, was established and a ratio was generated with the observed maximum urban area divided by the standard. This allowed the recognition of two distinct phases of urbanization and,
further, on generating separate regressions for each phase of urbanization it was
shown that the fractal dimension of each was essentially the same.
6. As in #5 a standard was established for total potential area of the world
system and the actual potential area of the system at each point in time could then
be used to generate a ratio of the standard to the actual so that any significant
trends in world system activity could be represented. Fractal analysis was performed, and it was shown that the fractal dimension for both the 2500 year periods and the entire extent of world system history did not vary significantly from
unity. This fact has significance with regard to prediction of the world system
trajectory into the future.
7. The parallel trajectories of the world system population as a whole and
that of maximum urban areas of that system was analysed, and it was shown that
the difference between the natural log-transformed values for both variables falls
within a range of values the difference of which is 1.6199.
8. The data on the parallel trajectories of both the natural log-transformed
world system population and maximum urban area sizes exhibit properties of
self-organized criticality. The consequences of complex systems exhibiting SOC
are discussed.
9. The potential of using these constraints and conditions to predict past,
present, and future positions of the world system was noted in terms of each of
the constraints analysed and each constraint was assessed for its particular contribution to understanding the (future) state of the system.
References
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Arrighi G. 1994. The Long Twentieth Century: Money, Power, and the Origins of Our
Times. New York: Verso.
Bak P. 1996. How Nature Works. New York: Copernicus Springer-Verlag.
Bak P., Tang C., and Wiesenfeld K. 1987. Self-Organized Criticality: An Explanation
of 1/f Noise. Physical Review Letters 59: 381–384.
Catton W. R. Jr. 1982. Overshoot: The Ecological Basis of Revolutionary Change.
Chicago, IL: University of Illinois Press.
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Cohen J. 1995. How Many People Can the Earth Support? New York: W. W. Norton
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von Forester H., Mora P. M., and Amiot L. W. 1960. Doomsday: Friday 13th, November, A.D. 2026. Science 134(3436): 1291–1295.
Grinin L. 2012. Macrohistory and Globalization. Volgograd: Uchitel Publishing House.
Grinin L., and Korotayev A. 2006. Political Development of the World System:
A Formal Quantitative Analysis. History and Mathematics. Historical Dynamics
and Development of Complex Societies / Ed. by P. Turchin, L. Grinin, A. Korotayev,
V. de Munck, pp. 115–153. Moscow: KomKniga/URSS.
Harper T. 2010a. The Macropattern of Urbanization over the Course of the Last 5000
Years of World-System History. Social Evolution & History 9(1): 115–133.
Harper T. 2010b. The Trajectory of the World System over the Last 5000 Years. History and Mathematics: Processes and Models of Global Dynamics / Ed. by
L. Grinin, P. Herrmann, A. Korotayev, and A. Tausch, pp. 13–63. Volgograd:
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Hutchinson G. E. 1978. An Introduction to Population Ecology. New Haven, CT: Yale
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Korotayev A. 2010. Globalization and Mathematical Modeling of Global Development.
Hierarchy and Power: Political Aspects of Modernity / Ed. by L. Grinin, D. Beliaev,
and A. Korotayev, pp. 225–240. Moscow: LIBROCOM/URSS.
Korotayev A., and Grinin L. 2006. Urbanization and Political Development of the
World System: A Comparative Quantitative Analysis. History and Mathematics:
Historical Dynamics and Development of Complex Societies / Ed. by P. Turchin,
L. Grinin, V. de Munck, and A. Korotayev, pp. 115–153. Moscow: KomKniga.
Korotayev A., and Grinin L. 2013. Urbanization and Political Development of the
World System. Entelequia 5: 197–254.
Korotayev A., Malkov A., and Khaltourina D. 2006a. Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. Moscow: URSS.
Korotayev A., Malkov A., and Khaltourina D. 2006b. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends. Moscow: URSS.
Korotayev A., Malkov A., and Khaltourina D. 2006c. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends in Africa. Moscow: URSS.
Li C. C. 1955. Population Genetics. Chicago, IL: University of Chicago Press.
Malthus T. H. 1798. An Essay on the Principle of Population. The Project Gutenberg.
URL: http://www.gutenberg.org/.
Mayr E. 1988. Toward a New Philosophy of Biology: Observations of an Evolutionist.
Cambridge: Belknap Press of Harvard University Press.
Modelski G. 2003. World Cities: –3000 to 2000. Cheshire, CT: Faros 2000.
Stavrianos L. S. 1976. The Promise of the Coming Dark Age. San Francisco: W. H.
Freeman and Company.
Tony Harper
107
Mathematical Appendix
The Derivation of T/Cmax = (Cmaxγ– 1 – 1)/(γ – 1).
From Eq. 2, Cmaxγ – Cmax – (γ – 1)T = 0, it can be seen that Cmaxγ – Cmax =
= (γ – 1)T, and that T = (Cmaxγ – Cmax)/(γ – 1). If Cmax is factored out of the numerator and both sides of the equation are divided by Cmax, this will yield:
T/Cmax = (Cmaxγ– 1 – 1)/(γ – 1).
The Derivation of [e5.9 – .0078t – 1]/[γ e5.9 – .0078t – Cmaxγ – 1] = 1.
The linear regressions of lnT and lnCmax yield respectively, lnT = 16.1681 –
– .0826t and lnCmax = 10.2681 – .0904t. Consequently, lnT – lnCmax = 5.9 –
– .0078t, and, further, T/Cmax = e5.9 – .0078t. As a result e5.9 – .0078t = [Cmaxγ – 1 – 1]/
[γ – 1] and [γ – 1]e5.9 – .0078t = [Cmaxγ – 1 – 1]. Rearrangement gives: γ e5.9 – .0078t–
– Cmaxγ – 1 = e5.9 – .0078t – 1, and dividing both sides by γ e5.9 – .0078t – Cmaxγ – 1
yields: [e5.9 – .0078t – 1]/[γ e5.9 – .0078t – Cmaxγ – 1] = 1.The expected value of this
ratio is clearly 1.0, and the observed value at each 100 year increment can be
calculated using appropriate values substituted for each variable of the ratio.
3
Another, Simpler Look:
Was Wealth Really Determined
in 8000 BCE, 1000 BCE, 0 CE,
or Even 1500 CE?
William R. Thompson and Kentaro Sakuwa
Abstract
Olsson and Hibbs (2005) and Comin, Easterly, and Gong (2010) make persuasive theoretical and empirical cases for the persistence of early biogeographical and technological advantages in predicting the distribution of national economic wealth. However, these results are challenged with an examination of
sixteen observations on economic complexity, GDP per capita, and city size
spanning as much as ten millennia and eight to eleven regions. The regional
complexity / wealth hierarchies are relatively stable only for finite intervals.
Early advantages, thus, have some persistence but do not linger indefinitely.
The rich do not always get richer or even stay rich, and the poor sometimes
improve their standings in the world pecking order dramatically. Early advantages are important but need to be balanced with the periodic potential for
overriding them.
Keywords: economic growth, early advantage, biogeographical advantage,
technological advantage, city size, societal complexity.
Introduction
We live in an era fraught with the potential for tectonic changes in relative economic positioning. The United States, long the leader in technological innovation and economic growth, is combating symptoms of relative decline and
an increasingly visible challenge from China, a state emerging rapidly from
a long period of relative underdevelopment. Japan, thought to be the most likely economic challenger to the United States less than two decades ago, is mired
in relative stagnant growth and facing a serious population aging problem. Russia, once a challenger to the United States, experienced an economic meltdown
when the Soviet Union fragmented. But Russia is re-emerging as an economic
competitor of sorts by exploiting the sale of raw materials. A state adjacent to
China, India, equally populous, seeks to catch up and surpass China. The region
that the United States once overtook, Western Europe, remains affluent but is
History & Mathematics: Trends and Cycles 2014 108–135
108
William R. Thompson and Kentaro Sakuwa
109
confronted currently with the prospect of the world's one successful regional
integration experiment breaking up. Throughout all of these potential changes
in the making, a large number of states remain poor and have few prospects for
any change in the near, or perhaps distant, future.
It is hardly surprising, then, that the question of how economies grow fast
and slow and why some economies get ahead of others while others fall back is
popular.1 Many of the arguments that have surfaced focus on more recent developments and yet many of these remain untested empirically. Olsson and
Hibbs (2005) and Comin, Easterly, and Gong (2010) are remarkable exceptions
to these generalizations. Not only do their studies encompass thousands of
years, they go to some lengths to test their perspective on long-term economic
growth. Olsson and Hibbs find that Diamond's (1997) argument, predicated on
the technological advantages associated with diffusion possibilities linked to
continental axes and the distribution of edible plants and large mammals prior
to the advent of agriculture, predict well to current national incomes.
The strong implication is that the world's distribution of income was determined even before the advent of agriculture. Comin, Easterly, and Gong find
that technological adoption in 1500 CE predicts well to national income in the
current period and that knowing about the distribution of technology in
1000 BCE and 0 CE predict respectively to technological distributions in 0 CE
and 1500 CE. They conclude that the world's distribution of technology has
been quite persistent. Wealth distributions, to the extent that they are predicated
on technological attainments, were not strictly determined in 1000 BCE but the
extent of path dependency is quite strong. Areas that have been technologically
ahead in the past tend to continue to be technologically ahead in the present.
Ambitious and largely unprecedented analyses, however, are likely to be
characterized by various empirical and design problems. Attempting to capture
changes in economic development over thousands of years is never easy or
straightforward. Assuming then that there will always be some problems, the
question is whether the problems appear to strongly influence the outcome. In
this case, the answer is that assumptions made in the research design appear to
have biased the conclusions significantly. We do not dispute Olsson and Hibbs
(2005) and Comin et al.'s (2010) specific findings as much as what we should
make of them. If the central question is whether technological differences persist over long periods and the answer lies in the affirmative, there are at least
several major caveats that need to be advanced based on the long-term analysis
of uneven economic development. By more than tripling the length of the
Comin et al.'s examination (from three millennia to ten millennia), expanding
the number of observations (to sixteen across the ten millennia), changing the
unit of analysis (from contemporary states to regions), and simplifying the indi1
In the past decade or so, Diamond (1997), Wong (1997), Frank (1998), Landes (1998), Pomeranz
(2000), Maddison (2001), Clark (2007), Findlay and O'Rourke (2007), Morris (2010, 2013), Galor (2011), Parthasarathi (2011), Rosenthal and Wong (2011), among others, have appeared.
110
Was Wealth Really Determined?
cators relied upon (substituting a different index of complexity for prehistorical
times and gross domestic product per capita and city size for historical times),
a more comprehensive picture of long-term development emerges. The persistence of earlier technological advantages does not disappear. On the contrary, it
is quite evident. But so too are major departures from persistence. We should
not emphasize one dimension over the other. Instead, we should strive to integrate both dimensions in understanding long-term changes.
The Persistence Analyses
Our problems with the two earlier studies differ by study. The Olsson and
Hibbs (2005) study develops, elaborates, and operationalizes Diamond's (1997)
argument well.2 Fig. 1 summarizes their theory and empirical model. Favorable
climate, larger continental size, and an east-west axis that permits diffusion of
seeds, animals, and technology increases the availability of plants and animals
that are suitable for agriculture. The greater is the availability of plants and animals, the greater is the opportunity to experiment with agrarian techniques.
Agrarian and industrial revolutions should occur earlier in such areas than in
less favored regions. The earlier is the timing of agrarian and industrial revolutions, the greater should be the contemporary level of income per capita.
Fig. 1. Logical structure of Olsson and Hibbs' theory (2005: 928)
2
The analyses of Chanda and Putterman (2005, 2007), Putterman (2008), and Bleaney and Dimico
(2011) reinforce Olsson and Hibbs' finding that an earlier start on agriculture is beneficial to income levels much later.
William R. Thompson and Kentaro Sakuwa
111
One can balk at various aspects of the Diamond argument or not but our main
criticism of the Olsson and Hibbs examination is that the tested argument relies
on one set of observations.3 Areas favored by geographical size, climate, continental axes that do not block pan-continental diffusion, more large mammals
that can be domesticated, and more plants that can be cultivated and consumed
will develop earlier. This argument implies that Eurasia will be favored over
Africa, Australia, and the Americas – a quite reasonable starting point for economic growth analyses.4 It helps to explain, for instance and with some substantial help from the spread of European diseases to the Americas, why Spanish conquistadors could defeat the Aztecs and Incas.5 It does not really specify
why different parts of Eurasia have fared much differently on economic development criteria – a topic on which Diamond (1997) waffles.6 Nor does it explain why Eurasia writ large has not linearly developed faster than Africa, Australia, and the Americas. Thus, if we use observations based on ten thousand
years ago to predict to the present, we skip much of what happened (or may
have happened) in between.7
The Comin et al.'s analysis (2010) looks at some of the things that happened in between the advent of agriculture and the contemporary period but
there are at least six problematic sources of bias. The first problem is ignored
almost entirely by the 2010 analysis. From the most macroscopic vantage point
conceivable, economic development was first manifested most spectacularly in
Sumer, and, later, Egypt and the eastern Mediterranean. The structural axis of
Eurasian growth then was transformed into a ‘dumb-bell’ shape with the Mediterranean on one end and China on the other. Both dumb-bell ends went into
3
See Acemoglu and Johnson (2012: 51–56), among others, for a critique of the Diamond argument.
Olsson and Paik (2012) develop and test a very interesting argument about the timing of agriculture that substantially modifies the idea of early biogeographical advantages. Basically, the idea is
that the earliest adopters of agriculture tended also to adopt highly autocratic political systems
which subsequently led to poor or poorer than might otherwise have been anticipated economic
performance. Later adopters tended to develop different, less extractive, institutions and, therefore, enjoyed better economic development.
4
See Turchin and Hall (2006) for an extension of the argument to imperial development.
5
There is no question that Eurasia is the largest populated continent and that it encompasses more
plants and large mammals that can be used for economic development purposes. Unlike the northsouth alignment of Americas and Africa with major, mid-continental blockages to diffusion, it is
not only possible for plants, animals, and technological innovations in one end of Eurasia to travel
to the other; it is difficult to account for Eurasian development without tracking the diffusions.
Parts of Eurasia certainly experienced earlier agricultural and industrial revolutions than elsewhere.
6
At one point, Diamond (1997) suggests that any part of Eurasia might have seized the development lead but later suggests that western Eurasia was favored over eastern Eurasia.
7
Actually, Olsson and Hibbs (2005) say that their initial observations are based on 11,000 BCE
because it is around this time that unequal levels of development began to emerge due to population migrations that had started in Africa some 70,000 years earlier and climate change that melted glaciers thereby making agriculture possible in the northern hemisphere.
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Was Wealth Really Determined?
decline around the same time but China re-emerged more strongly in the
Sui/T'ang/Song era (roughly 8th–13th centuries CE) than did the Mediterranean,
although the dumb-bell structure was initially rebuilt in terms of exchanges
between the now-Islamic Middle East and China. China then stagnated, thanks
in large part to the Mongol takeover, but its economic innovations were diffused across Eurasia to Europe thereby establishing a foundation for subsequent
industrial revolutions that catapulted first Britain and then other parts of Europe
into the economic lead after the 18th century CE. More recently, a few areas
settled by British and European migrants in large numbers have moved ahead
of Europe in terms of technological development and economic wealth.
Most of this story makes some tangential appearance in the Comin et al.
discussion but it does not figure very prominently in the analysis or conclusions. If technology advantages are persistent, why did the Persian Gulf area
(Sumer) not maintain its lead? Why did the Rome-Han exchange between the
two most advanced parts of the world collapse? Why did China surge ahead
only to stagnate in the same period Europe was catching up and forging ahead?
Why was Europe the initial beneficiary of industrial revolution but later
eclipsed by the United States? Put differently, why did some European colonies
out-perform their one-time metropoles? We have various answers for these
questions, although many remain contested areas of inquiry. Comin et al.
(2010) concentrate primarily on the role of European migration in the post1500 period which helps to answer one of the questions (the near-contemporary
and highly selective, colonial catch up with the metropoles) but do not really
address the earlier historical questions.
The problem here is that the European migration to less populated North
America and Australia / New Zealand was a fairly unique phenomenon.8 We
know a fair amount about how and why a few of the colonies attracted a disproportionate share of migrating labor and how that was then parlayed into disproportionate shares of international capital investment and global trade integration, in conjunction with optimal locations (in terms of climate and oceans)
and natural endowments.9 But while large-scale migrations did occur in earlier
periods, they cannot explain the decline of Sumer, Egypt, Rome, Han China in
ancient history or the fall of various empires in medieval history.10
8
Perhaps the main exceptions are the ‘out of Africa’ movements 50 to 100, 000 years ago in which
our species colonized the world and Greek and Phoenician colonization in the first millennium
BCE.
9
See, for instance, the analyses reported in Acemoglu, Johnson, and Robinson (2001, 2002); Sachs,
Mellinger, and Gallup (2001); and Krieckhaus (2006).
10
In some of these cases, migrations of ‘barbarian’ tribes are part of the decline explanations. However, it is easier to argue that imperial decline or weaknesses attracted the migrations and that because of the decline, the migrations were more difficult to manage than it is to contend that migrations were either the or a principal cause of the decline. Yet many of the countless tribal migrations did not involve individuals with technological skills moving into low-tech environments.
William R. Thompson and Kentaro Sakuwa
113
The second bias is that the analysis hinges on comparing observations at
only three time points – 1000 BCE, 0, and 1500 CE. If the analysis is to be restricted to three observations, analysts need to be careful that the selected observations are relatively neutral in their implications for economic growth assessments. The three chosen by Comin et al. are not exactly neutral. Towards
the end of the second millennium BCE, the most economically advanced centers in the world were located in the eastern Mediterranean littoral and China.
The initial observation date, 1000 BCE, encompasses a period of ‘dark age’
depression in the Mediterranean area that had begun around 1200 BCE and
lasted roughly through 800 BCE. The depression in economic and population
growth had been brought on by a combination of extensive drought, massive
migrations, urban destruction, and considerable conflict. China was not in much
better shape. The Western Chou regime in this time period was retreating from
tribal pressures in the west, becoming the Eastern Chou regime in the process,
and initiating a period of fragmentation that led to the Warring States era in the
second half of the first millennium BCE. The year 0 is a bit of a chronological
contrivance but, in marked contrast to 1000 BCE, it captures the high points of
the Roman and Han empires, ostensibly the economic growth leaders of the
ancient world. The third observation point, 1500 CE, of course, passes over
a millennium and a half of interesting developments vis-à-vis relative economic
growth but it also marks more or less the starting point of European oceanic
voyaging. If one of the main indicators of technological growth for this time
period is ships with guns and only one small corner of the world has ships with
guns in 1500, the observation point is hardly neutral.11 For example, if the same
indicator had been used in, say, 1400 CE, merely a hundred years earlier, only
China then possessed ships with guns. Europeans were still limited to firing
arrows from their ships at that time.
A third problem is associated with the unit of analysis. Comin et al. (2010)
carry out most of their analyses examining 104–130 current states and backdatIt was often the other way around although tribal warriors did sometimes possess superior weaponry technology – as illustrated by the Hyksos early second millennium BCE movement into
Egypt with chariots and stronger bows. However, exceptions on the order of the Phoenician
founding of Carthage certainly occurred.
11
One of the Comin et al. (2010) technology indicators for 1500 is ships with 180+ guns. It seems
highly unlikely that any ship in the world carried (or could carry without sinking) 180 guns or
cannon as early as 1500. At this time, Portuguese ships were armed with artillery that more closely resembled mortars more than cannons but the naos were fairly small and only a few pieces of
artillery could be carried on board ship. On the other hand, if the opposition possessed no maritime artillery, as in the Indian Ocean, a few guns often (but not always) sufficed. Henry VIII of
England did have several very large ships constructed in the second decade of the 16th century
and at least one (The Great Harry) carried 184 guns. But most of these guns were too small to do
damage to ships and were used to repel boarders. The ships proved hard to sail, at least one capsized in part due to the heavy guns carried, and by the 1530s, the surviving ships were carrying
fewer guns. See Hogg and Batchelor (1978: 11) and Archer et al. (2002: 262–263).
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Was Wealth Really Determined?
ing their attributes based on geographic location. The awkwardness here is that
earlier observations are based to some extent on prominent empires. All current
states that were once located in the Roman Empire, for instance, receive the
same score in the year 0. That means Libya, Syria, Romania, France, and the
United Kingdom are scored exactly the same. More generally, empires tended
to cover large territories in which some areas were more economically advanced than were others. The Comin et al.'s approach treats imperial peripheries as equivalent to imperial centers. It also implies that imperial technologies
persisted. In some senses, they did as exemplified by roads and canals that were
modified over the years. In other respects, however, the technologies survive
only in the form of scattered ruins that attract curious tourists.
Relying on the Peregrine (2003) Atlas of Cultural Evolution source for
coding technology creates a fourth problem.12 The Atlas of Cultural Evolution
(ACE), a database that provides systematic information on societal complexity
in all prehistorical areas, is indispensable for places less well known. Yet once
an area moves from prehistorical to historical, ACE ceases to code its complexity levels. If one begins an analysis in 1000 BCE, a respectable part of the ancient world has already moved beyond the ACE codings which were designed
mainly for earlier, less developed, pre-written history circumstances. Using
ACE in the year 0 is even more difficult to defend.
All efforts to enumerate technology run into the problem of filtering what
is included and excluded. For instance, more recent efforts to measure the pace
of change in industrial innovation, on occasion, have given equal weight to ball
point pens as they do to jet engines.13 Ball point pens and jet engines do not
figure in the Comin et al.'s study but they do abandon ACE for the 1500 CE
observation and apply a 24 item scale to measure technological development.
However, a fifth source of problems concerns the fact that eight of the twentyfour indicators are military in nature. They include standing army, cavalry, firearms, muskets, field artillery, warfare capable ships, heavy naval guns, and
ships with 180+ guns. Are these indicators of technology or military power? If
the latter, the more straightforward interpretation, the explanation has been altered substantially. Is it military technology that predicts to contemporary economic wealth? It is not clear, moreover, why some things are double- or triplecounted (two measures of firearms and three measures of naval capability for
instance).14 Another three indicators in the transportation category capture ships
12
13
14
ACE is based on the nine-volume Encyclopedia of Prehistory (Peregrine and Embers 2001).
See, for instance, the list of innovations examined in van Duijn (1983: 178).
While there is no reason to spend a great deal of time on a single indicator, the technological
significance of cavalry, at least on or after 1500, is questionable. At one point, the adoption of
cavalry and, later, the stirrup, reflected significant changes in military technology but in places
that had access to horses these changes long preceded 1500 CE. Central Eurasian nomads led the
way but did not necessarily create standing cavalries. Assyrians began to emulate their practices
William R. Thompson and Kentaro Sakuwa
115
capable of crossing the Atlantic, Pacific, and Indian Oceans respectively which
means one-fourth of the indicators privilege states with commercial maritime
capability. In 1500, there was very little in the way of state navies (Modelski
and Thompson 1988: 53). Only a few states such as Venice, Portugal, and
England maintained state fleets. Commercial vessels were more likely to be
pressed into military service when necessary. One can certainly imagine rationales for giving maritime capability heavy weight in technology measurement but no explicit argument is advanced. Similarly, mixing military with
non-military technologies can be viewed as problematic if there exist ongoing
arguments about whether it was military technology per se that enabled the
Europeans to dominate what used to be called the Third World.15 At the same
time, all sources agree that the European military advantage in 1500 was very
rudimentary.
Finally, there are 14 tables in Comin et al.'s work (2010), most of which
are devoted to regression analysis involving data pertinent to the three observation points. Perhaps not surprisingly, somewhat different outcomes are associated with each of the tables which complicate summarizing accurately and simply the bottom line of the empirical effort. But putting that issue aside, two tables focusing on descriptive statistics probably deserve more attention than they
receive. Table 1 synthesizes the core information of the two tables on average
scores for technology adoption in selected continents and civilizations.
Table 1. Average overall technology adoption by selected continents
and civilizations
Continent
Europe
W. Europe
Africa
Asia
China
Indian
Arab
America
Oceania
1000 BCE
.66
.65
.36
.58
.90
.67
.95
.24
.20
0 CE
.88
.96
.77
.88
1.00
.90
1.00
.33
.17
1500 CE
.86
.94
.32
.66
.88
.70
.70
.14
.12
Current
.63
.71
.31
.41
.33
.31
.43
.47
.73
Source: This table combines and simplifies tables 4 (on continents) and 5 (on civilizations) in Comin et al. (2010: 77).
early in the first millennium BCE, as did the Chinese some 600 years later. After 1500, the maintenance of large cavalry units in Eurasia were more likely to signify aristocratic and agrarian constraints on technological development. Thus, as a 1500 CE indicator, it really only serves to differentiate places that had horses and those that did not (the Americas, the southern half of Africa,
and Australia).
15
Compare Parker (1988) and Thompson (1999) on this question.
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Was Wealth Really Determined?
Table 1 demonstrates a simple pattern. All areas indicated a peak in the
year 1 and then decline. The Europeans decline least. The Americans and Oceanians make a comeback in the current time period while Africans and Asians
are showing as continuing to decline. Whether or not this pattern makes historical sense, it suggests that there are very real limits to the technological persistence argument. If the data are ‘right’, we need to explain what happened to
China, India, and the Arabs, all of whom were technological leaders at one time
and then far from it at other, later times, especially after 1500. Table 1 suggests
that the question should not be one of asking whether technological advantages
persist in general, but why are they sometimes lost and sometimes gained.
A Different Approach and Indices
We prefer to follow up on the tantalizing simplifications of Table 1. We first
recreate a Diamond/Olsson-Hibbs index for a very early biogeographical advantage. Using ACE data on development complexity for four observations:
4000 BCE, 3000 BCE, 2000 BCE and 1000 BCE, we then switch to Maddison's data on gross domestic product (GDP) per capita which begins in year
1 CE and continues through 1000 CE, 1500 CE, 1600 CE, 1700 CE, 1820 CE,
1870 CE, 1913 CE, 1950 CE, 1973 CE, and 2003 CE. Sixteen observations
should be better than one or three. Rather than attempt to create a different
technology scale for each observation, we rely primarily on summary biogeographical and ACE indexes for the BCE period and a standardized index of
economic development for the CE era.
Instead of looking at current countries, we use calculations for 8 ‘regions’
(Western Europe, Eastern Europe, the USSR, Asia, Japan, Latin America, Africa, and the Western Offshoots) that remain the same from 8000 BCE to
2003 CE. There is no claim made here that either regions in general or these
particular regional identifications are ideal units of analysis. Maddison's aggregations are more than a bit idiosyncratic. Yet using his older data means using
his choice of aggregations because dis-aggregated numbers are not made available. They do offer, however, several advantages. Regions could be said to
more closely approximate ancient empires than do countries, although there is
distortion either way.16 Current regions do at least resemble ancient regions
with little distortion. Maddison (2007: 382) makes regional GDP per capita
data available back to the year 1. One can certainly argue that the data are fabrications but an effort has been made to justify and standardize them as meaningful and systematic fabrications. Moreover, Maddison (1995: 21) raised
a similar issue to the present concern by stressing that the regional hierarchy of
16
Switching from states to regions does not eliminate the center-periphery problem but there does
seem to be some tendency for regions to become more homogenous over time in terms of existing
levels of economic development.
William R. Thompson and Kentaro Sakuwa
117
economic growth performance changed very little since 1820. The regions that
were ahead in 1820 have remained ahead. Similarly, the regions in the hierarchical cellar were still at the bottom nearly 200 years later. This affords us with
the opportunity to not only re-address Comin et al.'s persistence question
with Maddison's data but to also extend Maddison's version of the persistence
question backwards in time to 8000 BCE. If the regional hierarchy has been stable for the past two centuries, can we say the same for the past ten millennia?
If the hierarchy is more stable in the ‘short-term’ (i.e., centuries) than it is in the
long-term (millennia), what does that tell us about technological persistence?
One disadvantage of the Maddisonian regional approach is that it does distort ancient history in the sense that the regions with which we are familiar today, and the ones Maddison relied on, were regions before but they were not as
important as regions as they have since become. To give full justice to ancient
history, we would prefer data on Sumer to the Middle East (also not in Maddison's geographical lexicon), Indus to India, or China to Asia.17 Maddison's regions become more awkward and heterogeneous the farther back in time we go
but there is little choice once a decision has been made to utilize Maddison's
GDP per capita constructions and wed them with ACE complexity scores in
order to encompass ten millennia.18
Switching to GDP per capita also obscures the Comin et al.'s emphasis
on technology somewhat.19 A more straightforward measure of technology
across time would be preferable but hard to imagine. With sixteen observations across ten millennia, one would have to create a new technological complexity scale for each observation. While it might be possible to do that, it seems
preferable to simplify the task by relying on ACE indices for the BCE period and
Maddison's index for the CE era. Relying on GDP per capita as a crude proxy for
technological complexity is certainly not uncommon. Yet these indicator simplifications only suggest that our interpretation of the problem will not be the last
word on the subject, any more than was Olsson and Hibbs' (2005) or Comin
et al.'s (2010).20
At the same time, we can examine this question of path dependency in
an entirely different way and one that avoids the problems associated with using Maddison's data. If Maddison's regions are thought to be idiosyncratic and
17
Maddison seems to have preferred to ignore the Middle East as much as possible in his data
collection efforts. Presumably, that tendency reflects a desire to evade the problems associated
with small, oil rich states and, perhaps, poor data for the poorer members of that region. To the
extent that he dealt with this region, it is usually considered as a western extension of Asia. He
classifies Egypt as an African state.
18
That is to say that Maddison's older data are not available independent of his regional aggregations.
19
Yet consider Comin et al.'s (2010).
20
However, see as well the very strong correlations we find between regional GDP per capita and
regional technological standings and report in the Appendix.
118
Was Wealth Really Determined?
highly heterogeneous and his older GDP per capita estimates are difficult to
verify, we can avoid these liabilities by examining city size data regionally aggregated in more discrete geographical aggregations. City size data (Chandler
1987 and Modelski 2003) are available back to the beginning of cities and the
assertion that regions with more large cities are/were wealthier and more technologically advanced than regions with fewer large cities seems easy to advance. Networks of cities, after all, have provided the basic infrastructure of the
world economy for millennia.21 All large cities do not work exactly the same.
Some have served as agrarian hubs while others represent coastal, commercial
nodes. But economic development historically has been manifested in the urbanized centers of political-economic wealth and power ever since the rise of
Sumer and extending to the Pax Britannica and Americana, centered on London
and New York, respectively. The only caveat is that this argument can no longer be sustained in the contemporary era due to the emergence of very large third
world cities that confuse the issue of what large cities currently represent.
To operationalize this alternative, we isolate the 25 largest cities between
3700 BCE and 1950 CE at 23 points of observation.22 Each city is assigned to
one of eleven regions; Mesopotamia/Iran, Southern Mediterranean (extending
from Constantinople to Morocco), Northern Mediterranean / Western Europe
(initially extending from Greece to Spain and later farther north), South Asia
(primarily the areas that became Pakistan and India), Central Asia (encompassing states now designated as ‘stans’ except for Pakistan), Eastern Europe (east
of Berlin and Vienna and including what became Russia), Southeast Asia (essentially the areas that became Burma/Myanmar to Vietnam and south), East
Asia (encompassing China, Korea, and Japan), North America (basically the
United States), Central America (basically Mexico), and South America (the
continent south of what is now Panama).23
Once a city is assigned to a region, its population is aggregated with other
cities in the same region.24 Each region's relative share of the total population
of the top twenty-five cities then serves as an indicator of its relative regional
standing. Initially, the Mesopotamian/Iranian region monopolizes the large cit21
On this subject, see Chase-Dunn and Willard (1994); Chase-Dunn, Manning, and Hall (2000);
Chase-Dunn and Manning (2002); Modelski (2003); and Chase-Dunn, Hall and Turchin (2007).
22
Choosing to look only at the top 25 is arbitrary but in older periods, cities tend to become fairly
small as one moves beyond the first 25. Restricting our focus to the top 25 thus reduces some of
the noise that might be introduced by casting the net farther down the size line. It also helps that
Chandler (1987) provides more locational information for the first 25. However, Chandler identifies sources of imperial control whereas we are focused on geographical location.
23
There are a small number of large cities that do not fit in any of these regions (for instance, a few
cities rise to make the top twenty-five threshold in the Arabian Peninsula) but their relative prominence tends to be too short-lived to expand the number of regions.
24
Only one city changes its regional location. We code Constantinople as Northern Mediterranean
prior to the arrival of the Ottoman Turks and Southern Mediterranean thereafter.
William R. Thompson and Kentaro Sakuwa
119
ies but urbanization gradually diffuses to the east and west. Some regions, such
as East Asia, fluctuate in significance while others attain significance only early
or late. Our question is whether knowing something about the relative standing
of a region at one point in time is very useful in predicting its standing at successive points in time.
Creating a biogeographical index within the context of Maddison's regions
requires some adjustments. To be faithful to the Diamond/Olsson and Hibbs
argument, the maximal set of ingredients for such an index should include observations for climate, continental size, continental axis direction, numbers of
large mammals and plants that were domesticated, and the onset of agriculture.
But if we are differentiating within continents (Maddison has five Eurasian
regions: Western Europe, Eastern Europe, the former Soviet Union, Asia, and
Japan), continental size is no longer an issue. Climate is another casualty because most regions in our study are characterized by very different climate
zones.25
Differentiating east-west axes (Eurasia) from north-south axes (Americas,
Africa, and Australia) is not difficult.26 Olsson and Hibbs (2005) provide information on plants and large mammals for most of the regions, as indicated in
Table 2. Dates on the timing of agricultural revolutions in specific areas can be
linked to regional locations without too much distortion. The dates in parentheses are estimates based on discussion of the spread of agriculture to areas in
which it did not originate (Smith 1995; Imamura 1996; Thomas 1996; Frachetti
et al. 2010). To create a single biogeographical index, the binary axis information is scored as 5 points if a region is in the vicinity of the Eurasian east-west
axis and 0 points if the region is not located within Eurasia. The distribution of
plants and mammals is trichotomized as high (Western and Eastern Europe),
medium (Asia and the former Soviet Union), and low (all other regions). High
scores were assigned 10 points, the medium scores received 6 points, and low
scores were turned into 2 points.27 For the agricultural revolution timing,
25
Another problem is that some regions have experienced climate changes over the last ten millennia. See, e.g., Burroughs (2005).
26
A reviewer, contrary to Diamond, has argued that Africa has a long east-west axis stretching
across the Sahel to the Horn. We do not find this axis very compelling because of the difficulties
in crossing (we know French soldiers had problems making the crossing to set up the 1898 Fashoda crisis) and the limited historical traffic actually traversing it (at best, presumably, small
groups of desert nomads). More important, large and urbanized population centers at both ends,
which may be the most critical factor in differentiating between east-west and north-south interactions even though it goes beyond the Diamond argument, are missing in the African case. Eurasia's east-west axis was not all that easy to traverse but traders at least had strong profit incentives to make the effort. Just how important people were as carriers to the diffusion of seeds and
animals across Eurasia is not entirely clear. Nonetheless, we will check our results to see how
critical the presence or absence of an African east-west axis is to the outcome.
27
We did not give equal weight to the continental axis and plants/mammals indicators because
Eurasia already scores relatively highly on the distribution of domesticated flora and fauna. In
120
Was Wealth Really Determined?
the regional timing date was first subtracted from the Near Eastern timing of
8000 BCE and then divided by 1000.28 An aggregate regional score is then constructed by simply adding the axis, plant-mammal, and agricultural revolution
scores – reported in the last column of Table 2.
The biogeographical, rank order outcome puts Eastern Europe (13), Western Europe (12), and Asia (10.5) in the early lead, with Eastern Europe in the
first rank largely because agriculture diffused there from the Near East before it
reached Western Europe.
Table 2. Constructing a biogeographical index
Region
Western Europe
EW Axis
Direction
Yes
33
Large
Mammals
9
Plants
Agricultural
Revolution
(6000–4000
BCE)
2500 BCE
Score
12.0
Western Offshoots
Eastern Europe
Former
Soviet Union
Latin America
No
2–4
0
–3.5
Yes
Yes
33
9
(6000 BCE)
(2200 BCE)
13.0
5.2
No
2–5
0–1
–2.5
Africa
Asia
No
Yes
4
6
0
7
Japan
Yes
2600–2500
BCE
2000 BCE
5750–6500
BCE
(2500–2400
BCE)
–2.0
10.5
–0.55
Note: Cells left blank by missing data required estimation.
The former Soviet Union (5.2), part European and part Asian, falls in the middle of the regional pack. Lowest ranked are Japan (–0.55), Africa (–2.0), and
Latin America (–2.5). The outcome certainly mirrors Diamond's (1997) argument about the advantages of Eurasia over the rest of the world.
To measure complexity in the fourth, third, second and first millennia
BCE, we employed the ACE aggregate complexity score for some 289 prehistorical groups which were first assigned to one of Maddison's regions and then
averaged.29 The complexity score simply adds the sub-scores for 10 indicators:
some respects, the irony is that the super-region or continent that experienced the most diffusion
needed it least. The exception to this observation is the much later diffusion of industrial technology from China to Europe in the first half of the second millennium CE. On this point, see,
among a number of others, Modelski and Thompson (1996).
28
In cases in which the timing is indicated as falling within a range of years, the middle point between the high and low timing dates is used for this calculation.
29
Ideally, we might have weighted the averaging process by the size of the group but this information, unsurprisingly, is not available.
William R. Thompson and Kentaro Sakuwa
121
writing, residence, agriculture, urbanization, technology, transportation, money,
population density, political integration, and societal stratification. The scales
for each indicator are reported in Table 3 to give a better sense of what is involved in this computation.
One of the less expected byproducts of this analysis is that the western end
of Eurasia is portrayed as relatively rich in biogeographical and societal complexity terms. Europe is often thought of as a backwater that suddenly became
rich and prosperous only in the last half millennium. A longer term perspective
suggests otherwise. Keeping in mind that these regional aggregations are heterogeneous and the scores are averages across multiple groups residing within
their boundaries, Europe comes across as fairly consistent in its rankings across
ten millennia.30 The temporary exception is the long period of decline after the
fall of the Western Roman Empire.
Table 3. The ACE complexity score components
1
Indicator
Writing and Records
2
3
Residence Fixity
Agriculture
4
6
Urbanization
(largest settlement)
Technological
Specialization
Land Transport
7
Money
8
Population Density
9
Political Integration
10
Societal Stratification
5
Scale
1 = none, 2 = mnemonic or non-written records,
3 = true writing
1 = nomadic, 2 = seminomadic, 3 = sedentary
1 = none, 2 = 10 % or more but secondary,
3 = primary
1 = fewer than 100 persons, 2 = 100–399 persons,
3 = 400+ persons
1 = none, 2 = pottery, 3 = metalwork (alloys, forging,
casting)
1 = human only, 2 = pack or draft animals,
3 = vehicles
1 = none, 2 = domestically usable articles,
3 = currency
1 = less than 1 person per square mile, 2 = 1–25 persons per square mile, 3 = 26+ persons per square mile
1 = autonomous local communities, 2 = 1 or 2 levels
above local communities, 3 = 3 or more levels above
community
1= egalitarian, 2 = 2 social classes, 3 = 3 or more
classes or castes
The main results of our multiple observation approach to the long-term persistence question are reported in Tables 4 through 8.31 Table 4 reports the actual
biogeographical, ACE and average GDP per capita scores for the eight Maddi30
Olsson and Paik's (2012) argument and findings, for example, suggest differentiating Southern
from Northern Europe in terms of the timing of adopting agriculture and its implications.
31
Space considerations preclude reporting the full correlation matrices. Thus, only significant correlations are shown. The full matrices are available from the authors on request.
122
Was Wealth Really Determined?
sonian regions. Biogeographical advantage puts Western Europe, Eastern Europe, and East Asia in the earliest lead. In 4000 BCE, all five Eurasian regions
are scored as about equally complex, with Japan lagging slightly behind. In the
next several millennia, the European region scores steadily improve. The two
Asian regions fluctuate and fall behind both their European and South American / African counterparts. The other parts of the world register consistent gains
in average complexity, with North America and Australia / New Zealand
(the Western Offshoots) showing only marginal improvements.
Table 4. Biogeographical advantage / complexity / GDP per capita
averages (dates BCE are in italics)
Date
8000
4000
3000
2000
1000
1
1000
1500
1600
1700
1820
1870
1913
1950
1973
2003
Western
Europe
12.0
18.5
22.3
27.8
50.0
576
427
771
889
997
1202
1960
3457
4578
11417
19912
Eastern
Europe
11.1
18.5
22.3
27.8
50.0
412
400
496
548
606
683
937
1695
2111
4988
6476
Former
USSR
5.2
18.5
22.3
27.8
50.0
400
400
499
552
610
688
993
1488
2841
6059
5397
Western
Offshoots
–3.5
11.4
12.0
12.9
13.0
400
400
400
400
476
1202
2419
5233
9668
16179
28039
Latin
America
–2.5
13.0
16.2
17.8
19.4
400
400
416
438
527
691
676
1493
2503
4513
5786
Asia
Japan
10.5
18.3
19.6
20.1
15.5
457
466
572
576
572
577
548
658
639
1225
3842
–0.6
17.1
16.1
17.3
13.0
400
425
500
520
570
669
737
1387
1921
11434
21218
Africa
–2.0
13.7
14.1
15.7
20.3
472
425
414
422
421
420
500
637
890
1410
1549
Switching to the GDP per capita measure indicates a different story that suggests that ACE complexity scores probably cannot necessarily be translated
directly into GDP per capita terms. On the other hand, 1000 years have passed
between 1000 BCE and 1 CE. In the West, the Greek city state complex had
given way to the Roman Empire. In the East, Chinese fragmentation had been
reversed by the rise of the Qin/Han Dynasties. In the year 1, accordingly, Western Europe and Asia are in the lead, Africa is third, and the other regions are
rated as roughly equal. In 1000 CE, Asia retains its former lead, followed by
Western Europe, Japan and Africa (all three with near-identical averages), with
all other regions scoring at the 1 year minimum.
By 1500 CE, however, Maddison's data have Western Europe once more in
the lead with Asia a distant second. The USSR, Japan, and Eastern Europe fall
in the middle of the regional hierarchy. Latin America demonstrates some
William R. Thompson and Kentaro Sakuwa
123
slight gain while Africa manifests steady decline. North America and Australia's position and wealth/technology level is shown as remaining unchanged for
1500 years. Then the scores change dramatically. The western European GDP
per capita almost doubles by 1820. The Western Offshoots (North America and
Australia / New Zealand) are not far behind. Eastern Europe, the USSR, and
Latin America have made some progress with development levels that are
about half those of the leaders. Average 1820 Asian and African GDP per capita are little changed from their 1500 levels. By the end of the 20th century, the
Western Offshoots, Western Europe, and Japan have created strong leads. Latin
America and the USSR are in the middle of the hierarchy but considerably behind the leaders. Eastern Europe, Asia, and Africa occupy the bottom of the
regional hierarchy.
Table 5 reports the same data in regional rank order. The long-term outcome encompasses several significant shifts in relative standing. Western Europe is an early leader but falters in the Medieval Era before rising to the lead
after the industrial revolution – a lead it does not maintain beyond the 19th century. The Western Offshoots remain in the technology/growth cellar throughout
most of the ten millennia period studied before seizing the lead in the last century. Asia begins in the middle, rises to the lead in the first millennium CE, and
then falls back toward the bottom. Japan's position oscillates – initially middle,
then falling back to low, then to high, back to the middle, and then back to
high. Eastern Europe and the USSR begin relatively high and decline to the
middle. Latin America starts low and never exceeds a middle ranking. Africa
tends to stay near the bottom except in the first millennium CE.
Scanning rank orders is one thing. We can improve on this form of data inspection by calculating Spearman Rank Order coefficients from observation to
observation, as is done in Tables 6 and 7. Table 6 reports significant coefficients without any modification of the rank orders. Table 7 corrects for the
more recent European migrations, following a technique utilized by Comin
et al. (2010).32 In Table 6, there are basically four clusters of coefficients.
32
Comin et al. (2010) utilize Putterman and Weil's (2009) matrix on post-1500 migrations to correct 1500 and onward outcomes by the proportion of national population that has migrated into
the country. We do the same for regional aggregations. Putterman and Weil's original migration
matrix includes information of the migration from 1500 to 2000 for 165 countries. This statelevel matrix was converted to a regional-level matrix, so that the modified matrix gives the proportions of each region's population in the year of 2000 that resided in its own and other regions
in 1500. As in Comin et al., pre-1500 regional rankings were generated by pre-multiplying the
‘raw’ vectors of wealth/technology scores by the modified (regional) migration matrix. The resulting historical rankings thus reflect the post-1500 migration on the regional basis. For details
of the migration matrix, see Putterman and Weil (2009, 2010).
124
Was Wealth Really Determined?
Table 5. Regional rank orders
Western
Europe
2
1
1
1
1
1
2
1
1
1
1
2
2
2
3
3
Date
8000
4000
3000
2000
1000
1
1000
1500
1600
1700
1820
1870
1913
1950
1973
2003
Eastern
Europe
1
1
1
1
1
4
4
5
4
3
5
4
3
5
5
4
Former
USSR
4
1
1
1
1
5
4
4
3
2
4
3
5
3
4
6
Western
Offshoots
8
8
8
8
7
5
4
8
8
7
1
1
1
1
1
1
Latin
America
7
7
5
5
5
5
4
6
6
6
3
6
4
4
6
5
Asia
Japan
Africa
3
4
4
4
6
3
1
2
2
4
7
7
7
8
8
7
5
5
6
6
7
5
3
3
5
5
6
5
6
6
2
2
6
6
7
7
4
2
3
7
7
8
8
8
8
7
7
8
Table 6. Significant Spearman rank order coefficients (only entries
with P < 0.05 are shown; column numbers correspond to
row numbers)
Date
8000
4000
3000
2000
1000
1
1000
1500
1600
1700
1820
1870
1913
1950
1973
2003
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
.93
.85
.85
2
3
4
.93
.93
.77
1.0
.81
.81
.71
.85
.90
.85
.93
.85
.93
–
8
9
.93
.79
.91
–
11
.85
.92
.95
12
.88
.91
.83
.76
13
14
15
.88
.74
.76
.91
125
William R. Thompson and Kentaro Sakuwa
The first cluster encompasses coefficients in the BCE era and indicates that the
rank orders were similar between 8000 and 1000 BCE.33 A second cluster suggests significant similarity in the rank orders between 4000 to 2000 BCE and
1500–1700 CE. The third cluster indicates little change in the rank orders between 1500 and 1700 CE. Finally, the fourth cluster singles out the period between 1820 and 2003 CE as roughly similar in terms of rankings.
If we control for the well-known impact of the early modern and modern
European migrations, not too much changes. Table 7 still shows an early cluster
in the BCE era and the second cluster of similarity linking the BCE era to the
second period spanning from 1600 to 1913.34 The third cluster, focusing on
1500–1700 CE in Table 4, disappears in Table 7. The modern fourth cluster,
however, remains evident.
Table 7. Significant Spearman rank order coefficients adjusted for
migration (only entries with P < 0.05 are shown; column
numbers correspond to row numbers)
Date
8000
4000
3000
2000
1000
1
1000
1500
1600
1700
1820
1870
1913
1950
1973
2003
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
2
.74
.83
.76
.86
3
4
.93
.81
.93
5
6
–
–
11
12
13
14
15
.74
.91
.88
.74
.88
.85
.76
.73
.76
.76
.71
.85
.92
.95
.88
.91
.83
.76
.88
.74
.76
.91
Whatever these data represent, they do not support an argument for unmitigated
technological and economic wealth persistence. To put it another way, it is rather hard to argue that in general national wealth was determined in 8000 BCE.
The unadjusted regional rank order correlation in that year is –.143 (with the
migration adjustment, the correlation is still only .286. The first-ranked region
33
This first cluster is much diminished in terms of the number and size of the coefficients if Africa
is coded as possessing an east-west axis.
34
The first cluster almost disappears when provision is made for an east-west axis in Africa.
The second and third clusters remain roughly the same.
126
Was Wealth Really Determined?
in 8000 BCE has slipped to number three ten thousand years later. The lowestranked region has climbed to number one. One thousand BCE is no more determinative (the unadjusted spearman coefficient is –.356 and .214 with an adjustment for migration). As in 8000 BCE, the two lowest ranking regions in
1000 BCE were in the lead by 2003. Africa, in the middle in 1000 BCE, has
been at the bottom of the hierarchy for the past 500 years. Eastern Europe and
the USSR, once among the ACE leaders, have struggled to stay in the middle of
the rankings. Only the Asian and Latin American positions in 2003 closely resemble their 1000 BCE rankings.
What if we shift our focus to the year 1? The ability to predict from 1 to
2003 is about the same as when we use 8000 or 1000 BCE. The Spearman coefficient is –.380 if unadjusted and .262 if corrected for migration. Western
Europe, Eastern Europe, the USSR, and Latin America have similar rankings at
the end of the 20th century that they held in the year 1. Asia, Japan, Africa, and
the Western Offshoots do not. Shifting to a predictive base in 1500 yields
a better outcome. Although the unadjusted rank order coefficient is –.238,
the adjusted correlation is .619. All but Asia and the Western Offshoots have
similar rankings in 2003 that they held in 1500. What is missed, however, is
that the mis-predicted regions include the most populous (Asia) and the richest
(Western Offshoots) groups. Focusing on rank orders also downplays the size
of the gap between the leaders and followers in 1500 and 2003. In 1500,
the West European lead represented about a 2:1 lead over the lowest average
GDP per capita in Africa and the Western Offshoots (then, of course, far less
western and more indigenous North American and Australian). In 2003, the
Western Offshoots lead is 19 times as large as the lowest regional GDP per
capita (Africa).
But Comin et al. (2010) also encountered problems in using 1000 BCE and
0 CE data to predict to the current period. What about earlier shorter predictive
capability? Between 4000 BCE and 1000 BCE, as noted earlier, there are few
changes in the regional complexity hierarchy. All of the positions are not identical but they are very close. Between 1000 BCE to 1 CE, five regions retain
similar positions, while three (Eastern Europe and the USSR decline, Asia
vaults to a leading position) change their respective rankings. In the transition
from 1 CE to 1500 CE, there is again little change. Only Africa falls substantially in the rankings.
Thus, the Maddisonian regional rankings are fairly stable in what might be
called the ‘short’ or intermediate long-term, if we permit what is considered
short to become shorter over time since the observations are not equally spaced.
With sixteen observations over ten millennia, the rankings tend not to change
all that much when one moves three observations forward in time. Attempts to
predict beyond three observations, especially very long forecasts, work less
well. That would suggest that technology and wealth distributions persist to
William R. Thompson and Kentaro Sakuwa
127
some extent, but not indefinitely. With the partial exception of Latin America,
none of the regions examined occupies a roughly similar position across all
sixteen observations. Nor does it preclude substantial deviations from the persistence expectation. Asia was once very high in the hierarchy and then very
low. Conceivably, it might be very high again, as demonstrated in the case of
Japan (and perhaps China sometime in the future). The western offshoots, once
at the bottom of the hierarchy for a very long term, eventually took the lead.
Even if the offshoots should lose that lead, they are likely to remain near the
top of the hierarchy for some time to come. Granted, the western offshoots generated their remarkable shift in the growth hierarchy initially through a combination of technological borrowing and endowment, their subsequent growth
was due in part to the development of new technologies. Technological persistence, according to the Maddisonian data, is not destiny.
But what if we put the debatable Maddisonian data aside and look only at
the city size data which are grouped in more defensible aggregations and which
represent something more than one analyst's best retrospective guesstimate.
The correlation pattern that emerges in these data (see Table 8) is both different
and more simple than the one generated by Maddisonian GDP per capita figures. Yet, substantively, it leads to similar conclusions.
Three clusters are prominent. The first cluster encompasses 3700 BCE to
2000 BCE and represents the most ancient Mesopotamian concentration of cities.
A second cluster began to emerge half way through the first millennium BCE and
persists through 1800 CE. We might call this cluster the Silk Road grouping of
cities stretching from the Mediterranean through South Asia to East Asia.
The names and precise locations of the cities in each region that are most prominent in any given year vary but the regions retain their relative standings more
or less, as demonstrated in Fig. 2.
The third cluster has a short life span (1900 and 1950). It represents the ascendance of the West and the technological leadership of Britain (London,
Birmingham, Glasgow) and the United States (New York, Boston, Chicago,
Detroit, Philadelphia, and Los Angeles). However, even by 1950, the large
third world cities such as Calcutta and Bombay are also entering the top twenty-five cities in the world.
So, Table 8 demonstrates persistence as well. The first cluster predominated for 2000 years and then disintegrated, largely due to an inability to feed
its expanded population with declining grain productivity. The second cluster
of cities stretching from the Mediterranean to East Asia persisted for another
2000 years as the central armature of the world economy but was eventually
overtaken by technological changes that had first traveled the Silk Roads but
became concentrated in northwestern Europe and North America.
128
Was Wealth Really Determined?
Table 8. City size correlations across time
Note: Only entries with P < 0.05 are shown. Pairwise, year-to-year, correlation coefficients are obtained based on the analysis of each region's share of city population.
Years BCE in italics.
Fig. 2. Northern Mediterranean / West European and East Asian
regional city share scores
The third cluster seems unlikely to retain its prominence for another 2000
years. If nothing else, city size is no longer a reliable instrument for capturing
wealth and technological leadership as it once was. But the diffusion of wealth
and technology is taking place faster than it once did (Comin and Hobijn 2010).
The persistence of relative regional standings, as a consequence, must also be
expected to change to varying extents as some once low ranking areas rise in
the rankings. Yet there is also no reason to assume that all low-ranking regions
William R. Thompson and Kentaro Sakuwa
129
will rise equally. In that respect, some mixture of persistence and change
should be anticipated.
Since the patterns that emerge vary by indicator, do we need to pick and
choose which one seems to have the greatest validity? The city size data demonstrate what we earlier described as largely missing from the earlier analyses
of Olsson and Hibbs (2005) and Comin, Easterly, and Gong (2010). The city
data isolate the Sumerian starting point for relatively large cities and underscore
the ‘dumb-bell’ interaction between the Mediterranean and East Asia across
Diamond's east-west axis. They also capture the post-1800 shift in cities due to
industrialization. In these respects, the city size data most clearly conform to
our understanding of the major shifts in, and evolution of, world history. Yet as
long as all our indicators underline the limitations of persistence, there is really
no reason to focus on one index alone. Multiple indicators show roughly similar
mixtures of persistence and abrupt change.
Conclusion
Our point throughout has been that there are important limitations on path dependencies in historical economic growth patterns. Diamond's argument about
east-west axis and the number of plants and large mammals certainly helps explain Eurasia's advantages over Africa and the Americas. It does not tell us too
much about what happened within Eurasia after the creation of the world's continents. Whether we use biogeographical, societal complexity, GDP per capita,
or city size indicators, there are very clear limits on the ability to predict in the
long term who will be ahead in one year. Some places have been advantaged
over others but not to the extent of predetermining economic growth well into
the future. We cannot predict who precisely within Eurasia will get ahead based
on Eurasia's initial advantage. Nor could we have predicted how long any Eurasian advantage might persist, except to say that it did not last forever. Using our
indicators, we cannot predict who will be on ‘first base’ in 1 CE based on information in 1000 BCE. We cannot predict who will be ahead in 1950 or 1998
based on information in 1500. These prediction failures are not based on volatility in the data. There is substantial persistence across selected intervals. But
there are also substantial shifts due ostensibly to leads and lags in technological
leadership, demographic differentials, migration, climate change, disease, and
warfare.
If we grant that human existence on planet Earth is characterized by some
tendencies toward the stickiness of wealth and technological persistence subject
to strong temporal limitations, the most interesting questions involve why these
persistence tendencies fail to bar very substantial changes in regional and national rankings in economic wealth. We probably understand the reasons for
technological and wealth persistence best. We do less well explaining how
these characteristics are overwhelmed or in predicting how they may change in
130
Was Wealth Really Determined?
the future. It is conceivable, but by no means guaranteed, that an emphasis on
very long-term shifts in technology and wealth will give us a better perspective
on why the rich do not always get richer (or even stay rich) and why the poor
sometimes improve their standings in the world pecking order.
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133
Validation Appendix
Any examination of behavior over multiple millennia is apt to rely on questionable assumptions and data. There are at least four possible threats to the validity
of our results. One is that the Maddison data, especially for the earlier periods, are
not very accurate. The problem, however, is that we lack alternative estimates of
a similar nature to be able to assess Maddison's guesstimates about GDP per capita. Whether we will ever have alternative data, other than the city size data, encompassing the same period remains to be seen. In the interim, we have utilized
what is available. Better estimates in the future would of course be very welcome.
Similarly, using Maddison's older data forces us to use his regions as well. That is
the way the data are made available. Would we like to experiment with different
regional identifications? Certainly, but, again, we cannot at this time do so without abandon the GDP per capita scheme altogether.
However, there are two other debatable assumptions that we can assess.
We use gross domestic product (GDP) per capita data to assess a question that
is framed by Comin et al. as a matter of technological development. If we move
away from indicators of technology per se, either in terms of societal complexity in the BCE era or GDP per capita in the CE era, have we modified substantially the argument at stake? We cannot do much more with the BCE era but there
is a way to assess the relationship between GDP per capita and technological development in the more recent CE era. Less substantively perhaps, we also rely on
rank orders to evaluate regional movement. Rank ordering in this case loses information by imposing an ordinal hierarchy on raw interval data. Why not just
look at the raw interval data? The answer is that rank ordering simplifies the presentation of the findings. But it is worthwhile to check whether this simplification
makes any meaningful difference to the analytical outcome.
We can make use of the Cross-Country Historical Adoption of Technology
(CHAT) dataset developed by Comin and Hobijn (2010) and available at
http://www.nber.org/data/chat. This data set focuses on the annual development
of over 100 technologies in over 150 countries since 1800. We extracted
a sample of some of the more important technologies of the past two centuries:
steam ships, passenger trains, telegraph, telephone, electric power, cars, passenger planes, cellphones, and computers to create an overall technology score
based on average, standardized scores on these nine technology foci. To preclude possible problems in interpreting the data, we also calculated scores
based on the same data without technologies that had been introduced more
than 100 years earlier. We also computed the relationship between overall
technology scores and GDP per capita at the country and regional level, as
shown in Table A1.35
35
The 1870–1998 interval is dictated by the absence of much earlier and more recent information in
CHAT. In addition, one has to be careful in using CHAT data because there are some problems
134
Was Wealth Really Determined?
The overall technology level is calculated in the following procedure. First,
we take ‘raw’ technology indicators from the CHAT dataset which includes
quantities such as the number of cars registered. We then normalized the raw
values to population in order to obtain per capita indicators for the nine technology foci. Population data are taken from the National Material Capabilities
dataset version 4 (Singer, Bremer and Stuckey 1972 [2010]). Second, the
standardized score of each technology item k for country i is obtained as
Zik = (Xik – X k )/σk, where X k is the mean value. Finally, overall technology
level of country i is calculated by averaging Zik over all k's.
Table A1. Technology-GDP per capita correlations
1870
1913
1950
1973
1990
1998
Country-level
Original
0.840
0.850
0.798
0.760
0.898
0.910
Adjusted
0.840
0.850
0.854
0.778
0.884
0.915
Regional-level
Original
0.867*
0.954
0.949
0.940
0.918
0.991
Adjusted
0.867*
0.954
0.953
0.884
0.896
0.994
Note: The adjustment involves removing technology that is older than 100 years from
the calculation. Statistical significance is < 0.05 except for the two correlations
with asterisks where p = <.10.
The outcome is that since 1870 at least, the general relationship between technological development and GDP per capita is quite high, especially at the regional level. It does not seem to matter if we control for old technology, the
outcomes are quite similar. The possession of a high gross domestic product per
capita indicates a high technological development score and vice versa.
Of course, we do not find these relationships surprising in the contemporary
period. The correlations do not test our assumption that a similar linkage between technological development and wealth holds over the long term but they
do buttress our ability to make the assumption.
When we replace rank ordering with the raw scores suitably standardized,
Table A2 summarizes the statistically significant correlations over time.
The outcome looks much like the outcome reported in Table 6 using rank orders. There are some clusters of stability in the regional hierarchy, most notably
demonstrated in the BCE era and in the post-1870 era. In between, there is not
all that much correlation outside of the 1500–1700 CE period. It would appear
that our finding that there are strong constraints on regional hierarchical stabilwith data listed in non-equivalent units that can be traced back directly to the sources that were
utilized. We attempted to correct these problems prior to the analysis.
135
William R. Thompson and Kentaro Sakuwa
ity in the really long term is not due to using rank ordered data. Similar outcomes emerge from the raw data as well.
Table A2. Regional hierarchy correlations over time with adjustment
–8000
–4000
–3000
–2000
–1000
1
1000
1500
1600
1700
1800
1820
1870
1913
1950
1973
2003
–8
0
0
0
–4
0
0
0
–3
0
0
0
–2
0
0
0
.853
.888
.835
.695
.903
.835
.636
.977
.849
.941
.718
.707
.743
.741
–1
0
0
0
1
.815
.804
.744
1
0
0
0
1
5
0
0
1
6
0
0
1
7
0
0
.989
.947
.978
1
8
0
0
1
8
2
0
1
8
7
0
1
9
1
3
1
9
5
0
1
9
7
3
.964
.941
.875
.845
.818
.984
.943
.847
.811
.980
.873
.835
.851
.796
.976
Note: Only correlations significant at the < .05 level are reported.
II. CYCLICAL PROCESSES
IN PRE-INDUSTRIAL SOCIETIES
4
Cycling in the Complexity
of Early Societies
Sergey Gavrilets, David G. Anderson,
and Peter Turchin
Abstract
Warfare is commonly viewed as a driving force of the process of aggregation of
initially independent villages into larger and more complex political units that
started several thousand years ago and quickly led to the appearance of chiefdoms, states, and empires. Here we build on extensions and generalizations of
Carneiro's (1970) argument to develop a spatially explicit agent-based model
of the emergence of early complex societies via warfare. In our model polities
are represented as hierarchically structured networks of villages whose size,
power, and complexity change as a result of conquest, secession, internal reorganization (via promotion and linearization), and resource dynamics.
A general prediction of our model is continuous stochastic cycling in which the
growth of individual polities in size, wealth/power, and complexity is interrupted by their quick collapse. The model dynamics are mostly controlled by
two parameters, one of which scales the relative advantage of wealthier polities
in between- and within-polity conflicts, and the other is the chief's expected
time in power. Our results demonstrate that the stability of large and complex
polities is strongly promoted if the outcomes of the conflicts are mostly determined by the polities' wealth/power, if there exist well-defined and accepted
means of succession, and if control mechanisms are internally specialized.
Keywords: modeling, warfare, state, territory, rebellion.
Introduction
For most of humanity's existence people lived in small egalitarian bands or villages that were politically autonomous. However, a qualitative change happened roughly 10,000 years ago when villages began aggregating into larger
and more complex, hierarchically-structured polities (a general term that includes not only states and empires but also smaller-scale independent political
History & Mathematics: Trends and Cycles 2014 136–158
136
Sergey Gavrilets, David G. Anderson, and Peter Turchin 137
units, such as chiefdoms, acephalous tribes, and autonomous villages, see, e.g.,
Ferguson and Mansbach 1996). This process of aggregation first took place in
Mesopotamia, East Asia, South America, and Mesoamerica, followed by secondary developments elsewhere (Service 1975). The process of aggregation
led, over time, to the emergence of chiefdoms, states, and empires. Once established, these complex societies rose and fell over time, with centers of power
and authority shifting from one location to another over the landscape, a process that has been described as cycling (Wright 1977, 1984; Cordy 1981; Kirch
1984; Marcus 1992, 1998; Anderson 1994, 1996; Earle 1997; Cioffi-Revilla
and Landman 1999; Junker 1999; Hall 2001). The causes of this process have
fascinated scholars and been the subject of speculation for centuries (Engels
1884; Lenin 1918; Childe 1950; Wittfogel 1957; Adams 1966; Fried 1967;
Flannery 1972; Webster 1975; Wright 1977, 1984, 1986; Service 1975, 1978;
Ferguson and Mansbach 1996; Earle 1997; Trigger 2003; Cioffi-Revilla 2005;
Drennan and Peterson 2006; Turchin and Gavrilets 2009; Spencer 2010).
Here we are concerned with a set of influential theories that put special
emphasis on warfare between different polities (starting with villages). When
warfare first occurred in human (pre)history is controversial, although it is assumed to have been relatively small in scale and consequence until complex
and presumably multicommunity societies emerged (Ferguson 1984; Haas
2004; Trigger 2003; but see Keeley 1997; Cioffi-Revilla 2000). Besides warfare, there are of course a number of additional prerequisites for the evolution
of social complexity. One requirement, emphasized by Carneiro, is circumscription (environmental, due to the resource concentration, or social, due to the
presence of other human groups nearby; see Carneiro 1970, 1981). Circumscription was the factor that precluded losing communities from moving away
and thus separating themselves spatially and politically from victors. Other prerequisites include existence of agricultural potential capable of generating surpluses and significant variation in productive and/or demographic potential
among local communities (Webster 1975). Equally important was ability to
delegate power and the invention of hierarchically structured control mechanisms in which each superior directly controlled only a limited number of subordinates (Flannery 1972; Wright 1977, 1984; Turchin and Gavrilets 2009).
The latter was also important for the subsequent growth of polities given what
has been called ‘scalar stress’, a decrease in the ability of leaders to process
information and maintain efficient control over subordinates as their number
(herein, the number of subordinate villages) increased (Johnson 1982).
The outcome of these processes and factors was the emergence of simple chiefdoms (Steponaitis 1978, 1981; Wright 1984) in which one village controlled
(and received tribute from) several subordinate villages. More complex polities
were characterized by greater numbers of subordinate levels, with complex
chiefdoms, paramount chiefdoms, and state societies typically defined as those
138
Cycling in the Complexity of Early Societies
polities with two, three, and four or more administrative levels above the local
or primary community, respectively (Flannery 1972; Wright and Johnson 1975;
Steponaitis 1978; Wright 1984; Anderson 1994).
The paramount chief delegated power over a subset of his villages to
somebody else (a subchief), often a relative (e.g., Cordy 1981). Sometimes the
chiefs of vanquished groups were permitted to stay in power but had to pay
tribute (e.g., Kurella 1998). The hierarchical nature of this organizing principle
allows, in theory, for unlimited growth in the size and complexity of chiefdoms.
However, in early chiefdoms, constituent communities could exist autonomously. Moreover, in these societies control was vested in one or a few individuals, and such absence of internal specialization meant that subchiefs had
almost total control over their subordinate villages (Wright 1977, 1984; Earle
1987). Therefore rebellion and secession by subchiefs had a low cost and was
relatively easy to organize, although not always successfully accomplished. As
a result, the growth in the size and complexity of chiefdoms was counterbalanced by a tendency to fragment through rebellion and secession.
Although the argument just given is well accepted by anthropologists, historians, and political scientists, many questions remain. These concern the levels of complexity that can be achieved, its dynamic patterns and timescales, and
the qualitative and quantitative effects of various parameters and factors. Here
we use a stochastic spatially-explicit agent-based mathematical model to shed
light on these questions. The analyses that follow encompass developments
over large geographic and extended temporal scales, the processes that cause
chiefdoms, states, and empires to emerge, persist, and collapse at the scale of
decades to centuries, the longue durée of human history. Our approach is
a generalizing one, sacrificing specific detail for a glimpse of the reasons behind the broad patterns recorded by archaeology and history. At the same time,
however, our modeling approach aims to connect these broad processes to the
finer scale historical events generating those patterns under examination.
Until recently there has been only a limited amount of modeling work directly addressing the evolution of large-scale polities (Dacey 1969, 1974;
Bremer and Mihalka 1977; Cusack and Stoll 1990; Cederman 1997; Spencer
1998; Cioffi-Revilla 2005; Cederman and Girardin 2010). Most of this work
has focused exclusively on polity size, was limited to a small number of simulation runs, and was primarily motivated by questions of interest to political
scientists. Here, we build on earlier approaches by presenting a dynamic quantitative model exploring the origin and operation of early human complex society, focusing on both the size and complexity of emerging polities as well as
their longevity and settlement patterns. We systematically examine the effect of
parameters such as system size, the effect of polity power on the probability
of winning a conflict, tribute level, variation in productivity between individual
villages, span of control, and chief's average time in power. The polities in our
Sergey Gavrilets, David G. Anderson, and Peter Turchin 139
model exhibit a strikingly fluid nature resembling so-called ‘chiefly cycles’.
Unexpectedly, the largest effect on results is due to just two parameters: the
scaling of the polity power to the probability of winning a conflict, and the
chief's average time in power. At the end of the paper we discuss the implications of our results and some relevant empirical evidence. Some preliminary
results of our model were presented in Turchin and Gavrilets (2009).
The Model
Here we describe the model informally; readers interested in the mathematical
details will find them in the Mathematical Appendix. We consider a hexagonal
array of initially autonomous local communities (villages), consistent with earlier hex-based models (e.g., Cusack and Stoll 1990; Bremer and Mihalka 1977).
Each community is represented by a hexagon and has up to six neighbors
(Haggett 1965), reflecting a more natural modeling abstraction than square
cells. Time is discrete and the unit of time (‘year’) is the expected interval between two consecutive ‘decisions’ made by a community (explained below).
Each community i is characterized by a constant base-line resource level f0,i
which can be interpreted as a measure of the settlement's catchment size (Steponaitis 1981). The values f0,i are chosen randomly and independently from a
(truncated) normal distribution with mean 1 and constant standard deviation .
Parameter represents variation in productive/demographic potential between
local communities due to environmental heterogeneity. Each community is also
characterized by its actual resource level fi. Initially, for each community
the actual resource level is set at the base-line level (i.e., fi = f0,i), but different
actions in which the community takes part change its value (explained below).
Each community is a part of a polity (which can consist of a single community). The polities have a hierarchical structure. Each community in a polity
except for the one at the top of the hierarchy (the ‘chief community’) has one
superior community and may have up to L subordinate communities, where L is
a constant parameter measuring the maximum span of control (i.e. the maximum number of subordinates; see Johnson 1982). Each polity is identified by
its chief community (see Fig. 1). Each subordinate community pays tribute
by transferring a fixed proportion θ of its total resources to its superior.
The total resources of a community are the sum of the resources fi it produces
and the tribute received from subordinates (Steponaitis 1981). The power
(wealth) of a polity Fi is given by the total resources available to its chief community. The complexity of a polity ci is given by the number of levels of control above the level of individual villages.
Polities are engaged in warfare as a result of decision-making, similar to
earlier agent-based models of polity systems. The polities grow, decrease in
size, or disappear as a result of conquest, with the winner absorbing (all or
a part of) the loser. New polities also appear, and old polities decrease in size,
when a subordinate community secedes with all of its subordinates.
140
Cycling in the Complexity of Early Societies
3
a)
3
26
30
17
b)
Fig. 1. An example of a system with 37 villages and four polities.
a) Spatial view. The arrows indicate the direction of the tribute
flow. The circles are proportional to the polity power.
The numbers are labels identifying the chief communities.
b) A hierarchical representation of the polities. The complexity
of polities 3, 26 and 30 is two while that of polity 17 is one
Each chief community and each of their direct subordinates make exactly one
decision every year. For the chief community, the decision is whether or not to
attack a neighboring polity. For a direct subordinate of a chief community,
Sergey Gavrilets, David G. Anderson, and Peter Turchin 141
the decision is whether or not to attempt to secede. Warfare is modeled as follows. A polity selects its weakest neighbor and calculates the chance of success
of an attack upon it (which increase the probability of attack), as well as the
attack costs (which decrease the probability). The willingness to attack also
decreases as the amount of resources available decreases. An attack of polity i
on polity j succeeds or not with probabilities proportional to Fi and F j . Parameter α characterizes the importance of other factors (‘noise’) besides the
polities' power in controlling the outcome of a conflict, with larger α implying
less noise and more determinism. For example, let polity i be twice as strong as
polity j. Then with linear scaling (i.e., with α = 1), the probabilities of polities i
and j winning the conflict between them are in the ratio 2:1. However with
quadratic scaling (i.e., with α = 2) this ratio becomes 4:1. That is, as α increases, polity strength becomes a better predictor of the outcome of conflict.
The aggressor attempts to conquer communities of the victim, starting with
border ones, and proceeding in a series of ‘battles’ until either it suffers a defeat, or until the chief community of the victim polity is conquered. Thus, the
aggressor either fails completely, seizes a part of the victim polity, or the whole
victim polity is annexed.
Annexing communities may require reorganization of the successful aggressor polity (via linearization and promotion, see Flannery 1972), because of
the limit L on the number of subordinates of any community. Thus, if one
community is to become a subordinate of another, the latter must have at least
one open control slot. When all open slots are exhausted, new ones are created
by demoting some communities, that is moving them to a lower level in the
hierarchy (Flannery 1972). The winning polity attempts to maximize the flow
of tribute to the top, and therefore demotes poorer/smaller communities while
keeping wealthier/larger ones at higher levels of the hierarchy.
A community subordinate to the chief polity will secede if it estimates that
the attack of its old master will be successfully repelled and is willing to pay
the price of rebellion. The chief polity attempts to suppress the rebellion immediately. If a successful rebellion results in spatial separation between different
parts of the master state, all communities that become disjointed from their superiors secede as well. To account for a possibility of secession upon the death
of the paramount chief as a result of a struggle among subchiefs (which is
a major source of instability in chiefdoms, see Anderson 1994; Wright 1984;
Cordy 1981; Kirch 1984), we introduce an additional parameter τ, the average
time in power of the paramount chief. Upon the death of the paramount chief,
a random number of subordinate communities become independent without war.
The cost of warfare is a reduction in the amount of actual resources available to participants, with less likely outcomes being costlier for all participants.
Following conflict resolution resources are renewed at a fixed low rate.
142
Cycling in the Complexity of Early Societies
Analysis
To develop an intuition about the model's behavior, we ran numerical simulations with all possible permutations of the following six parameters: system
edge size S = 4, 5, and 6 villages (so that the total number of villages is 37, 61,
and 91, respectively); α = 1 and 2 (i.e., linear and quadratic scaling of the polity
power to the probability of a win); variation in productivity = 0.3, 0.4, and 0.5
(using data in Steponaitis 1981, can be estimated to be between 0.34 and
0.48), tribute θ = 0.1, 0.2, and 0.3 (in Steponaitis 1981 tribute level was estimated to be 0.16–0.22), span of control L = 5, 6, and 7 (Johnson 1982 argued
that the most common value of the span of control is 6), and the chief's average
time in power τ = 5, 10 and 20 years (for all model parameters, see Table 1).
Numerous sources, from Polynesian chiefly genealogies to the so-called ‘king
lists’ of many early states, indicate these are reasonable estimates of τ. Very
few leaders in chiefly or even state-level societies lasted longer than
20–30 years, with most reigns appreciably shorter; rulers who held power for
exceptionally long times are just that, unusual exceptions rather than the rule
(Kamakau 1872; Beckwith 1977; Dodson and Hilto 2004).
Each simulation ran for 1,000 years, and the statistics were evaluated using
the data from the last 800 years. Our focus was on the dynamics of the relative
complexity, and average ‘centrality’ (i.e., the ratio of the power of the chief
village and the one immediately below, see Steponaitis 1981) (Fig. 2c). We also
looked (see Supplementary Information) at the relationships between a polity's
base-line productivity and actual power (Steponaitis 1981) and between settlement power and rank on a log-log scale (Johnson 1980; Wright 1984), and at
the distributions of village power (Wright 1984).
Starting with a system of independent villages, we observe the rapid formation of polities of various size and complexity as a result of warfare.
The system quickly (within 50–100 years) reaches a kind of equilibrium in
size of the largest polity smax (Fig. 2a), the mean c (Fig. 2b) and maximum cmax
which our focal characteristics smax, c , cmax and are maintained at approximately constant values (see e.g., Fig. 2). However, this equilibrium is
stochastic and is characterized by the dynamic instability of individual polities, with quick collapse characterizing chiefdoms reaching relatively large
size and complexity.
Sergey Gavrilets, David G. Anderson, and Peter Turchin 143
0.5
s
max
1
0
750
800
850
900
950
1000
900
950
1000
900
950
1000
time
c
mean
6
4
2
0
750
800
850
time
ρ
mean
15
10
5
0
750
800
850
time
Fig. 2. Examples of the temporal dynamics of the relative size of the
largest polity, the mean complexity, and the mean centrality.
Black lines: S = 5, α = 1,
= 0.4, θ = 0.2, L = 6, = 10;
grey lines: the same but with α = 2
Table 1. Major model parameters and statistics
S
α
θ
L
τ
s max
c
c max
System edge size
Scaling exponent (of the polity power to the probability of a win)
Standard deviation of the baseline resource level
Tribute level
Span of control (the maximum number of subordinate communities)
The expected time in power of the paramount chief
Relative size of the largest polity
Mean complexity
Maximum complexity
Average centrality (i.e. the ratio of the power of the chief village and the one
immediately below)
To quantify this process, we identified all ‘significant complex chiefdoms’, that
is polities with complexity c ≥ 2 and size s ≥ 10 villages. Note that only a small
proportion of polities reaches this status. Fig. 3, illustrating the dynamics of
such polities, shows their rapid growth and collapse.
144
Cycling in the Complexity of Early Societies
a)
b)
Fig. 3. The dynamics of polities that have achieved a size of at least
s = 10 and complexity c = 2. Different curves correspond to
different chief villages:
a) S = 5, α = 1, = 0.4, θ = 0.2, L = 6, = 10;
b) the same but with α = 2
Sergey Gavrilets, David G. Anderson, and Peter Turchin 145
Table 2. Results of the analysis of variance: the effects of the parameters and of their pairwise interactions on system properties
Parameters
and their
combinations
S
α
θ
L
τ
S×α
S×
α×
S×θ
α×θ
×θ
S×L
α×L
×L
θ×L
S×τ
α×τ
×τ
θ×τ
L×τ
error
total
smax
c
c max
T
13.2
39.8
0.8
1.0
0.0
33.8
0.3
0.0
0.0
0.1
0.2
0.0
0.0
0.0
0.0
0.1
0.4
7.0
0.1
0.3
0.1
2.6
100.0
0.3
33.6
1.6
2.0
0.8
40.8
0.1
0.0
0.2
0.0
0.7
0.1
0.0
0.1
0.0
0.1
0.1
12.9
0.3
0.9
0.1
5.2
100.0
8.3
34.9
0.7
0.5
5.7
38.9
1.5
0.0
0.0
0.2
0.6
0.1
0.1
0.1
0.0
0.1
1.2
1.8
0.1
0.5
0.1
4.5
100.0
3.4
19.9
0.7
8.6
1.0
55.5
0.1
0.0
0.0
0.0
0.2
0.1
0.0
0.1
0.1
0.2
0.1
0.1
0.0
2.5
0.6
6.6
100.0
0.0
5.4
25.0
36.3
1.1
10.4
0.0
0.1
2.0
0.0
0.0
0.3
0.1
0.3
0.1
0.5
0.1
0.4
2.1
0.1
0.2
15.3
100.0
We studied the effects of parameters on system properties (see Table 2 and the
Supplementary Information). The relative size of the largest polity smax increases most significantly with the success probability exponent α and with the
chief's average time in power τ, but decreases with system size S (see Fig. 4 and
Supplementary Information). With α = 2 (i.e., quadratic scaling of polity power
to success probability) we occasionally observe cases when all villages are incorporated into a single polity. Such a state can last for up to 35 % of run time
and is most likely with maximum values of both τ and θ.
Average complexity c increases most significantly relative to α and τ. It also increases with system size S, but decreases with increasing span of control L.
Overall, c stays below c. 2 and 3.3 for α = 1 and 2, respectively. Average centrality increases most significantly with variation in productivity and with
tribute θ; it also increases with α, but decreases with τ.
146
Cycling in the Complexity of Early Societies
Fig. 4. The effects of parameters on the relative size smax of the largest polity. Each bar corresponds to a combination of four parameters: , θ, and L. The values of smax are simultaneously
reflected in the bar's height and in the number shown next to
it. Other parameters are S = 5, α = 2
Average lifetime of ‘significant complex chiefdoms’, T, increases with α and τ
(most dramatically), while growing with tribute θ, but decreasing with system
size S. Overall, the average lifetime of the ten most significant complex chiefdoms stays below 55 and 68 years for α = 1 and 2, respectively.
The rank-size curves describing the distribution of polity sizes (Haggett
1965; Johnson 1980; Wright 1986; Peterson and Drennan 2005; Drennan and
Peterson 2006) are always convex (see Fig. 5), as expected; polity power declines approximately linearly with the logarithm of its rank indicating the presence of poorly integrated competing centers. The scatter plots for the relationships between the actual and base-line power of polities (Steponaitis 1981) do
not show much clustering, suggesting that they are a poor indicator of the degree of complexity in the system (see Supplementary Information).
Sergey Gavrilets, David G. Anderson, and Peter Turchin 147
1
settlement
settlement power
power
10
0
10
−1
10
−2
10
0
1
10
2
10
10
settlement rank
settlement
a)
1
10
0
settlement
power
settlement power
10
−1
10
−2
10
−3
10
0
10
1
10
2
10
settlement rank
rank
settlement
b)
Fig. 5. Rank-size curves. Solid black lines: the time average. Dashed
black lines: the time average plus minus one standard deviation. The light grey line gives the lognormal curve. Medium
dark lines on top gives the rank-size curve at the final year of
simulations. Parameters are as in Fig. 3
Discussion
Our model provides theoretical support for a view that the formation of complex polities is ‘a predictable response to certain specific cultural, demographic
and ecological conditions’ (Carneiro 1970). Conditions explicitly accounted by
148
Cycling in the Complexity of Early Societies
our model include warfare, circumscription, variation in productivity between
different local communities, ability to generate surpluses, ability to delegate
power, and restrictions on the growth of polities due to scalar stress. Once these
conditions are present within a particular geographic area, the model predicts
rapid formation of hierarchically organized competing polities partitioning
available space.
A striking feature of the model output is the fluid nature of ‘significant’
polities, which continuously go through stochastic cycles of growth (both in
size and complexity) and collapse. Growth is driven by successful warfare
whereas collapse results from defeat in warfare, rebellion of subchiefs, or fragmentation following the death of the paramount chief. The lifetime of chiefdoms observed in our simulation – a few generations – is comparable to those
identified by archaeological studies (e.g., Anderson 1994; Wright 1984; Earle
1991; Hally 1996; Junker 1999; Blitz and Livingood 2004). The model suggests that the rapid collapse of chiefdoms can occur even without environmental perturbations (e.g., drought) or overpopulation.
While the characteristics of individual polities (such as size, complexity,
power, and centrality) undergo continuous change, the average values of these
characteristics across the whole system remain relatively stable. We have systematically studied how these characteristics are affected by the following six
parameters: variation in productivity between local communities , probability
of success in war exponent α, span of control L, tribute θ, system size S, and the
average chief's time in power τ. Our results show that most variation in system
behavior can be explained just by two parameters: α and τ, with higher values
strongly promoting the existence of larger, more complex, and more stable polities. Only in the case of centrality were the effects of α and τ small, with most
variation being explained by and θ.
The chief's expected time in power τ is one of the two most important parameters. This finding strongly supports arguments on the crucial importance of
having well-defined and legitimate mechanisms of succession for the stability
of polities (Anderson 1994; Wright 1984). Creating and maintaining complex
polities thus requires effective mechanisms to deal with both internal and external threats. In both cases, leaders (paramount chiefs) must solve collective action problems to overcome challenges. Even a most abbreviated reading of human history shows how difficult this task has been.
The other critical parameter of the model is the probability of success in
war (controlled by α), which sets the relative effectiveness of stronger (wealthier) polities in internal and inter-polity conflicts. In our model, the stronger of
the two polities does not necessarily win a conflict between them. This is reasonable as there are many other factors besides wealth that can affect the outcome of conflict. However increasing α implies a stronger dependence of the
outcome of the conflict on the polities' power (wealth). The degree of determin-
Sergey Gavrilets, David G. Anderson, and Peter Turchin 149
ism in the conflict resolution (and thus, parameter α) is expected to increase
with economic and political development (Carneiro 1970, 1981; Collins 1986).
Note that in our simulations, polities conquering the whole simulation domain
are observed only with α = 2.
Our model shows no qualitative differences between polities with a single
level of control above the level of individual villages (‘simple chiefdoms’) and
polities with two or more levels of control (‘complex chiefdoms’ or ‘states’).
During each individual run, the number of control levels is not stable but
changes dynamically and therefore cannot by itself serve as an indicator of the
presence of ‘true’ states. Our results support Carneiro's (1981: 38) insight that
‘the transcending of local sovereignty and the aggregation of previously autonomous villages into chiefdoms was a critical step in political development –
probably the most important one ever taken. It crossed a threshold, and once
crossed, unlimited further advance in the same direction became possible.
The emergence of chiefdoms was a qualitative step. Everything that followed,
including the rise of states and empires, was, in a sense merely quantitative’.
In our simulations it was possible for polities to conquer the whole spatial
domain, or a significant part of it. However, our analyses also show that such
polities are relatively short-lived. A major reason for this is the relative ease of
rebellion within larger polities. Additionally, our model explicitly assumes that
any ‘internal specialization’ is absent and that all mechanisms for autonomous
existence of a rebellious province are already in place. This model behavior
thus further emphasizes, through the effect of its absence, the importance of
‘internal specialization’ for the emergence of large and stable polities (Flannery
1972; Wright 1977, 1984).
Implications for Archaeological Research
Due to temporal resolution limitations archaeological analyses of settlement
hierarchies typically combine sites occupied over intervals of a half century to,
sometimes, hundreds of years. The hierarchies reconstructed by archaeologists
are commonly displayed as a series of maps showing site sizes during different
periods, often separated by a century or more, or else histograms or rank size
plots (Wright and Johnson 1975; Wright 1977, 1984, 1986; Johnson 1980; Hally 1996; McAndrews et al. 1997; Spencer and Redmond 2001; Liu and Chen
2003; Peterson and Drennan 2005; Drennan and Peterson 2006). These reconstructions suggest rigid formal hierarchies and static political landscapes. Our
analyses, in contrast, indicate that at a finer temporal scale the various factors
that produce these archaeological signatures are much more dynamic. This result is in agreement with written records of historical events (when available;
e.g., Earle 1987, 1991).
Our estimates of chiefdom duration are comparable with those based on archaeological evidence. In studying Southeastern Mississippian chiefdoms, Hal-
150
Cycling in the Complexity of Early Societies
ly (1993) examined the time periods when occupation and mound construction occurred at 47 mound centers in central and northern Georgia. He concluded that ‘paramount chiefdoms must have been unstable and short lived’
while ‘simple and complex chiefdoms endured for as much as a century or
more’ (Hally 1993). The actual duration of phases, or periods of occupation
and construction in his analysis (Ibid.: 145), however, could not be resolved
much below 75–100 years. Hally extended this analysis in a second paper
(Hally 1996) examining 45 mound centers, and including episodes of mound
stage construction. Where evidence for numbers of internal mound construction stages was available, duration of occupation was estimated to be between
75 and 100 years, with the average number of years per stage ranging from 12
to 25 years at the best understood sites (Hally 1996). This span may represent
the duration of a chiefly leader, or generation. At 29 of the 45 mound centers,
only a single period of use is currently known, indicating most ‘chiefdoms’
locally lasted no more than 75–100 years, and perhaps appreciably less (Hally
1996).
In a follow up, Hally (2006: 27) argued that ‘as many as 47 distinct chiefdoms rose and fell’ in 27 locations during the Mississippian period in northern
Georgia (some locations were occupied repeatedly, often with gaps in occupation of a century or more). The numbers of chiefdoms in his sample fluctuated
between 8 and 17 during the period of 1000–1500 CE (Hally 2006). Many polities in the sample were single-mound simple chiefdoms (Hally 2006).
Blitz and Livingood (2004) used mound volume as an alternate means of
measuring regional settlement hierarchies, using a sample of sites from across
the southeast USA. For a sample of 35 mounds they recorded a mound volume
index (basal length × basal width × height / 1000), the number of major moundconstruction stages, the duration of mound use in years, and the number of
mounds at the site where the sample mound was found (Ibid.: 293). Their analysis, while geographically broader than Hally's, yielded generally similar results, noting average mound center ‘duration of use range is 100–450 years,
with a mean of 183 years and a median of 150 years. Also, there appears to be
a rough periodicity in mound construction: the average occupation span per
construction layer is 25–50 years’ (Ibid.: 296). They were able to demonstrate
that mound stage construction might fall into two cycles, one of c. 12–18 years,
and another of c. 25–50 year spacing (Ibid.: 297).
Our finding that the duration of a chief's reign is a significant parameter
parallels that in the literature on state fiscal organization. In this literature, the
discount rate of rulers (that is, their expected time in office) is shown to be
a major determinant of the kind of taxation system employed, which in turn has
various implications for society, for example, for political stability of the Roman state and Ptolemaic Egypt (Kiser and Kane 2007; Levi 1988; Monson
2007).
Sergey Gavrilets, David G. Anderson, and Peter Turchin 151
In our model individual villages differ only in their base-line productivity
and geographic location but otherwise have equal ability to form complex societies. In human history some polities had a headstart, allowing them to
achieve large size initially (e.g., San Miguel Mogote or El Mirador in Mesoamerica; Uruk and Susa in Mesopotamia; Aspero in South America; see Service 1975); but the strategies for complex polities buildup and maintenance
would have spread quickly in a Darwinian fashion as a result of conquest and
imitation. Therefore once chiefdoms appeared, their organizational form would
itself have tended to spread, as neighboring societies adopted it for reasons
ranging from emulation to self defense (Carneiro 1981; Anderson 1994).
Conclusion
The dynamics generated by our model, in which hierarchical societies tend to
achieve at most medium levels of complexity, and only for relatively short periods of time, resembles the chiefly cycles observed prior to sustained Western
contact in eastern North America, southern Central America and northern South
America, Oceania, southeast Asia and the Philippines, and across large parts of
sub-Saharan Africa (e.g., Wright 1984; Marcus 1992; Earle 1991; Anderson
1994; Cordy 1981; Junker 1999; Drennan and Peterson 2006).
The model developed here can be extended in a number of ways. For example, instead of a simple conquest mechanism, one can consider a more nuanced dynamic in which external threat of conquest (or raiding) induces
a greater degree of cooperation between lower-level groups, which results in
a more stable higher-level polity. According to Cioffi-Revilla's canonical theory (2005), such a (‘fast’) process is common for producing stronger institutions of government. One possible direction is to generalize the model to allow
for the formation of coalitions between different polities (Carneiro 1998; see
Gavrilets et al. 2008 for a possible dynamic approach). Also, to adapt the
model for describing larger spatial scales (e.g., as necessary for modeling
the origin of states and empires), changes in population densities need to be
considered, as well as the propensity for cooperation (and, conversely, conflict)
should be allowed to depend on cultural similarity/dissimilarity between
the agents.
Over the past several decades mathematical methods and techniques have
become very important in life sciences and social sciences (Spencer 1998; Cioffi-Revilla 2002; Bentley and Maschner 2008; Costopoulos 2008; Kohler et al.
2005). In particular, mathematical and computational modeling are powerful
tools for better understanding the origins of new species (Gavrilets 2004) and
of general rules of biological diversification (Gavrilets and Losos 2009). Agentbased simulation modeling efforts like those advanced here offer fruitful avenues for future research on general patterns in historical dynamics and on the
emergence and diversification of human societies (Turchin 2003, 2006, 2009).
152
Cycling in the Complexity of Early Societies
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Mathematical Appendix
Here we provide some additional details on the model and simulations.
The model was implemented in the Matlab.
Attacks. A polity may attack only its weakest neighbor. The attack of polity i on polity j is successful with probability
F
Pij i ,
(Eq. 1)
Fi F j
where Fi is the power of polity i, and α is the success probability exponent. Polity i will attack polity j only if it estimates that the attack will be successful, is
willing to pay the cost of warfare, and is not too devastated by previous warfare. Specifically, the probability of attack is set to
F
Aij Pij exp[ cij ] i .
(Eq. 2)
Fi ,0
Here the first term is the probability of winning (estimated by the potential
aggressor via ‘scenario building’). The second term accounts for a negative
effect of costs of warfare, cij (defined below), on the willingness to attack; β > 0
is a parameter. The third term accounts for a reduction in the willingness to
attack caused by recent conflicts (and ensuing drop in available resources); Fi,0
is the maximum possible power of the i-th polity (observed at maximum possible level of resources; i.e., if all fi = fi,0). If attack is not successful, a war ends
in a draw.
We assume that attacks proceed through one or more stages. At the first
stage, the target is the wealthiest border community of the weakest neighbor.
The victim repels the attack successfully with probability Qij = 1 – Pij. If the
attack was successful, the aggressor proceeds to attack the superior of the target. Now the probability that the victim repels the attack successfully is reduced
to (1 – )Qij, where 0 ≤ <1 is a parameter characterizing the ‘loser effect’ (e.g.,
due to demoralization). If the second attack is successful, the aggressor proceeds to attack the superior of the superior of the target and so on. The process
stops when an attack is repelled or when the chief community of the victim polity is conquered. In the former case, the aggressor seizes a part of the victim
polity that was subordinate to the community attacked at the last successful
attack. In the latter case, the whole victim's polity is seized.
Linearization and promotion. Polity i attempts to maximize the flow of
tribute by the processes of linearization and promotion, after Flannery (1972),
Sergey Gavrilets, David G. Anderson, and Peter Turchin 157
subject to geographic restrictions and restrictions on the number of subordinates. If the chief community i has an open control slot, it will control polity
j directly. If there are no open control slots, then the chief community will control directly the L wealthiest communities chosen (i.e., promoted) from the set
of its L subordinates and the newly conquered polity j. The remaining
(i.e., the poorest) community will be demoted and reattached to its geographically closest neighbor of the higher rank (i.e., by-passed in a process akin to
linearization). If this neighbor has already filled all its control slots, further rearrangements will follow according to the same strategy.
Costs. Different actions (i.e., attack, defense, rebellion, or suppression of
rebellion) reduce the actual resource level for all participants by a factor (1 − c)
where the cost c of an action is equal to a constant δ times the probability of
loss for the winner (0 < δ ≤ 1). That is, if Pij is the probability that an attack
of polity i on polity j is successful, then the cost of a successful attack is
c (1 Pij ) ,
(Eq. 3a)
whereas the cost of an unsuccessful attack is
c Pij .
(Eq. 3b)
This simple model captures the idea that more likely outcomes are less
costly to all participants. For attacks involving several stages, costs are combined multiplicatively.
Resource dynamics. Each year the actual resource level fi grows towards
its baseline level fi,0 at an exponential rate. Specifically, we define the half-life
of resource recovery r measured in years so that it takes r peaceful years for the
resource to grow from 1 − δ to 1 − δ/2.
Implementation rules. We use a ‘parallel’ implementation of the model in
which different actions happen simultaneously rather then sequentially.
To handle multiple events potentially involving the same polity we use the following rules: 1) A polity that is subject to a rebellion does not attack other polities. 2) A polity that is subject to a rebellion is not attacked by other polities.
(The justification: since dealing with the rebellion will make the polity weaker,
potential attackers would prefer to wait and attack later.) 3) If there are multiple
rebellions within a polity, the polity's power is divided proportionally and multiple suppression attempts occur simultaneously.
Supplementary Information
1. Sample movies with α = 1 and α = 2. Other parameters are at the midpoints of the ranges used (S = 6, = 0.3, θ = 0.2, L = 6, τ = 10).
The movies are currently available at http://neko.bio.utk.edu/~sergey/
chiefdoms/chiefdoms.html.
2. Detailed simulation results for S = 4, S = 5, S = 6.
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Cycling in the Complexity of Early Societies
The files are currently available at http://neko.bio.utk.edu/~sergey/chief
doms/chiefdoms.html.
3. Effects of parameters on the properties of the system.
The files are currently available at http://neko.bio.utk.edu/~sergey/chief
doms/chiefdoms.html.
Acknowledgement
We thank the reviewers for valuable comments and suggestions. This research
was supported by a Guggenheim Fellowship (SG) and by the National Science
Foundation Grant NSF-HSD SES-0527720 (PT).
5
Demographic-Structural Theory
and the Roman Dominate
David C. Baker
Abstract
This article uses the theory of secular cycles to examine the Eastern and Western Roman Empires in roughly 285–700 CE. The analysis suggests that
the Eastern Empire conforms to an almost ‘standard’ cycle during that time.
The Western Roman Empire, on the other hand, appears to expand until
350 CE and then decline again, long before the Germanic invasions of the fifth
century. This decline may have been due to elite dynamics and the extremely
top-heavy social pyramid in the fourth century West. Elite overproduction and
infighting may have cut short the West's expansion phase and led to a premature decline. If correct, it is possible that demographic-structural theory explains the decline and fall of the Roman Empire.
Keywords: Cliodynamics, Roman Empire, Dominate, population, history.
Introduction
The work of Peter Turchin over the last decade has shown that population pressure exerts a powerful influence over socio-political instability, historical
events, and the ebb and flow of state power (Turchin 2003, 2006; Turchin and
Nefedov 2009). The dynamics can be identified in cycles of a few hundred
years of expansion and contraction.1 One interesting test of theory has recently
been done on Pueblo societies by Kohler et al. (2009: 290–291). Here is
a rough overview of the theory. When a population is low, there is plenty of
food and a labour shortage, and so food prices are low and wages are high.
A population enjoys a decent standard of living. This dynamics translates into
political stability. As a result, the population tends to grow. This is the expansion phase. Eventually a population approaches its carrying capacity resulting
in shortages of food and an oversupply of labour. Prices rise, wages drop, and
the standard of living declines. The average person is paid less and has to pay
more for the basic essentials. Famines increase in severity, the susceptibility of
1
The average appears to be roughly 300 years for a full cycle, but depends greatly on specific conditions.
History & Mathematics: Trends and Cycles 2014 159–189
159
160
The Roman Dominate
people to disease also increases, as does the possibility of widespread epidemics. At the same time, it is a ‘golden age’ for the elite. Landowners pay lower
wages and charge higher rents. Middling landowners are forced off their farms
and land is concentrated in the hands of the few. The inequality gap widens.
Elite numbers and appetites grow. This is the ‘stagflation’ phase (Turchin and
Nefedov 2009: 10–13).
Then a society hits a crisis. People starve, social cohesion collapses, the
number of people living at subsistence level grows, grain reserves disappear,
diseases ravage a malnourished population, there are rural and urban uprisings
and, ultimately, the population declines. As the general population shrinks, the
elites, cushioned by their status and their wealth, do not die at the same rate.
The social pyramid becomes top-heavy. Elites begin to see their incomes
shrink. The result is elite infighting and competition for the resources of the
state. In this period faction and civil war are prevalent. Thus the first crisis,
spurred mainly by demographic causes, is followed by a second crisis or ‘depression’ which is largely man-made. The man-made crisis holds recovery
down, and this can last for decades. Eventually, however, a population does
rebound. Elite numbers are reduced. Low numbers in the general population
combined with high wages and low food prices lead to another period of expansion, peace, and stability.
In this paper I apply the demographic-structural theory to the period of the
Roman Dominate. First I review the two secular cycles that were experienced
by the Roman Republic and Empire before 285 CE. Next I consider the demographic-structural trends in the Eastern Empire between 285 and 628 CE. Then
I look at the divergent cycle in the West between 285 and 400 CE and possible
demographic-structural explanations for the downfall of the Western Roman
Empire.
The Republican Cycle (350–30 BCE) and Principate Cycle
(30 BCE – 285 CE)
Rome underwent two previous cycles that have been examined by Peter Turchin and Sergey Nefedov in Secular Cycles (2009). There is even a theoretical
case to be made for an even earlier cycle spanning 650 to 350 BCE, seeing expansion and stagflation for the first 150 years, and crisis and depression falling
around the overthrow of Tarquin the Proud and the establishment of the Republic. The Republican Cycle entered an expansion phase during which Rome established hegemony over the Italian peninsula from c. 350 onward. The population losses of the Second Punic War (218–201), an exogenous variable, might
explain the elongated duration of the Republican cycle. Stagflation set in
around 180, and a disintegrative trend began somewhere between 133 and 90,
more likely the latter, and lasted through the wars of Sulla, Caesar, and the Triumvirate until around 30 BCE (Turchin and Nefedov 2009: 176–210).
The following period, the Principate cycle (30 BCE – 285 CE), precedes
David C. Baker
161
the one on which I focus in this article. The Roman Empire experienced growth
in the first and second centuries CE, crisis following the Antonine Plague in 165
and lasting until 197, and a secular ‘depression’ of elite infighting in the Third
Century Crisis (197–285).
In general I am in agreement with Turchin's findings, excepting one caveat.
Turchin states that the expansion phase (27 BC – 96 CE), which according to
the theory should have been stable, was ‘somewhat marred’ by political instability in the ruling class. He is referring to the violent overthrow of Caligula,
Nero, Galba, Otho, Vitellus, and Domitian (Table 1). He dismisses them as
mere ‘palace coups’. He then plays down the severity of the civil war following
Nero's death, 68–69 (Turchin and Nefedov 2009: 211). All this might be taken
by some historians of the period as an understatement and perhaps a hasty dismissal of something that might expose a weakness in the theory or necessitate
a refinement of the notion of elite dynamics. At any rate, the presence of such
sustained elite conflict, to speak nothing of the rising tension at the end of
the reign of Tiberius, is a too glaring variable to be quickly passed over.
Yet such a dismissal of the first century unrest is unnecessary even within
the theory. Rural settlement patterns show that the population in Italy peaked in
the first century CE, unlike in most other provinces of the Empire, which continued to flourish until the second century (Fig. 1). In the second century, while
Britain, Belgica, Gaul, and Spain continued to grow, the population of Italy
actually fell by 14 per cent. Even Turchin acknowledges this fact in his examination. There is no reason why this fact cannot account for the growing tension
among Italian elites at the end of the reign of Tiberius, during the reign of Caligula, and also the periods of violence in the late sixties, and above all the localised nature of a great deal of the first century unrest within Italy.
Nor should Italy's first century peak come as a surprise. Unlike the Social
War and the wars between Marius and Sulla in the Republican cycle, also explored by Turchin, the majority of the most brutal campaigning under Caesar,
Pompey and later Octavian and Marc Antony, was held outside of Italy, in
Spain, Africa, and above all in Greece. Although Italy undoubtedly experienced depopulation, not to mention the elite proscriptions of the second triumvirate, the ravages of actual military campaigning fell elsewhere in
the Empire. In 49 CE, Caesar took Rome with ease and hounded Pompey out
of Italy, while the most decisive battles of this latter part of the Republican
cycle: Pharsalus, Philippi, and Actium took place in Greece. The shortness
of Italy's period of expansion (27 BCE – 60 CE) as opposed to the flourishing
of the Empire (27 BCE – 165 CE) might therefore be explained by the fact
that the later campaigning of the Republican crisis (49–30 BCE) largely
spared Italy, unlike the earlier part of the crisis (91–70 BCE). Thus it is conceivable that the Italian population might have recovered earlier than the rest
of the Roman Empire.
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Table 1. Sociopolitical instability in Roman Empire, 0–100 CE (an
expanded list following Turchin and Nefedov 2009: 222)
Year
15
16
19
23
24
29
30
31
37
37
38
39
41
42
55
59
60–61
62
62–63
64
65
66–70
68
69
70
70
79–80
89
93–96
95
96
Event
Disturbances at Rome
Revolt of Legions in Pannonia and Germania
Alleged murder of a rival Germanicus by Piso, supposed acolyte of Tiberius
Mysterious death of Drusus, who had shared tribunician power with Tiberius
Rebellion of the slaves in southern Italy
First minister Sejanus begins purging senatorial class of all opponents
Sejanus exiles members of imperial family, some of whom die mysteriously
Sejanus falls from favour and is executed
Tiberius dies having become unpopular for his informers and treason trials
After a brief period of popularity, Caligula begins persecuting nobles
Caligula executes people without full trial
Famine strikes, Caligula seizes property of the wealthy, executes senators
Assassination of Caligula; proclamation of Claudius, stability returns
Conspiracy at Rome (Scribonianus)
Nero allegedly murdered Britannicus, a rival to the throne
Disturbances at Pompeii, Nero orders the murder of his mother
British revolt
Nero executes his ex-wife, Octavia
Persecution of senators for treason
Fire of Rome and disturbances
Conspiracy at Rome (Piso)
Jewish revolt
Uprising against Nero (Vindex and Galba), flight and forced suicide of Nero
Civil war. Galba destroys several towns, executes senators and knights without
trial, murdered by army, Otho succeeds, is beaten by Vitellius, and commits
suicide, Vitellius conducts a series of tortures and executions, and is killed by
Vespasian's men while attempting to flee
Uprisings in Egypt, Gaul, and Germania
Alleged string of ‘false Neros’ and conspiracies against Vespasian
Rebellion of Terentius Maximus
Revolt of Saturninus
Sharp rise in persecution of dissidents
Conspiracy at Rome
Murder of Domitian, accession of Nerva
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David C. Baker
Proportion of Sites Occupied
100
90
80
70
Western Empire
Italy
60
0
100
200
300
Year CE
Fig. 1. Proportion of rural sites occupied (per cent of the peak value)
in Italy compared to the whole of Western Empire (data from
Lewit 1991)
Trends in the Eastern Empire (285–628 CE)
The Dominate cycle developed in different ways in the two major parts of the
Roman Empire. The Eastern Empire after 285 enjoyed a period of demographic
growth and economic prosperity throughout the fourth and fifth centuries, continuing until the Justinianic plague struck in the mid-sixth. The West also enjoyed a partial recovery after 285 and it lasted until the mid-fourth century,
after which there was a sharp decline and eventual collapse.
Settlement patterns in northern Syria show that the population grew to
a peak around 540 CE, then stagnated and declined into the eighth century. For
example, east of Antioch, villages sprang up in the first century CE, and then
there was a decline during the Third Century Crisis, followed by growth in
small-scale farming and the development of new fields. Growth came to an end
around 550, after which sites were abandoned (Gatier 1994: 17–48). In Greece,
there was growth in rural settlements during the fourth, fifth, and sixth centuries.
This trend is seen in surveys in Attica and Boeotia. At Corinth in the same period,
there was a demographic recovery to a level which had not been seen since the
time of Alexander the Great in the fourth century BCE. The same pattern can
be seen in Methana, which saw nine sites occupied for the first time around
300 CE, and thereafter site numbers continued to grow (Alcock 1993: 38–48;
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The Roman Dominate
Bintliff 1994, 1997). In the eastern desert of Egypt, at Bir Umm Fawakhir,
a Byzantine gold mining town developed in the 400s and was occupied for
many years until it was abandoned at the end of the 500s (Meyer 1995). At
Ephesus, many parts of the city were being redeveloped in the fifth century. All
signs point to new buildings being erected as late as 600. Wealthy households
on Embolos street were exquisitely decorated during the late 300s or early
400s. In 614, a fire destroyed these buildings. It is telling that they were not
rebuilt (Foss 1977). Similar trends can be found all over the Eastern Mediterranean (for a survey, see Chris Wickham 2005: 442–453).
In the prosperous fourth century there was more equality among elites, but
few hyper-rich landowners. Most Eastern senators were elites on a provincial
level, and could not yet threaten the emperor (Wickham 2009: 37). The 300s
were clearly an expansion period. Archaeological evidence from Northern Syria shows that there were many small landholders and very few large estates
(Tate 1992). In Egypt tenant leases were short, peasant landholders were numerous (Fig. 2), wage labourers experienced high wages and low prices, and
there were no attempts by fourth-century Egyptian landholders to tie their peasants to the land (Bagnall 1993: 110–123, 148–153).
80
Family
Cultivated
Farms:
10-39 arouras
Proportion
60
40
20
Small Holdings
(below
subsistence):
0-9 arouras
Mid-size Farms
(hiring one or
two wage
labourers):
40-70 arouras
Large Estates
(tenants,
labourers,
slaves):
70-150 arouras
0
Fig. 2. Frequency distribution of farms by size: Kanaris, Egypt, the
fourth century CE (data from Bagnall 1993)
However, in the 400s one begins to see growth in the number and size of large
estates in the East. Landholders began to acquire trans-regional property, rather
than holdings in just one province (Sarris 2004). This prosperity was the classic
David C. Baker
165
result of an increase in the availability of labour, a decrease of wages that landholders had to pay, a rise in food prices, and consequently a rise in the incomes
of landholders (Turchin and Nefedov 2009: 10–11). In the fifth century, the
East began to acquire more elites at a time when the West was already glutted
with the hyper-rich. An increase in elite numbers and wealth is a symptom of
stagflation. The senatorial order expanded rapidly during the fifth century, particularly in the reign of Marcian (450–457). Stratification and inequality also
became a problem. Stratification culminated with the highest ranking elites, the
illustres, gradually excluding the less wealthy elites, the spectabiles and clarissimi, from the senate altogether by the reign of Justinian I (527–565) (Haldon
2005: 39).
The problem of intraelite conflict appears in Byzantine history after the
death of Marcian in 457. The reign of his successor, Leo I (457–474), was
marked by increased tension between the old Byzantine elite and the Isaurian
faction, whose new and disproportionate influence they resented. While the
reign was generally stable, it was marked by a number of assassination plots
between the two camps. Leo I nevertheless ruled for a long time and died of
natural causes at a ripe old age. The same could not be said of his grandson,
Leo II (474), who ruled for less than a year before dying under suspicious circumstances. His father, Zeno, an Isaurian who had married into the dynasty,
became emperor, but was soon overthrown by a revolt that slaughtered many of
his Isaurian officers. Zeno fought his way back to the throne, but elite revolts
persisted – in stark contrast to the stable fourth and early fifth centuries (Table 2). Elite competition exploded into open conflict in the 490s (Williams and
Friell 1999: 171–184). The reigns of Anastasius (491–518), Justin (518–527)
and Justinian (527–565) sustained a precarious equilibrium fraught with many
court intrigues and noble plots, where the emperor had to constantly remain on
his guard. Even the glorious reign of Justinian was witness to the Nika Revolts
in 532, in which the senators were heavily involved. Several changes to the
senatorial order followed the revolt. Sons of ‘full’ senators, the illustres, inherited the rank of clarissimus only. The emperor had to be petitioned for higher
rank (Haldon 2005: 39). This was an attempt to restrain elite overproduction
and to come to grips with the ‘over-mighty subject’.
Nevertheless, the wealthy upper orders of illustres continued to multiply
and proliferate. The lower spectabiles lost a lot of their military and administrative positions to the ever-growing horde of illustres. The late 530s saw the creation of ranks higher than that of illustris, those of magnificus, gloriosus, and
later, the superlative gloriossisimus. The title of illustris was further devalued
by being held by provincial elites (Ibid.: 40).
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Table 2. Sociopolitical instability in the Eastern Empire, 285–700 CE
(data from Williams and Friell 1999)
Year
306–309
311–313
316–317
324–325
351–353
353
364
365–366
378
387–395
450
471
474
475
476
479
484
484–488
492–497
512–515
532
565
574
582
588
602
608–610
602–628
634–718
Event
Galerius intervenes in Western infighting with limited success
Galerius dies, Maximin and Licinius compete for control of East
Licinius fights Constantine, peace and compromise
Licinius fights Constantine again, surrenders and later is killed
After a series of civil wars and coups in the West, Eastern emperor Constantius II goes to war and wins the entire empire
Gallus, Caesar of the East, is executed for irresponsible governance
Empire is split once again, Valens rules East
Revolt of Procopius
Valens killed at Adrianople
Theodosius I intervenes in Western infighting
Pulcheria and Marcian openly dispute succession with Chrysaphius
Zeno and the Isaurian faction displace the king-maker, Aspar
Leo II allegedly poisoned by Isaurian faction
Riots force Zeno to flee Constantinople, usurpers fight amongst themselves
Zeno besieges Constantinople
Revolt of Marcian the Younger
Revolt of the Samaritans
Revolt of Illus
The Isaurian War
Balkan Rebellion
Nika Riots
Clandestine succession engineered by Callinicus
Abdication of Justin II due to insanity
Alleged poisoning of Tiberius II
Mutiny on the Persian front
Mutiny on the Danube and murder of Maurice by Phocas
Civil war and murder of Phocas by Heraclius
Persian-Byzantine Wars
Arab Conquests
It is important to note, that for all the losses inflicted on the population by the
Justinianic plague in 541 and recurrent plague outbreaks in the following decades, there was no successful and permanent coup against an emperor until the
year 602. This lies in sharp contrast to the tumultuous elite dynamics found in
the West in the fourth and fifth centuries.
One more measure of the Eastern Imperial cycle ought to be mentioned
here. If susceptibility to foreign invasion is indeed a symptom of secular crisis
and depression, it is also reflected in the history of the Eastern Empire. It is
interesting to note that between the periods 296–502 and 502–628, the incidence of Persian invasions of Byzantine territory increased eightfold, despite
167
David C. Baker
Number of Incursions per Half-Century
the fact that the former period was nearly twice as long as the latter (Fig. 3).
Afterward both the Eastern Empire and Persia collapsed from exhaustion and
were overwhelmed by the Arab Conquests that soon burst upon the East.
10
8
6
4
2
0
200
250
300
350
400
450
500
550
600
650
Year CE
Fig. 3. Persian incursions into Byzantine territory (data from Lee 1993)
One might ask whether the defeat in the Battle of Adrianople in 378, in which
the Eastern emperor Valens was defeated and killed by the Goths, provides
a counter-example. The incident is often treated as a milestone in accounts of
the decline of the Roman Empire. Yet the year 378 falls within the Eastern expansion phase. A simple explanation is that secular cycles do not dictate the
outcome of individual battles, which are determined by a tangled web of variables: tactics, supply, numerical strength, weather, topography, and countless
others. The military defeat in 378 did not signal the secular decline of the Eastern Empire. It is testament to the high social cohesion of the region that after
the Battle of Adrianople, despite the death of an emperor, Gothic forces were
unable to take Constantinople, or indeed even the nearest town (Ward-Perkins
2005: 35).
In general, it appears that the Eastern Empire from 285–700 experienced
a secular cycle that fits well with the basic model (except for its length – approximately 400 years). To summarise, there was expansion in the fourth century, stagflation beginning somewhere in the fifth century, a crisis after the
mid-sixth century, and depression in the upheavals of the seventh.
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The Roman Dominate
A Possible Western Disintegrative Trend (c. 350–400 CE)
The Third Century Crisis resulted in a great deal of elite conflict and a decline
of the general population. By 285 the population was low enough to begin expanding again. Historiography is coloured by debate on when this expansion
came to an end. A number of historians have argued that there was very little
decline around the year 400 and see a ‘cultural transition’, while still others
refuse to see any decline or collapse whatsoever.2 Studies arguing for various
shades of continuity and cultural transition tend to downplay signs of economic
decay and the violent nature of many Germanic incursions, arguing for a ‘natural’ and ‘organic’ process. There was indeed a Western recovery after 285 continuing well into the fourth century. However, for some reason that recovery
failed to match the trends seen in the Eastern Empire. Within the period 350–
400 population recovery stalled. Settlement patterns suggest that the population
stagnated, declined, and fell to levels that can only be described as catastrophic,
particularly in Belgica and North Gaul (Fig. 4).
While the consensus among historians is that rural settlement patterns in
the Eastern Empire undoubtedly indicate a form of growth, there are some reasons for caution when it comes to settlement patterns in the West. Rural sites
were sometimes big, suggesting that many of them were possibly ‘commercial’
farms, rather than family farms. Thus, the decline in the number of settlements
in Western Europe may only tell us about the health of one sector of the economy: the sector that was ‘tied into commercial relations’ and produced for the
market. Of course, this argument ignores the fact that even if all rural sites that
have been excavated over the years were larger farms, an index of economic
development might at least to some extent imply trends in demography. While
signs of settlement abandonment are not perfect indicators of depopulation and
must be used with caution, there is not yet an alternative explanation for this
trend that decisively discounts depopulation as a factor, much less proving that
the population remained stable. The best arguments put forward now only indicate that settlement occupation ‘does not necessarily’ indicate a depopulation
and abandonment of land (Chavarría and Lewit 2004: 31).3
2
3
While the works are too numerous to list here, authors include: W. Goffart, R. W. Mathisen,
P. Amory, D. Shanzer, G. W. Bowersock, and T. Lewit. Merovingian continuity also figures
heavily in the controversial thesis of Henri Pirenne. While refreshing, stimulating, and dominating in academic settings, it has had very little impact on popular perception of the era.
In general, the world does not distinguish between growth in the first half of the fourth century
and signs of decline in the second half, but assign grow to the entire period (see also Chavarría
2004). The fourth century trends in Spain, however, particularly in South Spain, seem to differ
greatly from those seen in Britain, Belgica, Gaul, and Italy, and the work is largely preoccupied
with explaining trends of the fifth century.
169
David C. Baker
100
North Gaul
Percent Depopulated
80
Belgica
60
Britain
North Spain
South Spain
40
South Gaul
20
Italy
0
By 400 CE
By 500 CE
Fig. 4. Proportion of rural settlements that were completely depopulated (showing losses from peak levels c. 350; data from
Lewit 1991)
Another objection is that the degree of depopulation inferred from settlement
patterns appears to be too high. What could cause it: a plague similar in magnitude to the Black Death, impact of Germanic invasions, or mass migration to
the cities? There is no evidence for any of such explanations. Massive immigration to the cities is further implausible given that cities were falling into decline
in this period. However, few historians have yet taken into account demographic-structural theory, which suggests that depopulation often does not require a gigantic catastrophe, but happens more or less gradually as part of
a disintegrative phase.
The economic evidence displays the same trend as the decline of rural settlements. After a brief period of recovery in the 300s, the Western economy
apparently fell to a nadir point which was lower than anything seen in the disintegrative phase of the previous century (Table 3). Iron production may have
recovered c. 300–350, but it fell to an all-time low by the year 400. Thus, only
one-tenth of iron sites in Britain survived (Jones and Mattingly 2002: 180–
196). A study of mines in the Iberian Peninsula shows that of 173 Roman mines
in Spain, fewer than 21 were operating in the late 300s, and this number shrank
again to only two in the 400s (Domergue 1990: 215–224). An impressive group
of iron forges in southwest Gaul, which began recovering as early as the third
century, did not make it out of the fourth (Cauuet et al. 1993: 68–69, 123–125).
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The Roman Dominate
In eastern Gaul, another iron production site shows the same pattern. It was
active between the first and fourth centuries, but charcoal dated by radiocarbon
fails to show any operation past 400 (Mangin 1992: 222–242).
Gold mines follow a similar pattern. The coins at Tharsis in Iberia are dated no later than 350, while at Vipasca there is only evidence of dwindling occupation in the fourth century with nothing beyond. At Rio Tinto, a small settlement had coins from the reign of Honorius possibly dating as late as
the 420s, but no later. In Britain gold mines were active until c. 383. In Dalmatia, mining halted during the Third Century Crisis, revived on a small scale in
the fourth century, but by 400 these mining operations had ceased altogether.4
It is unlikely that these large mines were replaced by ‘small-scale’ sites
producing at the same level – or anywhere near it. Atmospheric pollution from
mining descended on Greenland and became packed down under layers of
snow and ice, with the spring thaw dividing one year from the next, similarly to
growth rings in a tree trunk.
Table 3. Last known mining and smelting activity from the West to
the East
Year
300s
300s
300s
Early 300s
417
By 400
417
417
By 400
360
By 550
By 550
500s
600s
400–600
600s
530
Location
Lusitania, North Hispania
Forest of Dean, Britannia
Weald, Britannia
Les Martyrs, Southwest Gaul
Bituriges, Central Gaul
Autun, East Gaul
Sardinia
Noricum
Illyricum
Dalmatia
Attica, Greece
Pangaios, Greece
Inner Egypt
Red Sea Coast
Cilicia
Cappadocia
Armenia
Source: see Domergue 1990: 215–224; Cauuet et al. 1993: 68–69, 123–125; Mangin
1992: 222–242; Hong et al. 1994: 1841–1843; Edmondson 1989: 84–102.
4
See J. C. Edmondson 1989: 84–102. While the research plainly shows the closure of most western
mines by 400, the author stresses a fifth-century ‘restructuring’ to ‘small-scale’ production for
‘local economies’. It is revealing that no such ‘restructuring’ happened anywhere in the East (see
Ibid.: 92).
David C. Baker
171
Ice cores taken from Greenland allow us to devise a timeline for hemispheric
pollution from lead production. They show that lead was being produced at
around 80,000 tons per year at the height of Roman power. Production peaked
around the time of the Principate's expansion phase, when it attained a level not
reached again until 1800. The 300–350 recovery did not reach peak Antonine
levels, and after the West's collapse production shrunk from 80,000 tons to only
a few thousand tons per year (Hong et al. 1994: 1841–1843). Copper mining
and smelting emissions show the same trend. The Roman period marked
a sharp rise in copper production to a peak of 15,000 tons per year in the first
century CE and fell to 2000 tons in the fifth century before declining further
(Hong et al. 1996: 246–249). The lead figures are corroborated by another unusual source, a Swiss peat bog, which also serves as an archive of atmospheric
metal deposition. The surface layers are isolated from groundwater and surface
water and receive inorganic solids from atmospheric deposition. As a result the
peat bog is a record of changing lead and scandium levels for the entire Holocene. In conclusion, the peak of Roman mining was in the first century CE.
Production remained high until it declined in the third century, with a possible
recovery thereafter, but production slowly dwindled in the fourth century to
an early medieval nadir (Shotyk et al. 1998: 1635–1640).
The number of shipwrecks discovered in the Western Mediterranean drops
significantly for those dated in the late fourth century (Fig. 5). What is more,
the number of shipwrecks found at the bottom of the sea and dated by archaeologists follows precisely the same pattern as what has been predicted for both
the Principate and Dominate secular cycles. The number of shipwrecks found
in the entire third century is only 49 per cent that of the second century.
The period 300–350 indicates a recovery in shipping but 350–399 yields less
than 13 per cent of the ships that sunk in the preceding fifty years. The entire
fifth century yields only 37 per cent of the fourth century total, including the
decline period (Parker 1992: 13–15). The use of shipwrecks as an indicator of
total volume must be done with caution, however, but it demonstrates an interesting parallel to the prevailing trend in other areas.5
In addition to many rural sites being abandoned, many others show a decline in condition. Slap-dash architecture and make-shift alterations from
5
Andrew Wilson (2009: 219–229) points out that the decline may have much to do with the shift
from the use of amphorae to barrels for containing wine. Wilson also treats the second century
peak as a statistical anomaly and distributes them among other periods, by using a range of probability for a wreck sinking in a particular year rather than using Parker's midpoint. This shifts the
peak to the first century CE. In the same book, see William Harris (‘A Comment on Andrew Wilson: “Approaches to Quantifying Roman Trade”’, Ibid.: 259–260), who points out that neither
textual nor material evidence on land leads us to suspect a decline of trade after 100 CE and that
the barrel hypothesis seems inadequate, since it is likely many regions of the Roman Empire were
suffering deforestation at that time. Harris also points out that metal ingots in shipwrecks follow
a contradictory trend from the amphorae first century peak.
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The Roman Dominate
the fourth and fifth centuries are often seen in villas. Certain parts of sites were
abandoned while only sections of them remain occupied. At Horath in the
Hunsrück, for instance, the principal building was definitely abandoned with
only the annexed buildings being used. The same was the case at Famechon in
Picardy. Even more, at Emptinne-Champion in Belgium, only part of the central building was occupied while the rest of the villa and the baths were deserted or even demolished (van Ossel and Ouzoulias 2000: 144–147).
160
Number of Roman Shipwrecks
140
120
100
80
60
40
20
0
0
100
200
300
400
500
Year CE
Fig. 5. The number of shipwrecks in the Western Mediterranean (data
from Parker 1992: 13–15)
Cellars were reused as bakeries or filled up with debris, a kitchen was used as
a boiler room, Roman living rooms were partly buried or transformed into firepits, an ornate gallery full of mosaics was used as a tool workshop, and a high
quality building was transformed into a cowshed, and central heating was
abandoned (van Ossel and Ouzoulias 2000: 147–148; Wightman 1985: 257).
The utilitarian use of villas may well indicate a form of living that is closer to
a subsistence level and it almost certainly indicates a drop in the number of
inhabitants at the site. However, alternative explanations involving ‘cultural
choice’ have been put forth, along with the argument that a wood building is
not inherently better than one built of stone, which is a convenient argument
since it leaves no evidence and one is free to imagine as an elaborate a building
as one pleases (for instance, Etienne Louis 2004).6
6
The works of T. Lewit will be highlighted later on.
David C. Baker
173
Paleopathology, or the medical examination of ancient corpses, shows the
deterioration of Western villas was matched by the deterioration of people's
health. Exhumations from a site at Saint-Martin-de-Fontenay, modern Calvados, in west Gaul shows that in the fourth century CE the life expectancy was
31.5 years. This was paralleled by a site at Frénouville which in the fourth century had a life expectancy of 32. The results of the dig at Calvados show the
period that was marked by ‘socio-economic troubles’. A low life expectancy
was accompanied by poor dental conditions, indicating malnutrition. Roughly
30 per cent of the teeth of intact mandibles were either rotten or missing. With
an average age of 31.5 this is considerable. There were also a number of anatomical peculiarities indicating intense muscular strain on the legs, the front of
which had bones that were almost grotesquely bowed inward (Pilet et al. 1994:
80–81, 93–96, 123–125, 145). A reduced stature might be attributed to poor
nutrition caused by population pressure. Population pressure mounts up in the
second century as is predicted for the Principate cycle, and it is subsequently
relieved during the devastation of the third. The Dominate expansion phase of
the fourth century witnesses population growth again, with pressure reducing
the average stature, while the depopulation of the fifth century appears to have
led to record heights.
A useful survey of settlement abandonment was devised by Tamara Lewit
(1991). Lewit looked at two hundred rural sites from several regions in the
West and determined when they were occupied. She then gave the proportions
for each half-century in the form of a percentage of the highest level of occupation. In the same fashion, Lewit also determined the percentage of the other
sites which were still expanding or ‘remaining prosperous’. Lewit's survey remains one of the best quantitative works on rural settlements, even two decades
later.7 A re-examination of her numbers reveals an interesting pattern.
7
Nevertheless, Lewit herself is a staunch advocate of continuity. Lewit's presentation of the percentages downplays the idea of gradual but severe decline in the late fourth century, even though
some of the regions seem to indicate it. She is incredulous at depopulation after 400. She advances an array of arguments to explain where all the people went and how continuity was maintained. Of course, if there was a more gradual decline from 350, it defeats necessity of such explanations. Subsequent works of Lewit follow the same theme of continuity (Lewit 2003, 2009).
For a critique of this article see Bowes and Gutteridge 2005.
174
The Roman Dominate
European average,
Including Scandinavia
and the East
Belgica, Gaul, SW Germania,
And Britain
Italy, Spain, Portugal,
and the Balkans
Fig. 6. Average heights (cm) of men and women from a sample of
9477 skeletons from the first century to the nineteenth (data
from Koepke and Baten 2005)
In Lewit's presentation, the settlement abandonment percentages were taken
from a peak index, whenever the peak occurred, whether it was the first century, as it was for Italy, the second century, where most regional peaks occurred, or the fourth century, where South Gaul and South Spain evidently
peaked. These multiple indexes unfortunately detract from the clarity of the
presentation. Accordingly I will use a second century index for all regions. The
two of the seven regions that exceeded their second century levels will simply
score over 100 (Table 4).
Table 4. Index of rural settlements occupied by region and by period
(2nd Century Index) (data from Lewit 1991)
Region
Britain
Belgica
North Gaul
South Gaul
North Spain
South Spain
Italy
200–250
98
91
82
94
96
109
90
250–300
94
43
45
73
61
100
71
300–350
98
55
64
104
93
109
85
350–400
79
36
55
104
96
100.5
81
400–500
47
19
9
73
54
67
71
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David C. Baker
The period 200–250 CE shows a decline from the second century peak, probably due to the Antonine Plague that initiated the crisis phase of the Principate.
The period 250–300 CE clearly reflects a deep decline of the worst infighting
of the Third Century Crisis and secular depression phase. It is interesting to
note that a region like Britain, which avoided the bulk of the fighting of this
phase, only declines modestly, more like a mild recoil from the carrying capacity than a severe decline from a manmade crisis. The period 300–350 CE witnesses a universal period of growth and recovery, which heralds the beginning
of the Dominate expansion phase. Then in the period 350–400 CE this growth
is dramatically cut off, in contrast to what we know of settlements in the Eastern Empire. In Britain, Belgica, North Gaul, and Italy there is slight or even
considerable decline well before the Germanic invasions. There are, of course,
regional variations. South Gaul evidently sees no growth but only stagnation,
while Spain sees stagnation or even mild growth. Lewit's figures for South
Spain were inflated, based on only one study where 25 per cent of sites surveyed in the Guadalquivir valley possessed no earlier pottery. This contrasts
dramatically with the drop in the fifth century. So instead an average between
the two periods is taken. Also Lewit inflates the figures for Britain by 8 points
after 350 because she does not accept the absence of post-350 coins as conclusive, and so counts them all as occupied. Here the original figure of 79 is upheld. Either way it demonstrates decline from the previous period well before
the Germanic invasions.
It is important to note that the occupation index includes those settlements
that declined, but were not totally abandoned after the second century. Lewit
also gave figures for settlements that were expanding or were ‘remaining prosperous’ in each fifty year period. The remainder from these two categories
shows the percentage of settlements that were neither expanding nor stagnating,
that is, contracting: either showing signs of decline, partial abandonment, or
destruction. The fourth century figures for Britain, Belgica, and North Gaul are
worth noting (Table 5).
Table 5. Percentage of occupied but contracting rural settlements
(data from Lewit 1991)
Region
Britain
Belgica
North Gaul
South Gaul
North Spain
South Spain
Italy
200–250
8
18
10
19
3
3
N/A
250–300
20
57
60
29
40
20
N/A
300–350
16
45
37
0
4
9
N/A
350–400
38
64
44
12
11
0
N/A
400–500
N/A
N/A
N/A
N/A
N/A
N/A
N/A
176
The Roman Dominate
Lewit states that it is startling that the 400s saw such a rapid decline because:
(1) it followed a period of continued occupation, which is only partly true, (2) it
contrasts sharply with archaeological signs of growth in 300–350 in the Eastern
Empire, and (3) it would require a massive depopulation surpassing the devastation of the Black Death to ‘account for the abandonment of nearly every farm
[sic] in North-West Europe within the space of about twenty years’ (Lewit
1991: 37–38). Fortunately, the theory of secular cycles answers each of these
points. First, the third and fourth centuries were not periods of continued occupation but one of fluctuating population levels due to the rise and fall of secular
cycles (Fig. 7). Second, the prosperity of the Eastern Empire does not dictate
a similar pattern in the West, since it is becoming increasingly clear that the
Dominate cycle evolved differently in the East. The reasons for this difference
are dealt with below: a lowered carrying capacity and the East-West disparity
in elite dynamics. Third, no holocaust like the Black Death would have been
necessary, if the decline in the West had begun earlier than 400, as has been
demonstrated with Lewit's own figures. The demographic-structural theory presents an alternative, more gradual, and therefore more conceivable, explanation
for depopulation.
Why did the Western Roman Empire Fall?
The key factor in the West's decline may have been elite overproduction.
The demographic structural theory states that a disproportionate amount of surviving elites next to a reduced common population can complicate an attempt at
population recovery. The historical record shows that while the East in the
fourth and fifth centuries had low inequality, low elite numbers, and mostly
provincial elites, each with a modest amount of wealth, the Western Empire
remained throughout the fourth century glutted with vast masses of elites and
the hyper-rich. This disparity may well have played a role in the decline of the
West as well as the survival of the East. At any rate, it is too glaring a difference to be ignored.
177
David C. Baker
Occupation Index
100
80
60
Italy
Gaul
Spain
Britain
40
200
250
300
350
400
450
500
Year CE
Fig. 7. Dynamics of rural settlement occupation for each major region
in Western Europe (data from Lewit 1991)
Firstly, we do know that the early fourth century saw an impressive boom in
large villa estates, which might indicate the concentration of land into the hands
of the few. The standard explanation, the retreat of the aristocracy to the countryside, is unlikely. Instead this pattern could be explained by an early fourth
century stagflation dynamic (Chavarría and Lewit 2004: 26–29). We also know
something about the immense inequality gap between elite and commoner at
this time. The Late Antique historian, Olympiodorus (c. 380 – ? CE), tells us
that the richest senators of the West had yearly incomes of four thousand
pounds of gold a year, while mid-level senators had around one thousand
pounds a year. A commoner, by comparison, could scratch together perhaps
five solidi in a year's toil, or less than one-fourteenth of a pound of gold.8 It is
interesting to note this disparity of wealth outstrips inequality ratios for the
stagflation period of the Principate and also the most extravagant periods of
later French or English history. Additionally, wealthy Roman nobleman Quintus Aurelius Symmachus (c. 340–405) spent around two thousand pounds of
gold at one go, on the celebration of his son's praetorship, by personally financing the games in Rome. This ritual was common among the Roman elite in Late
8
For senatorial incomes see Olympiodorus, in Photius, Bibliotheca (1920), frag. 44. For the estimate for a peasant's income see Ward, Heichelheim, and Yeo 1999: 446. This astounding inequality ratio and disparity of wealth is also dealt with in Turchin 2006: 160–161.
178
The Roman Dominate
Antiquity whenever a family member achieved such a distinction, and it was
a social obligation to match or even surpass the displays of splendour and consumption of a rival family (Olympiodorus 1920).
St. Melania the Younger (c. 383–439) came from a foremost senatorial
family. She married her cousin, Pinian, around 399. After a miscarriage of two
children they found religion, took vows of celibacy, and gave up their worldly
possessions. Pinian is said to have held an annual income of 120,000 ‘pieces’ of
gold, on top of his wife's income of about the same amount (Gerontius 1984: 15).
‘Pieces of gold’ has in the past been interpreted as either pounds or solidi. If
more realistically interpreted as solidi, that amounts to 1666 pounds annually,
and that roughly equates with what Olympiodorus tells us about the average
senatorial income. If multiplied by two, for it appears Melania held a comparable income separate of Pinian, the total income comes to around 3332 pounds
of gold annually. This point has been debated among historians. Whether or not
Melania and Pinian held a mid-level or a combined upper level senatorial income, it nevertheless appears that when they sold their lands, the sale temporarily caused panic and a fiscal crisis in the property market (Wickham 2005: 29).
Apparently one of the estates sold by Melania in North Africa was larger than
the nearest town, Thagaste, birthplace of St. Augustine (Gerontius 1984: 21).
The presence of such trans-regional hyper-rich is certainly at variance with
what one would typically expect to see of elite dynamics in a supposedly integrative period.
The paucity of sources from this period makes it next to be impossible to
find similar quantitative data for the late fourth century. However, various written testimonies confirm the income figures of Olympiodorus and those for
Melania the Younger. For instance, Ammianus Marcellinus (c. 325–390),
a prominent imperial official and the principal historian of the period, came to
Rome from Antioch and was disgusted with the decadence he saw. He writes of
a certain number of idle and frivolous senators, who gorged themselves with
food at luxurious banquets. They spent large sums of money on exotic dancers
and prostitutes.
During a food shortage in Rome, all foreigners were expelled from the city,
while the senators lobbied for three thousand dancers and ladies of negotiable
virtue to remain. The Roman elite gave hugely expensive shows featuring dramatic actors. The elite were given to the habit of conspicuous consumption, and
clothed themselves in effete, elaborately designed silk and dyed robes. They
lined the streets with gold plated statues of themselves and their ancestors.
At the baths, they were attended by as many as fifty servants. Now, some historians have suggested that Ammianus was just ‘rephrasing late antique commonplaces’ but that is precisely the point. They were commonplaces for a reason. Ammianus would hardly need to set up a stock figure to decry elite consumption unless there was something to decry. Furthermore, it is worthwhile
David C. Baker
179
to remember that where secular cycles are concerned, it is not so much the specifics of elite behaviour that are important, or the amount of elite wealth in an
absolute sense, but the gap between the rich and the poor. And that gap appears
to have been very large indeed.
Elites, like the extremely influential Petronius Probus, found political power absolutely vital to protect himself and his clan in their many quarrels with
hostile families and rival factions. Ammianus describes Probus as a man known
for his family, influence and great wealth throughout the world and his possession of multiple estates, some of which he appropriated ‘unjustly’. It was obviously an atmosphere not only of decadence but of intense intraelite competition. This is confirmed by the many court intrigues, plots, and violent coups
that characterise the entire era (Table 6). Furthermore, positions like the quaestorship or praetorship, once prestigious and influential offices along the cursus
honorum had by the fourth century become largely meaningless titles, ceremonially bestowed on the sons of rich men when they came of age. The only real
responsibility of the office was to throw a public celebration on its assumption.
This confronts one with the notion that the senatorial class was filled with the
idle rich, and only a fraction of them stood a chance of gaining any real power.9
As it happened, the richest Western families, the Anicii, the Caeonii,
the Petronii, the Symmachi, and a handful of others, owned the vast bulk of
estates throughout the regions of the Western Empire, and played a very dangerous game of faction, which often came at the expense of the state.
Table 6. Sociopolitical instability in the Western Roman Empire, 285–
476 CE (from Wood 1994)
Year
1
285
303–311
305
306
309
310
312
313
316–317
320
324
324–325
326
340
9
Event
2
Diocletian beats Carinus in battle, wrests power from him
Largest and bloodiest persecutions of Christians
Diocletian retires, Maximian forced to retire
Maxentius' rebellion, Severus is betrayed by his army
Maximian fails to overthrow Maxentius and flees to Constantine's court
Maximian betrays Constantine, later kills him; riots in Rome
Constantine invades Italy
Licinius gains control of the East
Constantine fights Licinius, a truce is declared
Licinius persecutes Christians
Civil war, battles of Adrianople, Hellespont, Chrysopolis
Licinius sent to live as private citizen but soon hung
Constantine executes his son and wife
Constantine II wars with Constans for control of the West and is killed
Ammianus Marcellinus 1973: 14.6.7–19 27.11.1–3, and 28.4.8–18. For an excellent analysis of
this source, see Matthews 1975: 1–20.
180
1
350
351
353
355
360–361
361–363
364
372
375
383
383–388
392
393–394
395–423
405–410
423–425
425–433
439
454
455
c. 457
461
465–467
472
473
474
475
The Roman Dominate
2
Western ruler Constans is assassinated and usurped by Magnentius
Constantius wars with Magnentius, Battle of Mursa Major in Pannonia
Battle of Mons Seleucus in South Gaul, Magnentius kills himself
Attempted usurpation in Gaul (Claudius Silvanus)
Julian proclaimed ruler of the West, Constantius dies on the way to
fight
Julian drastically reduces bureaucracy, executes many elites
Jovian dies, unclear by murder or natural causes
Valentinian I, emperor of the West, suppresses usurpation attempt
Valentinian II and Gratian have joint rule
Gratian assassinated by usurper Magnus Maximus
Civil war. Theodosius I emperor of the East fights Maximus and restores Valentinian II to the throne
Valentinian II is found hanged in his room, Arbogast selects Eugenius
as emperor of the West
Theodosius I elevates his son Honorius as Western emperor instead;
war
Honorius rules the West as a puppet of his generals, principally Stilicho
till he was ousted in 408; Honorius fights several attempts at usurpation
Sack of Rome, loss of much of the West
Joannes usurps the Western throne, civil war with the infant Valentinian III
Valentinian is ruled by the faction of his mother, supplanted by the
faction of Flavius Aetius
Loss of North Africa
Valentinian III treacherously murders Aetius
Valentinian III is murdered by Aetius' former faction, Petronius Maximus buys the loyalty of the army and becomes emperor, then is swiftly
murdered, a few days later the Vandals take Rome by sea and subject it
to a severe four days looting and pillage, much worse than in 410, Avitus becomes emperor, Visigoths invade Spain
Avitus overthrown by a coup of his generals, Majorian becomes emperor
Majorian tries to institute reforms that threaten wealth of the nobility,
he is killed and his fellow general Ricimer sizes power with senator
Libius Severus as his puppet
Severus dies, Ricimer rules West without an emperor, then elevates
Anthemius as his puppet
Anthemius, having defied Ricimer and fought a war against him, is
killed, Ricimer elevates another puppet, Olybrius, both men die of apparently natural causes in 472
Gundobad, a nephew of Ricimer, elevates Glycenius, an unknown
Julius Nepos, Eastern emperor Leo I's choice, deposes Glycenius
Nepos overthrown by general Orestes, who appoints the ill-fated Romulus Augustulus
David C. Baker
181
The historical record seems to imply that in the Western Empire, unlike the
East, the elites never really disappeared. The elite classes undoubtedly lost
some of their numbers in the wars of the Third Century Crisis, but it is questionable whether this decrease was enough to significantly reduce elite competition. Conversely, it appears that the events of the third century were enough to
accomplish this in the East. A combination of the Persian invasions, civil war,
the plague in the East from the 250s to 270s cited by Zosimus, the conquest of
the Palmyrene Empire, the summary execution of much of its elite, and the
sacking of Palmyra itself, seems to have been sufficient to quell the ‘overmighty subject’ of the Eastern Empire for nearly two centuries.10 As already
stated above, most elites operated on a provincial scale, large estates were rare,
and the number of middle and small landholdings was high.
In the West, third century fighting seems to have been no less severe. The establishment of the Gallic Empire in 260 did not prevent elite infighting within
that kingdom. Postumus ruled for eight years before he was murdered, and he
was followed by five more rulers within the short space of six years. However,
at the end of that period, Aurelian reconquered the entire Gallic Empire by cutting a deal with Tetricus II. In exchange for surrendering himself and his claim
to the territory, Tetricus was granted a high political office in Italy. It is possible this clemency was extended to a number of other Western elites. The Gallic
Empire fell in short order. The same clemency did not apply to the elites of the
Palmyrene empire, which saw many of them executed, even while many of its
towns were spared, and although Zenobia herself allegedly survived by blaming
the war on the influence of her fellows.11
Yet it is possible that Western elite competition did not end with the accession of Diocletian. He obtained the imperial purple by overthrowing Carinus in
a violent contest. There is no evidence to suggest that a decisive amount of elites perished in the Battle of the Margus (285) which decided the issue. It is
true Diocletian reigned through a largely peaceful period. But on closer examination, we see that he ruled for only one year alone, and then forged the Tetrarchy. On the one hand, this may be seen as a more efficient way of administering a sprawling empire, but, on the other hand, it may be seen as a powersharing deal among the elites. As it was, the peace brought about by the Tetrarchy did not long outlast the retirement of its founder. Furthermore, Diocletian is
known for making the bureaucracy larger and taxing higher than ever before.
According to the criteria, these are the traits of a stagflation phase, not the
dawning of a new expansion (Turchin and Nefedov 2009: 34). If the period
285–305 was one of dubious expansion and tenuous stability in the West,
10
For the mysterious plague which is said to have struck the Romans in their campaigns against
Persia in the 250s and 270s, see Zosimus 1982, vol. 1: 8–14, and 26.
11
For an excellent summary of the events of the Third Century Crisis see Loriot and Nony 1997:
9–17.
182
The Roman Dominate
the period 305–325 was characterised by open elite competition and a number
of violent clashes. It is noteworthy that the vast majority of such fighting took
place in the Western provinces, while the East remained relatively tame. In fact,
as Table 6 shows, this chaotic procession of violent elite competition in the
West apparently did not cease until the overthrow of Romulus Augustulus and
the ‘official’ end of the Western Roman Empire in 476.
The incidence of coin hoarding has been demonstrated by Peter Turchin to
coincide with periods of socio-political instability. The quantity of coin finds
from four excavated sites Britain, the most thoroughly studied province, shows
that hoarding peaked during the severest phase of the Third Century Crisis,
c. 260–274, when the Gallic and Palmyrene empires split off from the Roman
(Fig. 8). The reign of Diocletian marked a low point in coin hoarding, but there
was a rise during the wars of Constantine. The wars of his heirs were a period
of extremely active hoarding, surpassed only by the worst fighting of the Third
Century Crisis. There was only a slight contraction in hoarding during the usurpations and executions of the 350s and 360s. Hoarding decreased slightly in the
reign of Valentinian I and was restored to peaceful levels during the reign of
Valentinian II and Gratian, but then rose again by the end of the civil war that
followed Gratian's assassination. Hoarding stayed relatively high right through
to the turn of the disastrous fifth century.
British Coin Hoards
1.5
1.0
0.5
0.0
260
280
300
320
340
360
380
400
Fig. 8. Dynamics of British coin hoards at four sites, in percentages of
the total between 96 and 402 CE (data from Duncan-Jones
2004)
183
David C. Baker
These four sites demonstrate the near parity between the mid fourth century
hoarding peak and that seen in the worst phase of the Third Century Crisis.
Added to these are the average dates from 151 sites in Britain for the fourth
century alone and they seem to exhibit a similar pattern (Fig. 9).
Church-building in Rome yields a different but interesting pattern for elite
dynamics in the West (Fig. 10). While Gaul in section two exhibited a fourth
century peak in general economic growth before collapsing in the early fifth
century, elite-laden Rome shows growth to a peak in church-building well into
the 400s. It might be wondered why these building projects were underway
long after the West had begun to collapse. This is not so confusing when seen
in the context of elite dynamics. The fifth century peak is entirely due to private
patronage of the wealthy Roman elite (Fig. 10). In the fourth century, wealthy
individuals slowly ceased funding traditional civic architecture. Instead conspicuous consumption began in church-building, on supposed ‘religious
grounds’ to demonstrate the extent of one's devotion. This was nascent in the
fourth century, with only two of twelve churches being built by private patronage, but reached fever pitch in the fifth.
20
British Coin Hoards
15
10
5
0
300
320
340
360
380
400
Fig. 9. Dynamics of British coin hoards at 151 sites, in percentages of
the total between 294 and 400 CE (data from Ryan 1983)
While Gaul collapsed into a frontier zone in the early 400s, Rome did not fall
completely until 476. Most of the church-building happened in the period of
elite-overproduction and infighting that did not cease until the deposition
184
The Roman Dominate
of Romulus Augustulus in 476. There was no fifth century construction or adaptation definitively dated after 476, with only one possibly dated prior to 483,
and then nothing again until 514–523. Then in the sixth century there was
a contraction in the number of churches built, especially of those built by private patronage. This stands in stark contrast to the fifth century where roughly
half of the church-building in Rome was done by private patronage. This might
indicate the continued wealth stratification and conspicuous consumption of the
elite right up to the total collapse of the Empire. It certainly would accord with
the continuous infighting we see right up to 476.
By contrast to the West, the East had very few hyper-rich and saw a relatively stable chain of succession, after it was divided between Valentinian I and
Valens in 364. When Valens was killed at Adrianople in 378 he was replaced
by Theodosius I, an immensely powerful emperor, who ruled the East for nearly two decades and even expanded his influence into the West.
25
Churches Built
20
15
10
5
0
300
400
500
600
700
800
900
Fig. 10. Numbers of churches built in Rome per century (Randsborg
1991, who uses data from Ward-Perkins 1984)
The reign of Arcadius lasted another decade, 395–408 and the reign of Theodosius II lasted an impressive forty-two years until 450. As was stated before, no
successful and permanent coup was staged against an Eastern Emperor until the
year 602. That the West should have the monopoly on super-rich elites, and that
the East should be extremely prosperous and stable throughout the fourth cen-
185
David C. Baker
tury and beyond, while the West crumbled and collapsed, is hardly a coincidence.
Conclusion
In summary, I submit that the evidence from various quarters indicates that the
Eastern Empire underwent expansion and stagflation in the fourth, fifth, and
early sixth centuries as part of a more typical secular cycle. That is why it survived. The Eastern Empire enjoyed an expansion phase c. 285–450, when the
population and elite numbers were low. The stagflation phase spanned c. 450–
541, when large estates began to appear again, when elites became more numerous and powerful, and the frequency of elite infighting and socio-political
instability increased.
15
Churches Built
Imperial
Papal
Private
10
5
0
300
350
400
450
500
550
600
Fig. 11. Churches built in Rome by patronage (data from WardPerkins 1984)
The Justinianic Plague struck in 541 and reduced the common population,
gradually halting the expansion of the Eastern Empire, and culminating in the
usurpations and civil wars of the seventh century. This was followed shortly
thereafter by collapse in the Arab Conquests. By and large, the Eastern Empire
enjoyed a full secular cycle c. 285–700, marked by the typical phases of expansion, stagflation, crisis, and depression predicted by the theory.
Conversely, the Western Empire enjoyed only a temporary and failed attempt at expansion and recovery in the early fourth century. Even though the
186
The Roman Dominate
population in 285 was low enough to begin another integrative phase, and grew
admirably c. 300–350, the same force that kept the West in secular depression
in the Third Century Crisis still existed in the fourth century: elite dynamics. In
fact the inequality ratio was on an unprecedented scale in human history. Western elite infighting raged continually throughout the fourth century, in stark
contrast to the relative stability of the East. A recovery in the West seems likely
after 285, but it probably did not last much after 350. What is more, elite infighting appears to have carried on throughout this period of recovery. This is
significant since the most decisive variable which defines a period of secular
‘depression’ following a population crisis is the elite infighting which prevents
a full demographic recovery.
Therefore, within the confines of the theory of secular cycles, the Dominate conforms to the predictions laid out for it. It exhibits a number of trends
which perhaps explain the total collapse of the West and the survival of the
East. In evaluating these trends, we explore in new ways the well-travelled evidence and the age-old question: what caused the decline and fall of the Roman
Empire? Future studies along these lines may revolutionise the historiography
of Late Antiquity and irrevocably alter the discussion of questions left unanswered by older scholarship.
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6
Modeling Malthusian Dynamics
in Pre-industrial Societies:
Mathematical Modeling
Sergey A. Nefedov
Abstract
The discussion about the Malthusian character of pre-industrial economies that
has arisen in the recent years extensively uses simple mathematical models.
This article analyzes some of these models to determine their conformity with
Malthusian postulates. The author suggests two models that are more adequate
for the description of Malthusian patterns.
Keywords: Malthusianism, economic and mathematical models, population
oscillations, population growth, consumption dynamics, demographic crisis,
Cliodynamics.
Until recently, most economic historians have tended toward the opinion that
medieval economies in Eurasia had a Malthusian nature (Allen 2008: 951).
However, following the publication of Lee and Anderson's (2002) work, many
came to dispute this opinion. A discussion has arisen about how the available
data confirm the Malthusian relationship between demographic dynamics and
consumption (i.e., real wages). This discussion has largely involved simple
mathematical models of Malthusian economics.
In 1980, Lee published the first and most popular of these models. This
model describes the relationship between the real wage, wt (consumption), and
labor resources, Nt (population), using the following equation:
(Eq. 1)
wt = exp(μ + ρt + t) Nt– .
Or, in logarithmic form:
(Eq. 2)
ln wt = μ + ρt – ln Nt + t.
Here, t is time; μ, ρ, are some non-negative constants; and t is a variable
that takes into account the climatic effect and other exogenous parameters.
The factor ρ describes capital increase and technological advances, thus Malthusian economics features ρ = 0. If we take into account that t = 0 in the ideal
case, the model can be expressed with quite a simple equation: wt = С Nt– ,
where С is some certain constant. The drawbacks of this equation are evident:
a small population Nt results in a consumption rate close to infinity, while in
History & Mathematics: Trends and Cycles 2014 190–200
190
Sergey A. Nefedov
191
a large population the consumption becomes too small to ensure subsistence.
Additionally, this equation only shows the relationship between population and
consumption. The model contains no feedback to demonstrate how consumption influences population growth.
Wood (1998) has suggested one feedback option. Wood derives his equation from the same Eq. 1 as Lee, but formulates it as follows:
(Eq. 1a)
wt = θ (St/Nt) .
Here, θ is the minimum per capita consumption rate, and St is the maximum population that can subsist in the given territory when the consumption
equals θ. St can grow through technological advances, but the Malthusian case
features a constant St, St = S0. Wood believes that the birth rate bt and death rate
dt can be described with the following equations:
(Eq. 3)
bt = β0 + β1 ln wt + β2 dt ,
(Eq. 4)
dt = δ0 + δ1 ln wt + δ2 bt ,
where β0 , β1 , β2, δ0, δ1, and δ2 are certain constants. Thus, the equation below
describes population growth:
(Eq. 5)
dNt /dt = (bt – dt)Nt .
Deriving bt and dt from the system of Eqs 3 and 4 and inserting them into
Eq. 5 yields:
dNt /dt = (bt – dt)Nt = ( 0 + 1 ln wt)Nt ,
where 0 and 1 are certain constants. Substituting Eq. 1a here produces:
(Eq. 6)
dNt /dt = ( 2 + 3 ln Nt )Nt,
where 2 and 3 are certain constants. The differential Eq. 6 has the timeindependent solution Nt = N0 = exp(– 2/ 3); its chart will be a horizontal line.
According to the theorem of the unique existence of the solution, no other solutions (integral curves) may cross this horizontal line. The derivative dNt /dt is
positive below this line, in the area 0 < Nt < N0; the solutions monotonically
increase and the integral curves approximate the horizontal line. The derivative
dNt /dt is negative above this line; the solutions monotonically decrease and the
integral curves approximate the horizontal line from above. Finally, the solutions cannot oscillate: the population cannot first feature growth and then loss
due to ‘Malthusian crisis’. Wood justifies this behavior of his model stating that
Malthusian crises ‘are not a necessary feature of Malthusian systems… This
conclusion is contrary to the belief of many economic historians (e.g., Le Roy
Ladurie 1974: passim; Postan and Hatcher 1985: 69) though not to anything
that Malthus himself ever wrote’ (Wood 1998: 110).
Malthus did, however, write about population loss, depopulation:
The power of population is so superior to the power of the earth to
produce subsistence for man, that premature death must in some
shape or other visit the human race. The vices of mankind are active
and able ministers of depopulation. They are the precursors in the
great army of destruction, and often finish the dreadful work them-
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Malthusian Dynamics in Pre-industrial Societies
selves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and
sweep off their thousands and tens of thousands. Should success be
still incomplete, gigantic inevitable famine stalks in the rear, and
with one mighty blow levels the population with the food of the
world (Malthus 1798: 61).
Wood's model does not, therefore, describe the population dynamics envisioned by Malthus himself. It is nonetheless used in many studies dedicated to
the analysis of the Malthusian economics in traditional societies.
Sometimes an iterative version of this model is used, implying calculations
on an annual basis. Eq. 1a in the version put forth by Møller and Sharp (2009)
has logarithmic form:
(Eq. 2a)
ln wt = c0 – c1 ln Nt + ln A.
Birth and death rates are calculated from the simplified equations:
(Eq. 3a)
bt = a0 + a1 ln wt ,
(Eq. 4a)
dt = a2 – a3 ln wt .
The population Nt is related to the population Nt–1 in the previous year
through the following relationship:
(Eq. 7)
ln Nt = ln Nt–1 +bt–1 – dt–1.
Here, A, c0, c1, a0 … a3 are certain constants. Inserting Eqs 3a and 4a into Eq. 7
gives:
ln Nt = ln Nt–1 + (a1 + a3) ln Wt–1 + a0 – a2=
= ln Nt–1 + (a1 + a3)(c0 – c1 ln Nt–1 + ln A) + a0 – a2 = u ln Nt–1 + ln v,
where u and v are certain constants. The resulting equation is:
(Eq. 8)
Nt = v(Nt–1)u.
This equation generates a series of population values. If the population at
the initial moment equals 1 million (i.e., N1 = 1), then N2 = v, N3 equals v raised
to a power of 1 + u , N3 equals to v raised to a power of 1 + u + u2, etc. If ׀u > ׀1,
then Nt → ∞, which is impossible under the condition of limited resources in
the Malthusian theory. If 0 < u < 1, then Nt monotonically tends to a finite
bound. Finally, the case –1 < u < 0 produces a very specific series in which the
population increases in even years and decreases in odd years (or vice versa).
Thus, the Møller-Sharp model has the same drawback as Wood's initial model:
it cannot describe long-term population oscillations.
Another iterative version of the model is that developed by Ashraf and Galor (2011). Beginning with Eq. 1a, the authors of this model take into consideration the number of adults and children, and optimize expenses. They, nevertheless, ultimately come to the same Eq. 8.
One more version of Wood's model is that of Voigtlander and Voth (2009).
They use Eq. 1a, but replace Eqs 3 and 4 with Eqs 3a and 4a:
(Eq. 3a)
bt = b0 (wt / θ)m,
(Eq. 4a)
dt =d0 (wt / θ)n,
Sergey A. Nefedov
193
where b0 and d0 are certain constants. Inserting Eq. 1a into Eq. 5 yields:
dNt /dt = (bt – dt)Nt = (b0(S0/Nt) m – d0(S0/Nt) n)Nt = q(p – Nt (m–n)) Nt 1– m, (Eq. 6a)
where p and q are certain constants. The differential Eq. 6a has the timeindependent solution Nt = N0 = p 1/ (m–n), which represents a horizontal line. As
with the above model, the solution curves that are beneath this line monotonically increase, and those lying above the line monotonically decrease. Thus,
this model has the same limitation as Wood's model and its other derivatives: it
does not offer oscillating solutions.
Brander and Taylor (1998) have suggested another popular model. This
model analyzes some abstract renewable resource consumed in the course of
human activities. For example, it might be forest resources or soil yield. St is
the available amount of this resource (in year t), and K denotes its reserve in
nature. The equation for consumption of this resource is as follows:
(Eq. 8)
dSt /dt = rSt (1 – St /K) – uStNt,
where r and u are certain constants. The first term on the right side describes
the process of natural resource renewal; the second term describes resource
depletion owing to economic activity. The population is given by the following
equation:
(Eq. 9)
dNt /dt = (d + v S t)Nt,
where d and v are constants, and d < 0 in this case. This equation shows that
natural population growth depends on the availability of resource St.
Brander and Taylor have shown that the system of Eqs 8 and 9 has oscillating solutions: when the resource is abundant, the population grows, when it is
exhausted, the population decreases until the resource is renewed. Brander and
Taylor refer to their model as ‘Malthusian-Ricardian’. Initially, the model was
intended to describe the economy of Easter Island, but afterwards it got wider
application as a sufficiently general model of Malthusian economics (e.g.,
Maxwell and Reuveny 2000; D'Alessandro 2007). It is worth noting, however,
that resource St in the Brander–Taylor model is not the harvest gathered by
farmers. According to Brander and Taylor, the crop is denoted by the term
uStNt and it is deducted from the resource St. According to Szulga (2012), such
a model describes a society of gatherers (or hunters) rather than an agrarian
society. However, Malthus mainly studied agricultural economies. Thus, the
Brander–Taylor model cannot be referred to as a ‘Malthusian-Ricardian’ one.
Up to this point, I have confined my discussion to the analysis of simple
Malthusian economics models that contain no more than two differential equations. Naturally, more complicated models do exist (e.g., Usher 1989; Komlos
and Artzrouni 1990; Chu and Lee 1994; Galor and Weil 2000; Lee and Tuljapurkar 2008) that allow for better behavioral freedom and offer oscillating
solutions, as well. Many such models have been constructed within the framework of cliodynamic studies actively carried out in Russia and the USA (e.g.,
Tsirel 2004; Korotaev, Malkov, and Khaltourina 2005, 2006; Korotaev, Malkov,
194
Malthusian Dynamics in Pre-industrial Societies
and Grinin 2007; Turchin 2007, 2009; Malkov 2009). However, almost all
models described in the literature feature the same drawback: they contain uncertain coefficients whose values are unknown and cannot be determined in
principle. The more complicated the model, the more uncertain coefficients it
contains. Meanwhile, these coefficients determine the model behavior, and different coefficient values result in different population dynamics. Owing to this,
an uncertainty originates: as coefficient values are unknown, it is also unknown
which of the possible behavioral variants corresponds to the historical reality
and which of them could not possibly have been realized.
In the remainder of this article, I would like to discuss two simple models
that contain no uncertain parameters and, in my opinion, are sufficiently adequate for description of Malthusian population dynamics. In the first, Nt is the
population in the year t, as above; Kt is corn stock after the harvest estimated in
terms of minimum annual rations (1 ration approximately equals 240 kg of
corn); and r is the natality under the favorable conditions. The area under cultivation and the harvest depend on the population, and with the population
growth they tend to some constant determined by the maximum area under cultivation maintained by the agricultural community. We will consider that the
harvest is determined by the equation Pt = aNt /(Nt + d), where a and d are certain constants. To describe the population dynamics we use the standard logistic equation:
(Eq. 10)
dNt /dt = rNt (1 – Nt / Kt).
Kt in this logistic equation denotes the carrying capacity (i.e., the maximum
size of population that may live in this territory). In our case, this population
size corresponds to the number of minimum annual rations in storage. Annually, Nt rations are consumed, and the stock growth will be equal to:
(Eq. 11)
dKt /dt = Pt – Nt = aNt /(Nt+d) – Nt.
Thus, we have the simplest system of two differential Eqs 10 and 11. This
system has an equilibrium state, when the population and stock remain constant, namely in the point K0 = N0 = a – d.
If N in the equation for dP/dN tends to 0, we will obtain the harvest a/d
(number of rations) gathered by one farmer in favorable conditions (when the
population is small and he or she is able to cultivate the maximum area). Thus,
the value q = a/d shows how many households one farming family can support.
The history of agricultural societies shows that q usually varies within the limits 1.2 < q < 2. We can express a and d in terms of q and N0:
d = N0/(q – 1), a = qN0/(q – 1).
N0 can be conventionally set equal to 1 and there are two constants in
this model, r and q that have physical significance and vary within the
known limits: 0.01 < r < 0.02, 1.2 < q < 2. The usual methods used for
investigation of dynamic systems allow us to determine that system of Eqs 10
and 11 originates dying oscillations. The first oscillations can have differ-
195
Sergey A. Nefedov
ing periods; however, when the curve approaches the equilibrium state,
the period is close to:
T = 2π / √(r – r/q – r2/4).
The period T decreases when r and q increase, and increases accordingly
when these values decrease (Table 1 and Fig. 1).
Table 1. Period of oscillations with various r and q (in years)
q/r
1.2
2.0
0.01
154
89
0.02
110
63
Thus, the period of oscillations in this model is comparable to the duration of
secular demographic cycles observed in the history of many states (Turchin and
Nefedov 2009).
Fig. 1. Example of calculations using the model (r = 0.01; p= 1.2)
The dynamics of the agricultural population according to this model have
an oscillating nature. In theory these oscillations die out and the system tends to
the equilibrium state, but various random impacts and influences neglected
herein (e.g., catastrophic crop failure) disturb the system equilibrium, after
which a new series of dying oscillations begins. The peculiar feature of the agricultural society is that its economic dynamics substantially depend on such
a random value as the crop yield. The random factors that impact such systems
are generally assumed to be exogenous; however, the dependence on crop yield
variations is an intrinsic, endogenous feature of agricultural production. Therefore, one arrives at the conclusion that a special random value describing crop
yield must be incorporated into the ideal model of the Malthusian cycle. This
can be conveniently done within the iterative model where the calculations are
made from year to year.
196
Malthusian Dynamics in Pre-industrial Societies
For convenience, I consider production years that start with the harvest, not
a specific calendar date. The population size Nt at the beginning of year t is
expressed in terms of the number of households or families (conventionally
assuming that a household population is 5 people). In theory (i.e., when there is
enough land for cultivation), a farming household cultivates a standard parcel
of land (e.g., a Middle Eastern ‘çiftlik’) and one can measure the maximum
possible area of arable land in terms of standard parcels S. When the number of
households Nt exceeds S, two families can live on some parcels.
Let at represent the annual crop yield t, expressed in terms of minimum
family corn rations that can be gathered on a standard parcel. We will express
the crop yield in the form at = a0 + dt, where a0 is the average crop yield, dt is
a random value that accepts values from the segment (–а1, а1). The value а1 is
less than a0 and the crop yield at varies within the interval of a0 – а1 to a0 + а1.
With the units of measure that I have assumed, the harvest Yt (number of rations) can be expressed in the following simple form:
Yt = atNt if Nt < S, and Yt = atS if Nt > S.
If there is corn surplus in the year t, that is per-capita production yt = Yt/Nt
exceeds some value of ‘satisfactory consumption’ p1 (p1 > 1), then the farmers
do not consume the entire corn produced, but lay up some surplus portion in
store (for simplicity sake we will assume that they lay up half the surplus).
However, it is worth noting that, owing to the storage conditions, the household
stock Zt cannot grow to infinity and is limited by certain value Z0. If there are
surpluses exceeding this value, they all are consumed. If the year is lean and the
production yt falls below the level p1, the farmers take corn from the stock, increasing the consumption, if possible, up to the level p1. If the stock is not sufficient, it is consumed in full.
The population growth rate rt is determined as the ratio of the population
Nt+1 in the following year to the population Nt in the previous year. The growth
rate rt depends on the consumption pt. When the consumption is equal to the
minimum normal rate (pt = 1), the population remains constant (rt = 1). I designate the maximum natural growth r0, and the consumption rate needed to ensure it – p0. I believe that r0 = 1.02, that the maximum population growth is
2 % yearly. When 1 < pt < p0, population growth is linearly dependent on consumption, and in the case when pt > p0, it does not increase (r = r0). For pt < 1,
the dependence of rt on pt is taken as rt = pt (i.e., in case of crop failure the surviving population will be equal to the number of rations and all people that do
not have a sufficient annual food reserve will perish from starvation). Consequently, the population in the following year will be Nt + 1 = rt Nt.
Considering the typical case from the Middle East or Russia in the sixteenth to eighteenth centuries, in which each family could obtain two minimal
rations from one standard parcel, one can assume a0 = 2 for the numerical experiment. The scatter of crop yield (ratio а1 /a0) was large enough (e.g., it was
about 60 % of average crop yield in Egypt). Hence, it appears that one can as-
Sergey A. Nefedov
197
sume а1 = 1.2. As for the random value dt, it may be approximated using
squared uniform distribution: if w is a value uniformly distributed over the
segment (–1.1), then this random value can be taken as dt = а1 w2 sign (w) (Nefedov and Turchin 2007). The maximum number of standard parcels S can be
conventionally assumed to equal 1 million, and the maximum stock to equal
ten-year ones (Z0 = 10). Here, I consider a case in which farmers call upon the
experience gained by preceding generations and start laying the crop up in storage as soon as the per-capita production exceeds 1.05 of the minimum level
(p1 = 1.05). This calculation has an idealized character, allowing one to assume
N1 = 0.8 as the initial population value (in year t = 1). As the calculation results
depend on a random value (i.e., crop yield), they will vary with each program
run. Despite this variation, one can qualitatively observe a pattern of demographic cycles that seems typical: population growth periods alternating with
demographic catastrophes. The duration of this cycle is, as in the previous
model, 80–200 years (Fig. 2).
Fig. 2. Example of calculation using this model for r0 =1.02, p0 = 2,
a0 = 2, а1 = 1.2, p1 = 1.05
Naturally, this model describes just the basic mechanism of the demographic
cycle omitting many details (e.g., the existence of the state and military elite,
the emergence of large landowners). Such factors are taken into account in
other models (e.g., Nefedov and Turchin 2007) and the calculations made using
these models show that the qualitative pattern of cycles changes insignificantly
198
Malthusian Dynamics in Pre-industrial Societies
compared to the suggested model. On the whole, it seems quite certain that the
availability of corn stock in farms allows for long-term economic stabilization.
Population growth results in stock depletion, however, and, sooner or later,
major harvest failures provoke catastrophic starvations followed by events like
epidemics, uprisings of starving people, and/or invasions by external enemies
seeking to take advantage. As a result, the population size can decrease even by
half and a new demographic cycle starts. While the model calculations suggest
that this new cycle might start immediately after the catastrophe, in real life
such crises as wars and uprisings have some inertia and impede economic revival. In such cases, stabilization is delayed.
Finally, it is worth noting that after the publication of Wood's model economic historians came to see Malthusian economics as a system wherein
the population size cannot exceed the carrying capacity and, consequently, the
‘Malthusian crisis’ is not possible. For example, Read and LeBlanc (2003: 59)
‘… suggest that there is a standard model for the pattern of human population
growth and its relationship to carrying capacity (K), namely, that most of the
time human populations have low to nonexistent rates of growth… The model
is often implicit and may simply assert that, until recently, population sizes
have always been well below K and growth rates very low’. But Le Roy Ladurie, Postan, Hatcher and many other economic historians insist that ‘Malthusian crises’ were quite common phenomena in lived history, a fact acknowledged by Wood himself. The models described in this article show that
the inevitability of similar crises arises from the simple laws that govern the
functioning of agrarian economies.
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III. CONTEMPORARY HISTORY
AND PROCESSES
7
A Trap at the Escape from the Trap?
Some Demographic Structural Factors
of Political Instability in Modernizing
Social Systems*1
Andrey V. Korotayev, Sergey Yu. Malkov,
and Leonid E. Grinin
Abstract
The escape from the ‘Malthusian trap’ is shown to tend to generate in a rather
systematic way quite serious political upheavals. Some demographic structural
mechanisms that generate such upheavals have been analyzed, which has made
it possible to develop a mathematical model of the respective processes.
The forecast of political instability in Sub-Saharan African countries in 2015–
2050 produced on the basis of this model is presented.
Keywords: modernization, instability, Malthusian trap, mathematical modeling, youth bulge, urbanization, Africa, demographic dynamics, demographic
transition, political dynamics, political demography.
Malthusian Trap as a Factor of Political Instability
What is that trap which we mention in the title of this article (and at whose escape we claim another trap to be detected)? It is the so-called ‘Malthusian trap’.
The Malthusian trap2 is a rather typical for pre-industrial societies situation
when the growth of output (as it is accompanied by a faster demographic
growth) does not lead in the long-range perspective to the increase in per capita
*
This research has been supported by the Russian Science Foundation (Project No 14-11-00634).
This is a modified and extended version of the article originally published in Cliodynamics (A Trap
at the Escape from the Trap? Demographic-Structural Factors of Political Instability in Modern Africa and West Asia. Cliodynamics 2(2) (2011): 1–28. URL: http://escholarship.org/uc/item/
79t737gt).
2
Using the terminology of non-linear dynamics one can also denote it as the low-level equilibrium
attractor (cf. Nelson 1956).
1
History & Mathematics: Trends and Cycles 2014 201–267
201
202
A Trap at the Escape from the Trap?
output and the improvement of living conditions of the majority of population
that remains close to the bare survival level (see, e.g., Malthus 1798, 1978
[1798]; Artzrouni and Komlos 1985; Steinmann and Komlos 1988; Komlos and
Artzrouni 1990; Steinmann, Prskawetz, and Feichtinger 1998; Wood 1998;
Kögel and Prskawetz 2001; Grinin, Korotayev, and Malkov 2008; Grinin and
Korotayev 2009; Grinin et al. 2009; Grinin 2010).
In complex pre-industrial societies the Malthusian trap was one of the main
generators of state breakdowns (see, e.g., Korotayev and Khaltourina 2006;
Korotayev, Malkov, and Khaltourina 2006b; Chu and Lee 1994; Nefedov 2004;
Turchin 2003, 2005a, 2005b; Turchin and Korotayev 2006; Turchin and Nefedov 2009; Usher 1989; Grinin and Korotayev 2009; Grinin, Korotayev, and
Malkov 2008; Grinin et al. 2009; Grinin 2007; Korotayev 2006; Korotayev,
Komorova, and Khaltourina 2007; Kulpin 1990; Malkov 2002, 2003, 2004;
S. Malkov and А. Malkov 2000; S. Malkov, Kovalyov, and А. Malkov 2000;
Malkov et al. 2002; Malkov, Selunskaya, and Sergeyev 2005; Malkov and Sergeyev 2002, 2004а, 2004b; Mugruzin 1986, 1994; Nefedov 1999–2010; Nefedov and Turchin 2007; Turchin 2007; van Kessel-Hagesteijn 2009).
A typical example is provided by the last (Qing) of the ‘secular’ (see Korotayev, Malkov, and Khaltourina 2006b; Turchin and Nefedov 2009) cycles of
Chinese political-demographic dynamics. In 1700–1850 China managed to
achieve rather impressive economic results (due to, say, introduction of some
New World crops [first of all, maize and sweet potatoes], development of new
varieties of previously known cultivated plants, agricultural labor intensification, land reclamation, etc. [Ho 1955; 1959: 173–174, 180, 185–189; Lee 1982;
Bray 1984: 452, 601; Perkins 1969: 39–40; Dikarev 1991: 69–70; Fairbank
1992: 169; Lavely and Wong 1998: 725–726; Lee and Wang 1999: 37–40;
Mote 1999: 750, 942; Nefedov 2000a: 17; Myers and Wang 2002: 599, 634–
636; Rowe 2002: 479; Zelin 2002: 216–218; van Kessel-Hagesteijn 2009]). As
a result of these innovations the carrying capacity of land during this cycle was
raised to a radically new level, which also resulted in a rather significant
growth of the Chinese GDP.
Thus, according to Maddison's (2001, 2010) estimations, between 1700
and 1850 the GDP of China grew almost threefold (see Fig. 1).
Chinese GDP, millions of 1990
international dollars, PPP
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 203
250 000
200 000
150 000
100 000
50 000
0
1700
1750
1800
1850
Fig. 1. Economic macrodynamics of China, 1700–1850 (GDP, millions
of 1990 international dollars, purchasing power parities)
Data source: Maddison 2001, 2010.
Population of China, millions
However, the Chinese population grew during the same period of time more
than fourfold (see Fig. 2).
450
400
350
300
250
200
150
100
1700
1750
1800
1850
Years
Fig. 2. Population of China, millions, 1700–1850
Note: estimates of Zhao and Xie (1988: 539–540).
As a result, by 1850 we observe a rather significant decline of per capita GDP
(see Fig. 3).
204
A Trap at the Escape from the Trap?
450
400
GDP
Population
350
100 = 1700 level
Per capita GDP
300
250
200
150
100
50
0
1700
1720
1740
1760
1780
1800
1820
1840
Fig. 3. Relative dynamics of GDP, population, and per capita GDP in
Qing China, 1700–1850 (100 = 1700 level)
The decline in the level of life of the majority of Chinese (mainly resultant just
from the point that the Chinese population growth rates exceeded the rates of
economic growth) can be traced on the basis of a significant number of independent data series. For example, Fig. 4 reflects the dynamics of average real
daily wages of unskilled workers in this country. As we see, quite predictably,
as a result of population growth rates being higher than GDP growth rates, the
average real daily wages (that were not high at all even at the beginning of the
respective period [see Korotayev and Khaltourina 2006 for comparisons])
dropped to the level of bare physiological survival by the end of the period in
question.
Population growth rate being higher than the growth rate of GDP, Qing
China experienced a catastrophic decline in the level of life of the majority of
Chinese population, which is confirmed by the data of Chinese genealogies
(chia-p'u) (see Fig. 5).
It worth stressing that in this case we are dealing with a really mass source
(for example, Fig. 5 was compiled on the basis of several hundred thousand
Chinese genealogies). It also appears necessary to take into account the point
that representatives of really low class strata had rather poor chances to get into
the abovementioned genealogies. Thus, the data in Fig. 5 reflects the dynamics
of the level of life not of the real low class strata, but rather of the Qing ‘middle
classes’, whose members were represented in these genealogies on a really
mass scale.
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 205
3,5
3
2,5
2
1,5
1
0,5
0
400
300
200
100
0
1730–1750
1750–1800
1800–1820
Fig. 4. Population and food consumption in China in the Qing period
Note: - - - ▄ - - – consumption (daily wages, liters of rice);
––♦–– – population (millions).
Source: Adopted from Nefedov 2003: 5. The data on daily wages are from Chao 1986:
218–219. The data on population are from Zhao and Xie 1988: 541–542.
Fig. 5. Regional life expectancy from 1500 to 1800
Note: ‘The figures indicate the average age at death of the population already having
reached the Chinese age of 15’ (Heijdra 1998: 437); hence, the present diagram
does not take into account those numerous representatives of respective populations who died before reaching this age. It is perfectly clear that, if this part of the
population were taken into account, the values of the average age at death would
be radically lower. However, the present diagram gives important information on
the relative dynamics of this very important indicator.
Source: Heijdra 1998: 437, fig. 9.3.
206
A Trap at the Escape from the Trap?
As we see, at the beginning of the Qing cycle the average age at death among
the middle strata of the Chinese population was rather high – 55–60 years;
however, by the end of the period in question the value of the respective indicator falls to explicitly low values (around 45 years), whereas it seems appropriate to emphasize that we are not dealing here with the lowest strata of the Chinese population. Another impressive feature is a striking synchronicity of the
decline of the average age at death in various regions of China in the course of
the Qing sociodemographic cycle.
The fact that the excess of demographic growth rates over GDP growth
rates led in Qing China to a catastrophic decline in the level of life of the majority of population is confirmed by the data on dynamics of female infanticide
(see Fig. 6).
Fig. 6. Crude birth rates in Daoyi, 1774–1864 (per 1,000 married
women aged 15–45)
Source: Lee, Campbell, and Tan 1992: 164, fig. 5.5.
Fig. 6 displays the results of processing of data taken from one of the Qing registration offices that registered births of both boys and girls. As we see, even in
the beginning of the period covered by Fig. 6 the situation was far from problem-free – the office used to register just about 5 new-born girls per 10 newborn boys. However, by the late 1840s the situation became simply catastrophic – the office tended to register 1–2 new-born girls per 10 new-born boys.
It appears necessary to note that the historical economic research in this
field has revealed for the Qing China the presence of rather strong and significant
correlations between the levels of prices of basic food commodities and the
levels of female infanticide (see, e.g., Lee, Campbell, and Tan 1992: 158–175).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 207
This, of course, suggests that the catastrophic growth of female infanticide was
connected with the catastrophic decline of the living standard of the Chinese
population majority.3
The catastrophic decline of the majority's level of life in China quite naturally led to the growth of dissatisfaction with the government, which in 1850–
1870 produced a series of rebellions (the Taiping Rebellion was the largest
among them [see, e.g., Ilyushechkin 1967; Larin 1986; Nepomnin 2005: 395–
444; Perkins 1969: 204; Kuhn 1978; Liu 1978 etc.]); this was apparently the
bloodiest internal political collapse in the history of the humankind with
the total number of dead being estimated as high as 118 (one hundred and
eighteen!) million people (Huang 2002: 528). It worth noting that the majority
of them died not as a result of direct violence, but because of diseases, famine,
floods, etc. that took place in direct connection with the abovementioned
events. The most destructive results were produced by the break of the dams by
the Yellow River in 1853. As a result the great Chinese river changed its course
(before these events it flew to the ocean south of the Shandung Peninsular, and
afterwards it began to flow north of it), and a large part of densely populated
Northern China was literally washed down. Numerous people died directly as
a result of the flood, still more were left without sustenance, had to fled to the
cities where the Qing government totally exhausted by the Taiping War had no
resources to provide them with food. As a result, millions of undernourished
people died of diseases and famine (see, e.g., Kuhn 1978 for more details).
It should be emphasized that even the catastrophic change of the Yellow
River course had evident Malthusian causes. The point is that in the preceding
period the growing relative overpopulation of the Yellow River valley led to
the increasing cultivation of the marginal lands upstream. This resulted in the
acceleration of soil erosion and, consequently, the increasing silting of the Yellow River bottom; the bottom was rising more and more that increasingly
raised the threat of floods. A whole system of counter-flood dams was built in
order to counteract this threat – naturally, their height grew with the rise of the
Yellow River bottom. As a result, by the beginning of the Taiping Rebellion
the great Chinese river flew in its lower course well above the level of the North
Chinese Plain, and in order to prevent its breaking the dams enormous (and constantly growing) resources were needed. After the Taiping rebels4 captured
the Chinese ‘breadbasket’ in the Lower Yangtze region, the revenues of the Qing
budget shrank in the most catastrophic way; this was accompanied by an impetuous increase in military expenses that were necessary to counteract the deadly
Taiping onslaught. As a result, the Qing government failed to secure the neces3
This was already noticed, for example, by Mann: ‘The … decline in population growth during the
nineteenth century owed much to a rise in female infanticide, itself a direct response to declining
economic opportunity’ (Mann 2002: 451).
4
Note that the colossal sweep of their rebellion was determined up to a very significant degree just by
Malthusian factors.
208
A Trap at the Escape from the Trap?
sary (and very costly) support of the extremely complex counter-flood system,
and the catastrophic break of the dams by the Yellow River became inevitable
(see Korotayev, Malkov, and Khaltourina 2006b: ch. 2 for more details).
Note that Malthus himself considered warfare (including, naturally, internal warfare) as one of the most important results of overpopulation (in addition
to epidemics and famines). What is more, he regarded wars, epidemics, and
famines (and all of these were observed in China in 1850–1870) as so-called
‘positive checks’ that checked overpopulation in pre-industrial systems (Malthus 1978 [1798]). Thus, in pre-industrial societies bloody political upheavals
frequently turned out to be a result of the respective social systems being
caught in the Malthusian trap.
By now the students of social systems entrapped in the Malthusian trap
have a rather significant number of mathematical models of politicaldemographic dynamics of such social systems describing the development of
bloody political upheavals at the phase of socio-demographic collapse of preindustrial political-demographic cycles (see, e.g., Korotayev and Khaltourina
2006; Korotayev, Malkov, and Khaltourina 2006b; Usher 1989; Chu and Lee
1994; Malkov 2009; Komlos and Nefedov 2002; Turchin 2003, 2005a, 2005b;
Nefedov 2004; Turchin and Nefedov 2009; Turchin and Korotayev 2006 etc.).
Demographic transition and the increase in agricultural productivity due to
major technological advances in the recent centuries (see, e.g., Grinin 2006)
allowed most states to escape the Malthusian trap. The first phase of the demographic transition is characterized by a decline in mortality due to improved
nutrition, sanitation, advancement and spread of modern medical technologies,
etc. This leads to the acceleration of population growth. In the second phase of
demographic transition, the development of medicine in combination with other
processes (especially with mass education among women) leads to a widespread use of family planning technologies and, as a result, to a decrease of
population growth rates (see, e.g., Chesnais 1992; Korotayev, Malkov, and
Khaltourina 2006a).
However, these modernization processes started later in Sub-Saharan Africa than in the rest of the world; and even in the recent decades the Malthusian
trap tended to produce state breakdowns in this region.
For example, in the period preceding the fall of Mengistu Haile Mariam's
regime, from 1981 to 1991, Ethiopia's GDP grew by 12.5 %, but during the
same period the population grew by 40 %. As a result, GDP per capita fell from
very low $608 to catastrophic $500. Another dramatic fall occurred in per capita calorie intake: 1831 kcal/day in 1981 was already very low, 1657 in 1991
was below physiological minimum (see Table 1).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 209
Table 1. Ethiopian economic-demographic dynamics, 1981–1991
Economic growth 1:
total GDP production
Year
international
dollars 2005,
PPP, blns
21.76
22.50
24.47
1981
1986
1991
% of
1981
level
100
103.4
112.5
Demographic
Economic growth 2:
growth: population
per capita GDP
mlns
35.8
42.1
49.7
% of
% of
international
1981
1981
dollars 2005
level
level
100
607.85
100
534.24
87.9
117.6
492.85
81.1
138.7
Per capita
calorie
intake
kcal per
person
per day
1831
1711
1657
Sources: World Bank 2014; FAO 2014.
140
Economy (GDP)
Population
120
Per capita GDP
100 = 1981 level
130
110
100
90
80
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991
Fig. 7. Ethiopian economic-demographic dynamics, 1981–1991
210
A Trap at the Escape from the Trap?
1840
1820
1800
1780
1760
1740
1720
1700
1680
1660
1640
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
Fig. 8. Per capita food consumption, Ethiopia, 1981–1991, kcal/day
Such a low level of per capita food consumption means that a large part of
a country's population is on the edge of serious starvation. In this situation,
many inhabitants of this country might choose joining rebels (or bandits; in
fact, as it is well known that rebels could be quite easily transformed into bandits, and vice versa). It can be quite a rational choice when continuation of usual ways of obtaining subsistence means an almost unavoidable hungry death,
whereas joining rebels/bandits gives at least some realistic survival chances
(see Korotayev and Khaltourina 2006 for more details). We do not say that this
was the only cause of the fall of Mengistu Haile Mariam's regime, but we believe that this factor definitely contributed to this fall.
Some Features of Political-Demographic
Dynamics of Modernizing Systems
Against this background it appears interesting to consider a few cases of major
political upheavals in recent decades.
Albania – Sociopolitical Collapse of 1997
In 1997 Albania was swept by a wave of violent riots caused by the collapse of
financial pyramids, as a result of which hundreds thousand Albanians lost all
their savings. As is well known, many postsocialist European countries confronted this sort of problem (like the famous collapse of the MMM pyramid in
Russia), but nowhere did this lead to a sociopolitical collapse comparable with
the Albanian one:
By early March 1997, Albania was in chaos… The army and police had
mostly deserted. Armories had been looted…, evacuation of foreign nationals and mass emigration of Albanians to Italy began. The govern-
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 211
ment's authority… had evaporated. When Tirana fell into civil disorder
in late March, the government resigned… Some 2,000 people were
killed… Almost one million weapons were looted… Large parts of the
country were… outside of the government's control (Jarvis 1999: 18).
The order in the country was only restored after the deployment of foreign (first
of all, Italian) troops (Ibid.: 17). With a view to what we have already considered in the previous section, it appears rather seductive to suppose a certain
‘Malthusian’ component in the above-described events. Indeed, in the 1960s –
1990s Albania was the poorest European country with anomalously high (by
European standards) birth and fertility rates (see, e.g., Korotayev et al. 2010).
Within such a context there seem to be all the possible grounds to expect the
development of a classical Malthusian scenario: population growing faster than
output – decline of per capita food consumption to the level of bare survival (or
even below) – social explosion.
Against this background it appears interesting to consider the actual dynamics of per capita food consumption in Albania in the three decades preceding the sociopolitical collapse of 1997 (see Fig. 9).
3500
Per capita food consumption
(kcal/day)
3000
2500
2000
1500
1000
500
0
1961
1966
1971
1976
1981
1986
1991
1996
Fig. 9. Per capita food consumption in Albania, 1961–1996, kcal/day
Data source: FAO 2014.
As we see, for the period in question the dynamics of this indicator in Albania
turned out to be almost contrary to the ones predicted by the Malthusian scenario.
212
A Trap at the Escape from the Trap?
Still in the early 1960s in Albania the problem of malnutrition was very serious
and the average per capita food consumption was below the norm of 2300–
2400 kcal/day recommended by the WHO (see, e.g., Naiken 2002).
However, in the 1960s and 1970s Albania managed to achieve evident successes in the solution of the food problem; in the late 1960s – early 1970s in
this country the per capita food consumption exceeded the norm recommended
by the WHO – and afterwards it has never dropped below it. In the late 1970s
and early 1980s the growth rate of this indicator slowed down, and in 1983–
1991 a certain trend towards its decline was observed, which, of course, reflects
very serious economic difficulties that were experienced by Albania in the last
years of the ‘communist’ period of its history (see, e.g., Sandstrom and Sjöberg
1991). However, even in 1991 (the hardest year in Albania) per capita food
consumption did not drop below the norm recommended by the WHO. On the
other hand, after 1991 Albania managed to achieve new successes in solving
the food problem, and in 1993–1996 per capita food consumption in Albania
reached record values for the whole Albanian history; by 1997 it was closer to
what would be more appropriately called ‘overeating’ rather than ‘undernourishment’ level.
In any case, we may maintain with a high degree of confidence that with
respect to Albania in 1961–1997 it appear impossible to speak about anything
like a drop of per capita food consumption to the level of bare survival as
a result of the population growing faster than output. It appears much more
appropriate to say that these were precisely those years when Albania managed
to escape quite successfully from the Malthusian trap.5
South Korea – The 1980 Kwangju Uprising
After the end of the Korean War the largest popular uprising in South Korea
took place in 1980 in the city of Kwangju (with 300 thousand participants,
about 2000 dead, 5 divisions of regular army taking part in the suppression of
the rebellion, etc.). This uprising was accompanied by a series of popular riots
in neighboring cities (Lewis 2002).
Against this background, the dynamics of per capita food consumption in
South Korea in the two decades preceding the abovementioned popular rebellion looks rather noteworthy (see Fig. 10).
5
Naturally, the 1997 sociopolitical collapse led to a certain decline in the average per capita food
consumption (below 2700 kcal per day), which was still above the level recommended by the WHO;
whereas later the growth of this indicator resumed (FAO 2014).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 213
Per capita food consumption (kcal per day)
3500
3000
2500
2000
1500
1000
500
0
1960
1965
1970
1975
1980
Fig. 10. Per capita food consumption in South Korea, 1961–1980,
kcal/day
As we see, South Korea was another country that in the early 1960s encountered the undernourishment problem, the average per capita food consumption
being below the norm recommended by the WHO. On the other hand, this was
another country that in the 1960s and the early 1970s managed to achieve very
noticeable achievements in solving the food problem; note that these achievements were even more considerable than in Albania, it was already in the mid1960s that the average per capita food consumption in this country exceeded
the norm recommended by the WHO (and it has never gone below that level
afterwards). After 1973 the growth rate of this indicator in South Korea decreased, and in the late 1970s its certain (though quite insignificant) decline
was observed. It does not seem to be a coincidence that this occurred simultaneously with the start of the period of an especially rapid growth of the South
Korean economy (the so-called ‘Korean economic miracle’) when an unusually
high proportion of the South Korean GDP was used for the gross capital formation purposes (see, e.g., Akaev 2010); hence, an unusually low GDP share was
left for the consumption purposes. In the meantime, it appears necessary to
stress that, notwithstanding some (incidentally, very small) decline of the per
capita food consumption in the late 1970s, the value of this indicator remained
at a very high (about 3000 kcal per day) level by the start of the abovementioned popular rebellion.
214
A Trap at the Escape from the Trap?
In any case, with respect to South Korea in 1961–1980 we again get across
the case when it is impossible to note any fall of per capita food consumption to
the level of bare survival as a result of the population growth rates exceeding
the output growth rates. We rather get across one more case when a social system escaped rather successfully from the Malthusian trap just in the decades
preceding a social explosion.
Egypt – 1977 ‘Bread Riots’
The largest political unrest in Egypt after 1952 took place in 1977 (the so-called
‘Bread Riots’). The participants were chanting
Yā batl al-`ubūr! Fēn al-futūr?‘Hero of the Crossing, where is our breakfast?’
(addressing President Sadat).
The riots took place in all the large Egyptian cities, several hundred thousand
people participated in them, not less than 800 fell victim (see, e.g., Hirst 1977).
Seemingly, we should deal here with nothing else than Malthusian scenario, as
the protesters clearly complained about food insufficiency, while in the 1960s –
1970s the Egyptian population was growing exceedingly fast (see Fig. 11).
Fig. 11. Egyptian population dynamics, thousands of people, 1836–
1989
Data sources: for 1950–2005: Maddison 2001, 2010; U.S. Bureau of the Census 2010;
World Bank 2014; for 1897–1950: Craig 1917; Cleveland 1936: 7;
Nāmiq 1952; McCarthy 1976: 31–3; Vasilyev 1990: 205; for 1800–1897:
Panzac's (1987) estimates.
In this regard it seems reasonable to view the actual dynamics of per capita
food consumption in Egypt in the 1960s and 1970s (see Fig. 12).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 215
Fig. 12. Per capita food consumption in Egypt, 1961–1982, kcal/day
Source: FAO 2014.
Evidently, Malthusian scenario does not work here. Indeed, in the early 1960s
the problem of undernourishment was still quite acute for Egypt, and per capita
consumption was lower than the WHO recommended norm of 2300–
2400 kcal/person/day (Naiken 2002). In the mid-1960s Egypt reached this level, but could not exceed it before 1974. After 1973 per capita food consumption
increased rapidly, getting over 3000 kcal/day in 1982 (next year after Sadat's
death) and never after decreasing beyond this level. Thus, the problem of overeating became more relevant for Egypt than the one of undernourishment. This
success should be attributed to the Infitah economic reforms launched by Sadat
administration in 1974 (see, e.g., Weinbaum 1985: 215–216). Indeed, though
population grew by 36.1 % from 1970 to 1982, Egyptian GDP grew by 141.1 %
during the same period, the major part of this growth taking place during Infitah. As a result, GDP per capita grew almost twofold, which correlated with
the similarly rapid growth in per capita consumption (see Table 2 and Fig. 13).
216
A Trap at the Escape from the Trap?
Table 2. Egyptian economic-demographic dynamics in the ‘Sadat epoch’
(1970–1982)
Year
Economic growth 1:
GDP production
Demographic
Economic growth 2: GDP
growth: population
per capita production
Per capita
food consumption
Bln internaInternational dol% from Millions % from
% from 1970 Kcal/person/
tional dollars 1990, 1970 level of people 1970 level
level
day
lars 1990
PPP
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
42.1
43.9
44.7
45.9
47.7
52.5
60.6
68.5
73.8
79.6
88.2
91.7
101.5
100.0
104.2
106.1
109.1
113.2
124.7
144.0
162.8
175.3
189.1
209.5
217.9
241.1
33.6
34.2
34.8
35.5
36.2
37.0
37.7
38.8
40.0
41.3
42.6
44.2
45.7
100.0
101.8
103.7
105.7
107.9
110.1
112.4
115.5
119.2
122.9
127.0
131.6
136.1
1 254
1 283
1 284
1 294
1 317
1 421
1 606
1 767
1 844
1 930
2 069
2 076
2 223
100.0
102.3
102.4
103.2
105.0
113.3
128.1
140.9
147.0
153.9
165.0
165.5
177.2
2355
2341
2361
2376
2443
2481
2555
2600
2702
2811
2887
2992
3067
Data source: Maddison 2001, 2010; FAO 2014.
260
240
220
100 = 1970 level
Economy (GDP)
Population
200
Per capita GDP
180
160
140
120
100
1970
1972
1974
1976
1978
1980
1982
Years
Fig. 13. Egyptian economic-demographic dynamics in the ‘Sadat epoch’
(1970–1982)
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 217
Thus, ‘bread riots’ occurred in Egypt at that very time when the country was
successfully escaping from the Malthusian trap.
Syria – The 1982 Hama Rebellion
Per capita food consumption (kcal/day)
In Syria after the end of the Second World War the largest popular rebellion
took place in 1982 in Hama. The rebellion was suppressed with regular army
units, aviation, artillery, and tanks. According to some estimates, the number of
dead reached 40 thousand, including 1000 soldiers of regular army (see, e.g.,
Fisk 1990; Friedman 1998; Wiedl 2006).
After the cases considered above the picture of dynamics of per capita food
consumption in Syria in the two decades preceding the Hama rebellion should
not look surprising. Yet, with respect to this country the ‘counter-Malthusian’
dynamics looks especially impressive – indeed, in the nine years preceding the
rebellion the per capita food consumption in Syria was growing continuously
and very rapidly (see Fig. 14).
3100
2900
2700
2500
2300
2100
1900
1961
1966
1971
1976
1981
Fig. 14. Per capita food consumption in Syria, 1961–1982, kcal/day
Source: FAO 2014.
In general, as we see, in the two decades preceding the largest popular rebellion
in its post-war history Syria had escaped the Malthusian trap in a rather successful way, having moved within a historically very short period quite far from
the level of explicit undernourishment of the early 1960s and reaching by 1982
a level that could be more accurately characterized as overeating.
218
A Trap at the Escape from the Trap?
Civil War in El Salvador
In 1980 a civil war began in El Salvador; it continued till 1992 and led to the
death of 75 thousand inhabitants of this country – a colossal number for a country with total population of about 4.5 mln people at the moment of the civil war
start (see, e.g., Montgomery 1995).
In the meantime, the per capita food consumption dynamics in El Salvador
looked as follows (see Fig. 15):
Per capita food consumption (kcal per day)
2600
2500
2400
2300
2200
2100
2000
1900
1800
1700
1961
1971
1981
1991
Fig. 15. Per capita food consumption in El Salvador, 1961–1992,
kcal/day
Source: FAO 2014.
We obviously see here a picture that is generally similar to the cases observed
above; however, it has some noticeable nuances. As we see, still in the early
1960s the majority of the Salvadorian population confronted the most serious
(in comparison with all the other cases considered above) undernourishment
problems. The situation with food consumption somehow improved in this
country in the 1960s. However, it improved in the most significant way just in
the decade that preceded directly the outbreak of the Salvadorian civil war. It
was just the year of the civil war start when per capita food consumption in this
country reached the level recommended by the World Health Organization.
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 219
Civil War in Liberia
In 1989 a civil war started in Liberia which continued up to 2003. About
200,000 – 300,000 Liberians were killed (of the total population slightly more
than 2 mln at the war start) (Frenkel 1999; Huband 1998; Williams 2006). General dynamics of per capita food consumption in Liberia during 3 decades preceding the civil war looked as follows (see Fig. 16):
Fig. 16. Per capita food consumption, Liberia, 1961–1989, kcal/day
Source: FAO 2014.
Thus, in the 1960s – 1980s (before civil war) per capita food consumption
tended to grow in Liberia. While in the early 1960s there was some undernourishment, in the 1980s per capita consumption was thoroughly higher than the
recommended norm of 2300–2400 kcal/day. Besides, in the year of civil war
start Liberia occupied the FIRST place in Tropical Africa according to the level
of per capita food consumption (see Fig. 17).
220
A Trap at the Escape from the Trap?
Per ca pita food c onsumption, kca l/da y
2500
2300
2100
1900
1700
Uganda
Gambi a
Nig eri a
Ma li
B eni n
B urki na F aso
Guinea B is sau
Cong o, Dem. Rep.
Tanzani a
Seneg al
To go
Zim babwe
Cam eroon
K eny a
Niger
Rwan da
Ghana
Mal awi
Z ambi a
Congo
G uinea
S ierra Leo ne
Central A frican
Dj ibout i
B urundi
Mozam bique
A ngola
Chad
E t hiopia
Libe ri a
Gabon
Côte
C?t e d’ Iv oire
1500
Fig. 17. Average per capita food consumption (kcal/day) in various
countries of Tropical Africa in 1989 (i.e., in the year of the
Liberian civil war start)
Source: FAO 2014.
Liberian case is among the most tragic ones, as not only did the country ‘stumble’ at the escape from the Malthusian trap, but also fell back into the trap again
(see Fig. 18).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 221
Fig. 18. Per capita food consumption in Liberia, 1984–2005, kcal/day
Source: FAO 2014.
Thus, in 2005 per capita food consumption had not yet approached the pre-war
level and was significantly lower than even the early 1960s level. After civil
war started, an unfavorable mechanism of positive feedback formed in Liberia,
as civil war destroyed economy, which reduced the per capita consumption,
which increased the unrest and worsened the civil war. During the short breaks
the renewed (even before economy restoration) rapid demographic growth did
not allow for any remarkable improvement in living standards (nor in per capita
consumption) or even led to its worsening, which resulted in new unrests and
new stages of civil war. Currently Liberia is again trying to escape from the
Malthusian trap, but there is no warranty against its getting into ‘a trap at
the escape from the Malthusian trap’ once more.
Civil War in Côte d'Ivoire
One of the most recent civil wars in Africa occurred in Côte d'Ivoire in 2002
(Akokpari 2007). Per capita food consumption dynamics thereby looked as
follows (see Fig. 19):
222
A Trap at the Escape from the Trap?
Fig. 19. Per capita food consumption, Côte d'Ivoire, 1961–2003,
kcal/day
Source: FAO 2014.
Thus, undernourishment problem was solved in the 1960s, and at the civil war
start per capita food consumption was stably higher than the WHO recommended norm. Besides, in the civil war start year Côte d'Ivoire rated among the
top Tropical African countries according to per capita food consumption indicator (see Fig. 20).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 223
Per capita food consumption, kcal/day
2700
2500
2300
2100
1900
1700
Nigeria
Ghana
Gabon
Cote d’Ivoire
Côte
Benin
Burkina Faso
Guinea
Mali
Togo
Senegal
Gambia
Cameroon
Djibouti
Mali
Congo
Niger
Malawi
Kenya
Chad
Mozambique
Rwanda
Angola
Guinea-Bissau
Zimbabwe
Tanzania
Central
Liberia
Sierra Leone
Zambia
Ethiopia
Burundi
DRC
Eritrea
1500
Fig. 20. Average per capita food consumption (kcal/day) in various
countries of Tropical Africa in 2002 (i.e., in the year of the
civil war start in Côte d'Ivoire)
Source: FAO 2014.
Islamic Revolution in Iran
Against the background of the material considered above the dynamics of per
capita food consumption in Iran in the years preceding the successful Islamic
Revolution of 1979 in Iran should not look really surprising (see Fig. 21).
224
A Trap at the Escape from the Trap?
Per capita food consumption (kcal/day)
2700
2600
2500
2400
2300
2200
2100
2000
1900
1800
1700
1961
1964
1967
1970
1973
1976
1979
Years
Fig. 21. Per capita food consumption in Iran, 1961–1979, kcal/day
Source: FAO 2014.
This diagram suggests that the system of socioeconomic reforms (the so-called
‘White Revolution’ [see, e.g., Abrahamian 2008: 123–154]) started by the last
Iranian Shah Mohammad Reza Pahlavi in 1963 brought conspicuous positive
results. Indeed, the Iranian population grew very rapidly in the years preceding
the Iranian Revolution. For example, between 1965 and 1979 it grew from 25
to almost 38 million (see, e.g., Maddison 2001, 2010), that is by about 50 %.
However, in the same period of time the agricultural output in Iran grew by
more than 100 % (see Fig. 22).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 225
Agricultural output of Iran, millions of
constant 2000 dollars
6000
5500
5000
4500
4000
3500
3000
2500
1965
1967
1969
1971
1973
1975
1977
1979
Years
Fig. 22. Dynamics of agricultural output in Iran, 1965–1979 (in millions of constant 2000 dollars)
Source: World Bank 2014.
In the meantime Iranian GDP in this period grew by more than 150 %, as a result of which per capita GDP increased by 75 % (Maddison 2001; 2010).
Hence, the salient positive trend of per capita food consumption dynamics in
Iran reflects up to a rather high degree the real economic successes that were
achieved by this country as Mohammad Reza Pahlavi's administration was implementing the system of socioeconomic reforms known as the ‘White Revolution’.
Civil War in Algeria
Let us consider in some greater detail the structural-demographic dynamics of
Algeria 1962–1991, that is in the period after independence and before the start
of the civil war (1992–2002) which can be characterized as a failed Islamic
revolution (Kepel 2004: 164–180, 247–266). Per capita consumption dynamics
in Algeria during the two decades preceding the civil war looked as follows
(see Fig. 23):
226
A Trap at the Escape from the Trap?
2900
2700
2500
2300
2100
1900
1700
1500
1962
1967
1972
1977
1982
1987
Fig. 23. Per capita food consumption, Algeria, 1962–1991, kcal/day
Sources: FAO 2014; Zinkina 2010: 260.
Obviously, the dynamics observed is just contrary to the one that could be expected on the basis of the Malthusian trap assumption. Indeed, in the first years
after independence the Algerian population was far below the WHO norm and
greatly undernourished. Only in 1973 did it manage to go over the critical level of
1850 kcal/day. However, there was no unrest in this period. By the late 1970s
Algeria exceeded the WHO 2300–2400 kcal/day recommended level and did not
fall below this level any more. By the late 1980s it was more than 2800 kcal/day.
This dynamics correlates very well with the rapid growth of agricultural labor
productivity proving the significant success achieved by Algeria in the modernization of agriculture (see Fig. 24).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 227
Fig. 24. Labor productivity in Algerian agriculture, 1962–1991 (constant 2000 dollars per agricultural worker)
Source: World Bank 2014.
A Trap at the Escape from the Malthusian Trap:
Empirical Data
During the three decades preceding the start of the civil war Algeria successfully came out of the Malthusian trap; in fact, as we shall see below, this very
escape to a large extent generated the forces that played a crucial role in the
genesis of the Algerian civil war.
By definition, the escape from the Malthusian trap implies the solution of
the famine problem, which in its turn implies a significant decrease in the death
rates. Indeed, for countries with per capita consumption up to 2900 kcal/day
there is a strong negative correlation observed between this indicator and the
crude death rate (see Fig. 25 and Table 3).
A Trap at the Escape from the Trap?
Crude death rate, per thousand
228
Per capita food consumption, kcal/day
Fig. 25. Correlation between per capita food consumption and crude
death rate (according to 1995 data for countries with consumption up to 2900 kcal/day)
Note: r = – 0,64, R2 = 0,41, p << 0,0001. Source: SPSS 2010.
Table 3. Regression analysis
Non-standardized
coefficient
B
Stat. error
38
5.1
Standardized
coefficient
β
Model
(Constant)
Per capita food
consumption,
–0.012
0.002
–0.639
kcal/day
Dependent variable: Crude death rate (per 1000)
t
Statistical significance
(p)
7.45
<< 0.0001
–5.45
<< 0.0001
As escape from the Malthusian trap usually occurs at the first stage of demographic
transition, the results of regression analysis imply that this escape (usually accompanied by more than 1000 kcal/day growth in per capita consumption) must be accompanied by population growth rates increase by not less than one per cent, which
implies a very significant acceleration. This can be seen in Algeria. The escape
from the Malthusian trap was accompanied by a dramatic fall in death rate (see
Fig. 26).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 229
Fig. 26. Crude death rate (per 1000) dynamics in Algeria, 1960–1992
Source: World Bank 2014.
Thus, in three decades preceding the start of the civil war the Algerian death
rates declined threefold! During the most of this period birth rate was stably
high, so population growth rates were increasing and started to decline only in
the mid-1980s, but in 1991 (civil war start) they were still very high (2.4 % or
600,000 a year) (see Figs 27 and 28).
Fig. 27. Relative population growth rates, Algeria, 1970–1983,
% a year
Source: Maddison 2001, 2010.
230
A Trap at the Escape from the Trap?
Fig. 28. Absolute population growth rates, Algeria, 1970–1985, thousands per year
Source: Maddison 2001, 2010.
Infant mortality rate, per 1000 live births
Naturally, such an impetuous population growth would almost inevitably create
serious structural strains in any social system. However, within the Algerian
social system this was not the only generator of structural strains.
Within socioeconomic systems escaping from the Malthusian trap per capita
consumption growth correlates in an especially strong way with the decrease of
infant and child mortality (see Figs 29 and 30):
Per capita food consumption, kcal/day
Fig. 29. Correlation between per capita food consumption and infant
mortality rate (per 1000 live births) according to 1995 data,
for countries with less than 2900 kcal/day
Note: r = – 0.69, R2 = 0.475, p << 0.0001 (for interval < 2700 kcal the value of r
achieves – 0.74).
Source: SPSS 2010.
Child mortality rate, per 1000
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 231
Per capita food consumption, kcal/day
Fig. 30. Correlation between per capita food consumption and (underfive) child mortality rate (per 1000) according to 1995, data
for countries with less than 2900 kcal/day)
Note: r = – 0.68, R2 = 0.46, p << 0,0001 (for interval < 3000 kcal value of r achieves
– 0.7).
Source: SPSS 2010.
Predictably, Algerian escape from the Malthusian trap was also accompanied
by a precipitous fall of infant and child mortality rates (Figs 31 and 32):
Fig. 31. Infant mortality, Algeria, 1960–1995, per 1000 live births
Source: World Bank 2014.
232
A Trap at the Escape from the Trap?
Fig. 32. Under-five mortality, Algeria, 1960–1995, per 1000
Source: World Bank 2014.
Thus, while crude death rate in Algeria in 1960–1995 decreased threefold, infant
mortality declined almost fourfold during the same period, while child (underfive) mortality fell almost fivefold!
Thus, at the first phase of demographic transition (that tends to coincide
with the escape from the Malthusian trap) death rate declines dramatically
(Vishnevski 1976, 2005; Chesnais 1992; Korotayev, Malkov, and Khaltourina
2006a), the greatest decline occurring in infant and under-five mortality, while
birth rates still remain high. Thus, out of six-seven children born by a woman,
five-six children survive up to reproductive age, not two or three as earlier. This
leads not only to the demographic explosion, but also to the formation of the
‘youth bulge’, as the generation of children turns out to be much larger in
number than their parents' generation. Thus, in Algeria the share of youth
cohort in the total population greatly increased at the escape from the Malthusian
trap (see Fig. 33).
23
22
21
20
19
18
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
Fig. 33. Youth cohort (aged 15–24) in the population of Algeria, 1970–
2005, with a forecast up to 2015, %
Source: UN Population Division 2010.
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 233
A number of researchers, first of all Goldstone (1991, 2002), regard the rapid
growth of the youth share in population as a major factor of political instability.
For example, Goldstone maintains that ‘the rapid growth of youth can undermine existing political coalitions, creating instability. Large youth cohorts are
often drawn to new ideas and heterodox religions, challenging older forms of
authority. In addition, because most young people have fewer responsibilities
for families and careers, they are relatively easily mobilized for social or political conflicts. Youth have played a prominent role in political violence throughout recorded history, and the existence of a ‘youth bulge’ (an unusually high
proportion of youths aged 15–24 years relative to the total adult population) has
historically been associated with times of political crisis. Most major revolutions … [including] most twentieth-century revolutions in developing countries – have occurred where exceptionally large youth bulges were present’
(Goldstone 2002: 10–11; see also Goldstone 1991; Moller 1968; Mesquida and
Weiner 1999; Heinsohn 2003; Fuller 2004).
Let us consider the ‘youth bulge’ factor in Algeria in more detail. This will
allow specifying some other channels of this factor's impact upon the political
instability genesis. First of all consider the dynamics of absolute number of
young Algerians (see Fig. 34).
6000
5500
5000
4500
4000
3500
3000
2500
2000
1970
1975
1980
1985
1990
1995
Fig. 34. Dynamics of young (aged 15–24) Algerian population, thousands, 1970–1995
Source: UN Population Division 2010.
Thus, number of Algerian youths was growing explosively at the eve of the civil
war, more than doubling within 20 years (1970–1990). In 1980–1995 it grew by
65 %. Accordingly, in order to prevent catastrophic unemployment, new
workplaces had to be created at a proportionate rate, which is difficult even for
a fast-growing economy. If an economy is not growing as fast, unemployment
234
A Trap at the Escape from the Trap?
rockets up (in Algeria it reached 40 % in the late 1980s: Haldane 1989; Zinkina
2010: 261), especially among the youth (i.e., among that very age cohort which is
most inclined to aggression). Against such a background it usually becomes more
and more difficult to prevent major political upheavals.
There is one more force generated by modernization in general (and the
escape from the Malthusian trap, in particular) that can contribute to the genesis
of political instability, namely urbanization (see, e.g., Grinin and Korotayev
2009; Grinin 2010). Indeed, the start of escape from the Malthusian trap leads to
a stable decline in death rates, stipulating the first phase of demographic
transition. The escape itself is achieved through agricultural labor productivity
growth (as was mentioned above, in Algeria it grew fivefold during the two
decades preceding the civil war).
In general, the escape from the Malthusian trap stimulates urban population
growth in several ways. Death rate decline in conjunction with still high birth
rates leads to a rapid increase of population growth rates, so excessive rural
population appears. This population is pressed out of the rural areas, as labor
productivity grows, and less workforce is required for agricultural work. This
population may well be supplied with food resources as per capita food production and consumption increases at the escape from the Malthusian trap, so such
escape strongly supports the rapid intensification of urbanization processes,
allowing for the urbanization levels which could not be achieved in agrarian
societies.
Let us consider this with respect to the Algerian case (see Fig. 35).
55
50
45
40
35
30
1960
1970
1980
1990
Fig. 35. Dynamics of urban population percentage in Algerian, 1970–
1990
Source: UN Population Division 2010.
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 235
Thus, less than one-third of Algerians resided in cities at the eve of independence. At the eve of the civil war the urban population constituted more than
a half of the whole population. This increase took place against the background
of a very fast demographic growth. Thus, urban population was growing particularly fast in absolute numbers (see Fig. 36).
15000
13000
11000
9000
7000
5000
3000
1960
1970
1980
1990
Fig. 36. Total urban population of Algeria, 1970–1990, thousands
Source: UN Population Division 2010.
Thus, during 30 years preceding the civil war start in Algeria the urban population grew fourfold, which evidently could serve as a major destabilizing factor.
The escape from the Malthusian trap engenders a rapid growth of urban
population due to both natural increase and rural-urban migrations. This causes
social tensions, as jobs and accommodation need to be supplied for the fastgrowing mass of people. Besides, rural migrants usually have no skills appropriate for urban settings and can only find unqualified and low-paid jobs, which
causes growing discontent among them.
The situation is exacerbated by the fact that most of the rural-urban migrants are usually young. The ‘youth bulge’ and intensive urbanization factors
act together, making the number of young urban population rocket up.6 For
example, during 30 years of independence in Algeria its young population grew
almost threefold, while its urban population increased fourfold, so the number
of the urban youth increased by an order of magnitude (which was just a logical
consequence of the country's escape from the Malthusian trap). Thus, not only
did the most radically inclined part of population rocket up in numbers, but it
also got concentrated in cities (that, we should not forget, are centers of political system), which is a serious danger for political stability, especially if economic decline occurs.
6
Note that, as these are young males (rather than females) that tend to migrate from the rural to urban
areas, we have an especially explosive growth of young male urban population, which has
a particularly destabilizing effect.
236
A Trap at the Escape from the Trap?
It appears quite useful to consider the action of the above-described factors
at the ‘grassroots’ level. For this we find it appropriate to reproduce Kepel's
description of the events in Algeria that preceded the October riots of 1988,
which served as an omen of the forthcoming civil war:
…A population explosion had thrust the children of the fellahs (farmers)
into the cities and their outskirts, where conditions were precarious… In
1989, 40 percent of Algeria's population of 24 million were under
15 years of age; the urban population was in excess of 50 percent of the
total population… The official unemployment rate was 18.1 percent of
the working population, though in reality joblessness was much higher;
in 1995 it rose – again officially – to 28 percent. The young urban poor
of Algeria were mocked as hittistes – from the Arab word hit, ‘wall’.
This jibe derived from the image of jobless young men with nothing to
do all day but lean against a wall. The joke was that, in a socialist country where in theory everyone was supposed to have a job, the profession
of a hittiste consisted in propping up walls that would otherwise collapse. The hittistes were assumed to be passive – unlike the Iranian ones,
who were glorified by religious movements and hailed as the messengers
of history and the Revelation.
At the time of the October 1988 riots, oil and gas represented
95 percent of the nation's exports and supplied more than 60 percent of
the government's yearly budget… The Algerian state was a kind of popular democracy cum oil. The state used its oil revenues to buy social
pacification… This balance of power, maintained by subsidies, socialism, repression, and official ideology, was ultimately dependent on the
fragile economic equilibrium created by the high price of oil. In 1986,
when oil prices collapsed, half of Algeria's budget was wiped out and the
whole structure fell down in ruins. Worse, the population explosion had
created a demand for… urban infrastructure, housing, and employment
that continued to increase… The construction industry in particular had
failed spectacularly to keep pace with the housing demand; the result
was the kind of slums and overcrowded urban conditions that invariably
lead to social eruption.
It was in this deteriorating climate, punctuated by continual strikes,
that riots broke out on October 4, 1988. Mobs of impoverished Algerian
youths attacked such symbols of the state as buses, road signs, and Air
Algeria agencies, along with any automobile that looked expensive…
These days… marked the emergence of the young urban poor as a force
to be reckoned with. The once ridiculed hittistes had shown that they
could seize and hold power in the streets, shaking to its foundations a regime that had excluded them and whose legitimacy they scorned (Kepel
2006: 159–161).
A Trap at the Escape from the Malthusian Trap:
Logical and Mathematical Models
Thus, the emergence of major sociopolitical upheavals at the escape from the
Malthusian trap is not an abnormal, but a regular phenomenon. So, a special
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 237
explanation is rather needed for exceptions, when social systems managed to
avoid such shocks.
Why should such upheavals be treated as a regular phenomenon? The answer may be summarized as follows:
1) Start of the escape from the Malthusian trap tends to bring about a precipitous death rate decline and, consequently, an explosive acceleration of the
population growth rates (which in itself can lead to a certain increase in sociopolitical tensions).
2) The start of the escape is accompanied by especially strong decreases in
infant and under-five mortality, which raises the proportion of the youth in the
overall population (and especially in the adult population) – the so-called
‘youth bulge’.
3) This increases sharply the proportion of the part of population most inclined to radicalism.
4) The impetuous growth of the young population requires the creation of
enormous numbers of new jobs, which is a serious economic problem, while
the youth unemployment growth can have a particularly strong destabilizing
effect, creating an ‘army’ of potential participants for various political upheavals, including civil wars, revolutions, and state breakdowns.
5) Escape from the Malthusian trap stimulates a vigorous growth of the urban population. Besides, excessive population is pressed out from the countryside by the growth of agricultural labor productivity. Massive rural-urban migration almost inevitably creates a significant number of those dissatisfied with
their current position, as initially the rural-urban migrants mostly can only get
unskilled low-paid jobs and low-quality accommodation.
6) Escape from the Malthusian trap is achieved through the development of
new economic sectors and decline of the old ones. Such structural changes cannot proceed painlessly, as old qualification of workers loses its value and, not
having necessary new skills, these workers are obliged to take up low-qualified
jobs, which makes them socially discontent.
7) The young people make up the majority of rural-urban migrants, so the
‘youth bulge’ and intensive urbanization factors act together, producing a particularly strong destabilizing effect. Not only does the most radically inclined
part of population rocket up in numbers, but it also gets concentrated in major
cities / political centers.
8) This can result in serious political destabilization even against the background of a rather stable economic growth (see Fig. 37). The probability of
political destabilization naturally increases dramatically if an economic crisis
occurs, or if the government loses its legitimacy due to any other causes (such
as military defeats), though the recent ‘Arab Spring’ events have demonstrated
once again in a rather salient way that even this is not really necessary (see,
e.g., Korotayev and Zinkina 2011).
238
A Trap at the Escape from the Trap?
As regards mathematical models describing the formation of the ‘youth bulge’
(that, in combination with some other factors, can lead to major sociopolitical
upheavals even against the background of an apparently rather successful escape from the Malthusian trap), they are rather well-developed and are widely
used in demographic research.
We can regard a model by Ototsky (2008) as an example. It uses component
method (or cohort analysis) to describe mathematically the dynamics of society
age structure. The method of components implies dividing the whole population into groups of people of one age, so-called ‘year cohorts’, which are divided into male and female ones for correct estimation of the population reproductive potential. For each cohort their own birth, death, and migration rates are
determined. Birth year of people subsumed under the cohort is regarded as
a serial number of this cohort. Number of males (or females) in a cohort is expressed in the following way:
Nmti Nmti1 kUmt i Nmti1 M t i kMmw , t i ,
(Eq. 1)
where Nmit is a number of males in cohort i; kUmt – age-specific death rate;
Mt – age-specific net immigration; kMmwt – share of males in net immigration;
i – cohort serial number (corresponds to the year of people in the cohort); t –
year of calculation; t-i – age of people in cohort i.
Number of newborn boys (and girls) is calculated with the following equation:
Nmti kRmw
kR Nw
t j
t 1
60
j 0
j
M 0 kMmw , t i ,
(Eq. 2)
where Nmit is a number of newborn boys; Nwt – number of women in age cohorts; kR*t – age-specific birth rates according to cohorts of mothers; i – cohort
number (accords to birth year of people in the cohort), for newborns i = t; kRmw t –
share of boys in the newborn.
Nw
Number of the newborn in an age group is calculated in the following way:
R* kR*
ni
k li
k
,
(Eq. 3)
where R* is number of the newborn in mothers' age group; kR* – age-specific
birth rate of mothers' cohort; Nwk – number of women of age k; i – age group
index (the maximum age in the group); li – the minimum age in age group i;
ni – the maximum age in age group i.
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 239
Fig. 37. ‘A trap at the escape from the Malthusian trap’. A cognitive
model
240
A Trap at the Escape from the Trap?
General number of the newborn by mother cohorts is calculated with the following equation:
Ri
R*
i
g 0
g
.
(Eq. 4)
Distribution of age-specific death rates among yearly age cohorts of males and
females is calculated through the interpolation of the integral of the number of
dead according to age groups:
Um * i kUm *
Nm
ni
k 1 i
k
,
(Eq. 5)
where Um* is number of men who died within the age group; i – age group
index (the maximum age in group); kUm* – age-specific male death rate by age
group; Nmk – number of males of age k; li – the minimum age in an age
group; ni – the maximum age in age group.
Um* .
Integral of dead males by age cohorts:
Umi
i
g 0
(Eq. 6)
g
The same way is used to calculate the number of dead females in age group
(Uw*i) and integral number of dead females by cohorts (Uwi).
Age-specific of male and female death rates by age cohorts are calculated as
follows:
Um i ,
Uw i
kUm i
kUw i
.
(Eq. 7)
Nm
Nw
i
i
Detailed statistical data are needed for making calculations with the model (1)–
(7). If detailed data lack or approximate estimations suffice, the analytical
McKendrick – von Foerster model can be used (McKendrick 1926; von Foerster 1959). According to it, equations for defining the number of people of age τ
at a moment of time t are written in the following form:
u ( , t ) u ( , t )
d ( , t ) u ( , t ) ,
t
(Eq. 8)
u ( 0, t ) 0,5 u ( , t )b ( , t ) d , u ( ,0 ) g ( ),
0
where u(τ,t) is the number of people of age τ at a moment of time t; b(τ,t) is the
intensity of childbearing among females of age τ at a moment of time t; d(τ,t) is
the age-specific death rate for people of age τ at moment of time t; g(τ) is the
age structure of society at the starting moment of time (for simplicity it is implied that the difference between numbers of males and females is negligibly
small, and the number of born boys is equal to that of girls, the death rate d(τ,t)
is the same for males and females).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 241
Model (8) is capable of describing the emergence of ‘youth bulge’ in a society escaping from the Malthusian trap.
Assume that up to some moment of time t0 the society was demographically
stable (its age structure did not change, see Fig. 38), while fertility rate was
high (7 children per woman) and infant mortality was high, too.
Age cohort share in the whole
population (relative units)
4
3,5
3
2,5
2
1,5
1
0,5
0
0
10
20
30
40
50
60
70
Age
Fig. 38. Initial age structure of the society (simulation)
If at moment t0 infant mortality starts declining and decreases fivefold in 30 years,
then according to Eq. 8 society age structure will substantially change with the
unchanged structure of birth rate (see Fig. 39, lines correspond to successive
change of the society demographic structure during 55 years from the t0 moment).
242
A Trap at the Escape from the Trap?
10
)
8
6
(
Age cohort share in total population
(relative units)
12
4
2
0
0
10
20
30
40
50
60
70
Age
Fig. 39. Change of the age structure with the decrease of infant mortality (simulation)
Obviously, infant mortality decline leads to an increase in proportion of the
youth within total population. Thereby a ‘youth bulge’ emerges (see Fig. 40
reflecting the change of percentage of population aged 15–24 in the overall
population starting from t0 + 20 years).
Share of the youth (population
aged 15–24) in total population
0,25
0,23
0,21
0,19
0,17
0,15
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Years
Fig. 40. Change of the youth (population aged 15–24) proportion in the
total population with infant mortality decline (simulation)
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 243
Obviously, despite their simulation character the results of calculations correlate with the empirical data rather well (see Fig. 33 above).
The excessive young population not required in the rural areas moves to cities searching for better life, which affects the development of socioeconomic
and political processes in the society. The result of these processes depends on
particular conditions. In any case, it is a critical period in the life of any society
escaping from the Malthusian trap.
Figs 41 and 42 represent the results of calculations on urban population
growth and urban population percentage increase with an assumption that the
increasing demographic pressure in rural areas presses the excessive population
(and especially the young population) to move to the urban areas with probability about 0.5 (calculations are presented for the same conditions as in Figs 38–
40 starting from t0 + 20 years).
Urban population (relative units)
300
250
200
150
100
50
0
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Years
Fig. 41. Urban population growth under the impact of migration
inflow from rural areas (simulation)
244
A Trap at the Escape from the Trap?
0,6
0,55
0,5
0,45
0,4
0,35
0,3
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Fig. 42. Increase in proportion of urban population under the impact
of intensifying rural-urban migration (simulation)
Naturally, mass rural-urban migration is possible only in conditions of general
economic growth when some ‘surplus’ product appears which allows to feed
the growing urban population. In order to account for this condition we can use
the general dynamic urbanization equation developed in our earlier works (see,
e.g., Korotayev 2006):
du
aSu ( u lim u ),
dt
(Eq. 8)
where u is the proportion of urban population (‘urbanization index’); S is per
capita ‘surplus’; а is a constant; ulim is the maximum possible urban population
proportion (which can be estimated as lying between 0.8–0.9 and in this context
may be viewed as the ‘saturation level’; in calculations presented below this
value was taken as 0.9).
The sense of this equation is as follows: urbanization being low, the probability of a rural resident migrating to town is the higher, the greater urban
population proportion. Indeed, the higher this proportion, the greater the probability of having some relative or acquaintance in town, who will be able to
supply the rural migrant with the necessary information and initial support (an
ordinary peasant will hardly decide to move ‘into nowhere’). However, urban
population growth rates slow down when approaching the saturation level.
Besides, both in our equation and in real life urbanization rates depend also
on the level of economic development, which in our equation is calculated
through the per capita surplus. Indeed, if rural areas do not produce surplus,
urbanization becomes impossible, while in order for it to start (and accelerate)
significant economic growth is required. It also requires the labor productivity
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 245
growth, for example, in agriculture, which would allow feeding the urban population, on the one hand, and creating a surplus of workforce in agriculture encouraging the rural residents to move to cities, on the other.
Uniting Eqs 1 and 8 into a system we obtain a mathematical description of
the young urban population dynamics.
Correlation between Young Urban Population Growth
Rates and Intensity of Internal Violent Conflicts: A CrossNational Test
Our cross-national test indicates that violent internal conflicts should be expected in cases when the young urban population grows by more than 30 %
during 5 years; if this indicator exceeds 45 % it turns out very difficult for corresponding countries to avoid such upheavals (see Table 4 and Figs 43–45):
Table 4. Correlation between the maximum growth rates of young
urban population (% per five-year periods) and internal violent conflicts’ intensity, 1960–2005
The maximum (for 1960–2005) young urban
population growth rates,
% per five-year period
Internal violent conflict intensity
0 (Very low, < 15 %)
1 (Low, 15–20 %)
2 (Medium, 20–30 %)
3 (High, 30–45 %)
4 (Very high, > 45 %)
1 (low, < 500
violent deaths)
2 (medium
and high, 500–
100 000)
3 (very high
> 100 000)
8
1
0
88.9 %
11.1 %
3
2
60.0 %
40.0 %
14
12
53.8 %
46.2 %
14
26
13
26.4 %
49.1 %
24.5 %
0
18
17
52.9 %
47.1 %
0
0
Note: ρ = 0.59 (p << 0.0001); = 0,74 (p << 0,0001). Values of the young urban population growth rates have been calculated on the basis of the UN database (UN
Population Division 2010). Data there are provided for data points separated by fiveyear periods; so, this stipulated our choice of five-year periods. For sources on internal conflict intensity see notes to Table 5. Only countries with not less than one
million population in 1960 are accounted for in this Table, in Table 5, and in
Figs 43–45.
246
Percentage of countries with low
intensity of internal violent conflicts
A Trap at the Escape from the Trap?
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
89%
60%
54%
26%
0%
Very low ,
<15%
Low ,
15–20%
Medium,
20–30%
High,
30–45%
Very high,
>45%
The m axim um (for 1960-2005) young urban population
grow th rates (% per 5-year period)
Percentage of countries with
especially high intensity of violent
internal conflicts
Fig. 43. Percentage of countries with low (< 500 violent deaths) intensity of internal violent conflicts (for 1960–2005 period) in
respective groups
50%
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
47%
25%
0%
0%
Very low ,
Low ,
<15%
15–20%
0%
Medium,
20–30%
High,
30–45%
Very
high,
>45%
The m axim um (for 1960-2005) young urban
population grow th rates (% per 5-year period)
Fig. 44. Percentage of countries with very high (> 100,000 violent
deaths) intensity of internal violent conflicts (for 1960–
2005) in respective groups
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 247
0
Very low, < 15 %
16
Angola
Afghanistan
13
Bangladesh
Algeria
Burundi
Burma
Vietnam
Bosnia
Iraq
Guatemala
Cambodia
Congo, Dem. Rep.
Laos
Indonesia
Liberia
Iran
Lebanon
Yemen
Mozambique
China
Nigeria
Sudan
Rwanda
The Philippines
Somalia
Eritrea
Uganda
0
Ethiopia
Chad
Medium, 20–30 % High, 30–45 % Very high, > 45 %
0
Low, 15–20 %
The maximum (for 1960–2005) young urban population growth rate (% increase per five-year period)
Fig. 45. Distribution of countries with an especially high (> 100,000
violent deaths) intensity of violent internal conflicts (for
1960–2005 period) among respective groups
Table 5. Internal political conflicts of 1960–2005 that resulted in
especially numerous (> 100,000) violent deaths
Year of Year
the be- of the
ginning end
1
2
3
4
1 Algeria
1992
2002
2 Angola
1975
2002
3 Afghanistan 1978
*
No
Country
Event
Violent
deaths
5
Islamist rebellion, civil war
Civil war
Afghan revolution, civil wars
(complicated by foreign interventions)
War for independence from West
Pakistan
Civil wars
6
~100,000
~550,000
~1,800,000
~175,000
4
Bangladesh
1971
1971
5
Before
1960
1992
*
1995
The Bosnian civil war
7
Burma/
Myanmar
Bosnia and
Herzegovina
Burundi
1993
1993
8
Vietnam
1965
1973
Civil war, mass killings of hutu
~200,000**
and tutsi (mainly hutu were killed)
Civil war in South Vietnam with
~1,700,000
interventions on the part of the
USA and North Vietnam
6
~1,250,000
~130,000
248
A Trap at the Escape from the Trap?
1
2
9 Guatemala
10 Congo,
Dem. Rep.
(Zaire)
11 Indonesia
12 Iraq
3
1960
1960
1998
4
1996
1965
2009
5
1965
1961
1966
*
13 Iran
14 Yemen
15 Cambodia
1978
1962
1970
1979
1970
1991
16 China
1966
1969
17 Laos
1960
1973
Civil war within the Second Indochina War
18 Liberia
19 Lebanon
1989
1975
1997
1990
20 Mozambique
21 Nigeria
1975
1992
Civil wars
Civil war complicated by numerous cases of foreign intervention
Civil war
1966
1970
Coup, civil war of Biafra
22 Rwanda
1994
1994
23 Somalia
1991
*
24 Sudan
1955
1983
2003
1972
*
*
Civil war, mass killings of the
Tutsi
Civil war, state breakdown, chaos,
anarchy
Civil war
Civil war
Darfur conflict
25 Uganda
1979
1986
Civil wars
26 The Philippines
Since
1972
*
Civil war
Congolese crisis
Civil wars
Coup attempt, mass executions
Kurd upsurges in the north, Shia
insurrections in the south, political
upheavals of the 2000s
Islamic revolution
Revolution and civil war
Civil wars and their consequences
(complicated by foreign interventions)
‘Cultural revolution’
War against guerillas
6
~200,000
~100,000
~3,800,000
~400,000
~100,000
~100,000
~100,000
~2,500,000
From
2,000,000
to 7,000,000
From
70,000 to
250,000
~150,000
~150,000
~1,000,000
From
600,000 to
1,000,000
~937,000 **
~400,000**
~500,000
~1,900,000
From
70,000 to
more than
180,000
~300,000**
From
50,000
to 150,000
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 249
1
2
27 Chad
3
1965
4
1997
28 Eritrea
1962
1992
29 Ethiopia
1962
1992
5
Civil wars
War for independence and internal
conflicts
Civil wars
6
From
50,000
to 100,000
~1,400,000
~1,400,0007
Note: * Events unfinished, violence continuing in some form.
Sources: Grinin and Korotayev 2009; Bercovitch and Jackson 1997; Clodfelter 1992;
Crowder, Fage, and Oliver 1986; Lorraine 1995; Palmowski 1997; Project
Ploughshares 2008; Rummel 1994; Small and Singer 1982; Totten 1997;
Wallechinsky 1995; White 2010a; 2010b.
The research reveals that for 1960–2005 period the probability of major internal
violent political conflicts in countries with very low (less than 15 % increase
per five years) young urban population growth rates was very low. For countries with intermediate values of these rates (20–30 % increase per five years)
the probability of such conflicts was close to 50 %, that is one chance out of
two. However, even for this group of countries there was not a single occurrence of a particularly violent internal political upheaval in the given period. In
countries with high (30–45 % increase per five years) young urban population
growth rates the probability of avoiding the major internal political upheavals
falls down to a very low level (about one chance out of four). Besides, the
probability of particularly violent civil wars becomes very high in these countries (also about one chance out of four).
However, particularly deep internal political problems were encountered in
those countries in which the young urban population growth rates were very
high (> 45 % increase per five years) in the period under consideration. Out of
34 countries of this group NOT A SINGLE ONE managed to avoid major political shocks. Besides, the risk of particularly violent civil war occurrence was
very high for these countries (about one chance out of two).
Forecasting the Dynamics of Sociopolitical Instability
in the African Countries in 2020–2050
The results obtained in our research can well be used for predicting the risks of
sociopolitical instability for the countries being on the verge of escaping from
the Malthusian trap, in the process of escape, or having escaped from it recently.
Working out of such forecasts is currently made remarkably easier by the
fact that UN Population Division has developed urbanization dynamics fore7
General number of deaths in Ethiopia and Eritrea in 1962–1992.
250
A Trap at the Escape from the Trap?
casts for all the African countries, as well as age structure dynamics forecasts
up to 2050 (UN Population Division 2010). Synthesis of these predictions allowed us to make a synthetic forecast regarding the dynamics of structuraldemographic instability for the African countries in this period.
It is noteworthy that in our prediction only ‘positive results’ are really significant (i.e. the results revealing the presence of high political instability risk
in a certain country in a certain period). We are inclined to interpret such results
as an evidence of a real risk of political instability in the given place at the given time (if, of course, respective governments do not undertake adequate measures in proper time). On the other hand, in our opinion, ‘negative results’ cannot be viewed as a guarantee of absence of political upheavals in the given
country up to 2050 (as we do not claim that the reasons of violent political upheavals can be reduced to structural-demographic factors only).
* * *
Our forecast has produced rather different results for different Subsaharan
African countries.
No serious demographic structural risks of the type in questions are forecasted after 2015 for some Subsaharan countries (especially in Southern Africa). Let us regard, for example, the forecast for Botswana (see Fig. 46):
Fig. 46. Young urban population dynamics (thousands) in Botswana,
forecast up to 2050
No serious structural-demographic risks of this type are forecasted for many
countries of Tropical Africa, for example, Gabon (see Fig. 47):
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 251
Fig. 47. Young urban population dynamics (thousands) in Gabon,
forecast up to 2050
While in the Gabon case the young urban population growth curve quite clearly
demonstrates the absence of major structural-demographic risks, for some other
Tropical African countries it is necessary (in order to detect it) to carry out
an analysis of time series generated by our forecast. A bright example here is
represented by the Ghana case (see Fig. 48).
6000
5000
4000
3000
2000
1000
0
2005
2015
2025
2035
2045
Fig. 48. Young urban population dynamics (thousands) in Ghana,
forecast up to 2050
Indeed, in application to Ghana the forecasted situation may seem truly threatening, as by 2050 the young urban population there is likely to grow almost
threefold (i.e., 200 %; while in the cases considered above this growth did not
exceed 50 %).
252
A Trap at the Escape from the Trap?
However, a simple analysis of the corresponding time series shows that
the situation is not so threatening. Indeed, the forecasted dynamics of relative growth rates of the young urban population has the following shape
(Fig. 49).
Fig. 49. Forecasted dynamics of relative growth rates of the young
urban population in Ghana up to 2050, % per five-year periods
Thus, in the following decade urban youth relative growth rates are forecasted
to be decreasing in Ghana up to a quite safe level of less than 14 % during
five years; in the 2020s these rates are going to stabilize (at the same rather
safe level), while after 2030 they will decline further on. A similar dynamics is demonstrated by the absolute growth rates of the young urban population (see Fig. 50).
Fig. 50. Forecasted dynamics of absolute growth rates (in thousands)
of the young urban population in Ghana up to 2050, per fiveyear periods
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 253
Thus, no increase in absolute growth rates of the young urban population is
forecasted in Ghana for the next decade. According to the same forecast, a certain increase in these rates is expected in the 2020s, but it will be very moderate
(25 % during ten years). After 2030 the absolute growth rates are forecasted to
start declining, and by the 2040s they are expected to fall below the current
level.
However, the forecast indicates the presence of high structural-demographic risks for a wide range of Tropical African countries (see Table 6 below
for a full list). Fortunately, in no case the urban youth growth rates are forecasted to exceed the critical level of 45 % per five years (let us remember that
in the recent decades not a single country which crossed this level managed to
avoid major internal sociopolitical conflicts, while in half of the cases particularly violent internal political upheavals occurred). Along with that, a number
of tropical African countries are forecasted to get into a very dangerous zone of
30–45 % (let us remember that in the recent decades only a quarter of countries
found in this zone managed to avoid major internal political conflicts, while in
a quarter of cases particularly violent internal political upheavals were observed).
Tanzania is among the countries of high structural-demographic risk.
The general dynamics of the urban population in this country is forecasted as
follows (see Fig. 51):
12000
10000
8000
6000
4000
2000
0
2005
2025
2045
Fig. 51. Young urban population dynamics in Tanzania up to 2050,
thousands
254
A Trap at the Escape from the Trap?
Thus, in 2005–2050 an almost six-fold increase in the young urban population
is forecasted for Tanzania, while in the 2020s the relative growth rates of this
indicator will exceed the critical level of 30 % per five years.
However, the most serious structural-demographic risks are predicted for
Niger (see Fig. 52):
Fig. 52. Young urban population dynamics in Niger up to 2050, thousands
Thus, in 2000–2050 the young urban population of Niger will increase by
an order of magnitude, while in the second half of the 2010s the relative growth
rates of this indicator will exceed the critical level of 30 % per five years, while
in the early 2020s they will exceed an even more dangerous level of 40 % during five years. These rates will decrease to relatively safe levels only in the late
2040s (see Fig. 53).
Andrey V. Korotayev, Sergey Yu. Malkov, and Leonid E. Grinin 255
Fig. 53. Forecasted dynamics of relative growth rates of the young
urban population in Niger up to 2050, % per five-year periods
Besides, in Niger an increase by an order of magnitude (in comparison to 2000
level) in the absolute growth rates of the young urban population is forecasted
by 2030 (see Fig. 54).
Fig. 54. Forecasted dynamics of absolute growth rates (in thousands)
of the young urban population in Niger up to 2050, per fiveyear periods
256
A Trap at the Escape from the Trap?
In conclusion, let us present a summary forecast of structural-demographic risks
of political destabilization in the Subsaharan African countries up to 2050 (see
Table 6).
Table 6. Summary forecast of structural-demographic risks of political destabilization in Subsaharan African countries up to
2050
Country
Niger
Malawi
Burkina Faso
Uganda
Eritrea
Tanzania
Kenya
Rwanda
Chad
Burundi
Congo, Dem.
Rep.
Mozambique
Somalia
Ethiopia
Gambia
Sierra Leone
Madagascar
2021–2025
2016–2020
2021–2025
2021–2025
2021–2025
2021–2025
2021–2025
2021–2025
2016–2020
2026–2030
2016–2020
Urban
youth
growth rates
(% in five
years) in
those years
41.8
39
38.7
33.1
32.5
30.6
30.2
29.6
28.5
28.1
27.7
Period of particularly high
structuraldemographic
risks of political
destabilization
2021–2030
2015–2025
2021–2030
2021–2030
2021–2030
2021–2030
2021–2030
2021–2030
2016–2025
2026–2035
2016–2025
2021–2025
2016–2020
2016–2020
2016–2020
2016–2020
2016–2020
27.4
27.4
26.7
26.5
25.4
25.2
2021–2030
2016–2025
2016–2025
2016–2025
2016–2025
2016–2020
Years of maximum urban
youth growth
rates
Structuraldemographic
risk level
Very high
High
High
High
High
High
High
Medium
Medium
Medium
Medium
Medium
Medium
Medium
Medium
Medium
Medium
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8
Labour Migration and
‘Smart Public Health’
Arno Tausch and Almas Heshmati
Abstract
Public health research debates for two decades the effects of inequality on public health. More recent research also considered the additional effects of international trade and world economic openness. These investigations analyse
public health outcomes in such terms as infant mortality rates, life expectancies, etc. But with the growing environmental crisis, ideas to weigh economic
or social or public health progress by the ‘environmental input’ necessary to
achieve it are increasingly gaining acceptance. We might call such a weighting
of infant mortality rates, or life expectancies by the ‘environmental input’ necessary to achieve them ‘smart public health’. Which factors of social organization now contribute then to a responsible use of the resources of our planet
Earth to achieve ‘smart public health’?
We use standard OLS non-linear regressions of ecological footprints per
capita and their square on combined public health performances. The residuals
from this regression are our new measure of ‘smart public health’.
Our research results suggest that not inequality, but migration is a very
important determinant of ‘smart public health’. Migration sending countries
find it relatively easy to enjoy combined good public health performances at
a relatively small environmental price. Other drivers of ‘smart public health’
are the share of a country's population in world population, and the UNDP
education index. The main bottleneck of ‘smart public health’ is constituted by
the crowding-out effect of public education expenditures on smart health performance.
In contrast to earlier research, we come to the conclusion that migration
sending countries reap substantial benefits from receiving worker remittances,
while inequality and globalization indicators hardly affect the smart public
health performance of the sample countries (all countries with available data).
Keywords: Index Numbers and Aggregation, public health, infant mortality,
female survival probability of surviving to age 65, UNDP human development
index (HDI), average life expectancy (years), life satisfaction, international
migration, remittances.
History & Mathematics: Trends and Cycles 2014 268–280
268
Arno Tausch and Almas Heshmati
269
Objectives
This article is motivated by the fact that public health research debates for two
decades now the effects of inequality on public health.1 More recent research also
considered the additional effects of international trade and world economic
openness. But these investigations analyse public health outcomes in such
terms as simple, unweighted infant mortality rates, life expectancies, etc. With
the growing environmental crisis, ideas to weigh economic or social or public
health progress by the ‘environmental input’ necessary to achieve it are increasingly gaining acceptance. Such a research question is typically motivated by
economics: to achieve a maximum of results under the constraint of existing
scarce resources. Under such given constraints, is the price mechanism, free
flows of globalization, and the absence of government intervention much better
suited to achieve good results for public health than government interventions
to redress inequalities?
We might call such a weighting of infant mortality rates, or life expectancies by the ‘environmental input’ necessary to achieve them ‘smart public
health’. Which factors of social organization do now contribute then to a responsible use of the resources of our planet Earth to achieve ‘smart public
health’?
The essence of the by now dominant paradigm in public health about
a strong correlation between high inequality and low life quality seems to suggest that inequality negatively determines a number of public health variables,
like physical health, mental health, drug abuse, and teenage births (Pickett and
Wilkinson 2007). Recent contributions, further elaborating the approach, initiated by R. G. Wilkinson, highlighted, for example, the role played by international trade and world economic openness in determining public health outcomes. But in large sections of the economics profession, such as paradigm,
critical of inequality and globalization, will not go uncontested.2
1
2
The Equality Trust (homepage on the Internet), 32–36 Loman Street, London SE1 0EH. London
(UK) (cited 30 May 2011) Why More Equality? URL: http://www.equalitytrust.org.uk/research/
why-more-equality.
The flagship article of the school of thought, featuring the trade-offs between inequality and public
health outcomes is undoubtedly Wilkinson's ‘For Debate – Income Distribution and Life
Expectancy’ (1992). This article was followed according to the Web of Science's Documentation
system (accessed on May 20th, 2014 at Vienna University Library) by 463 studies. One of the central
public health profession articles linking trade, world economic openness and globalization to public
health outcomes is Blouin, Chopra, and van der Hoeven's, ‘Trade and Social Determinants of Health’
(2009). This study initiated 18 follow-up studies to this day. By contrast, let us just recall here that
major sections of Economics hold a sceptical or even very sceptical view about efforts to change
existing income distribution patterns and inequality structures by government intervention. Perhaps,
the most uncompromising attack in this direction was published by Economics Nobel laureate von
Hayek in 1960 in his The Constitution of Liberty. His attack on egalitarianism is a true classic of
Economics (90 editions were published between 1959 and 2010 in 9 languages and held by
270
Labour Migration and ‘Smart Public Health’
This question is already intriguing enough by itself and is being dealt with
today by a growing number of studies, focusing on the environmental price of
human progress. Even more intriguing, however, is the question, which factors
of social organization contribute to a responsible use of the resources of our
planet Earth. In this essay, we will present the first systematic study on how
outward migration – or rather, more concretely, received worker remittances
per Gross Domestic Product (GDP) – helps the nations of our globe to enjoy
a good overall public health system at a relatively small environmental price
(henceforth called ‘smart public health’). According to our study, it is not inequality or globalization, which primarily determines this ‘smart public health’,
but the existence of a system of the economic freedom to migrate, measured by
worker remittances. This is potentially an important new start in the entire debate about the societal drivers and bottlenecks of global public health performance, dominated in recent years by the thought that inequality is mainly to
blame for the cross-nationally observed public health shortcomings.
The indicators of public health, which we use in this essay, are derived
from standard recent international data3 on infant mortality, female survival
probability of surviving to age 65, the United Nations Development Programme
(UNDP) Human Development Index (HDI), average life expectancy (years)
and life satisfaction (0–10).
3
2,201 libraries worldwide according to Worldcat Identites; see http://www.worldcat.org/identities/
lccn-n80-126331 [Date accessed: 20.05.2014]). Major sections of Economics also would believe that
world economic openness is good for the poor, on all fronts and not just by promoting economic
growth. Efforts to hinder the process of globalization will be to the detriment of economic wellbeing. One of the most important studies in this direction is Dollar and Kraay's ‘Growth Is Good for
the Poor’ (2002), which led to 276 follow-up studies and which showed that average incomes of the
poorest quintile rise proportionately with average incomes in a sample of 92 countries over the last
four decades. Dollar and Kraay state that the share of income of the poorest quintile does not vary
systematically with average income. It also does not vary with many of the policies and institutions
that explain growth rates of average incomes, nor does it vary with measures of policies intended to
benefit the poorest in society. This evidence emphasizes the importance of economic growth for
poverty reduction. Another influential study in this direction was published by Dreher (2006). His
work led to 109 follow-up studies, showing that an index of globalization covering its three main
dimensions: economic integration, social integration, and political integration is well associated with
good economic outcomes. Dreher used panel data for 123 countries in 1970–2000 and analysed
empirically whether the overall index of globalization as well as sub-indexes constructed to measure
single dimensions affect economic growth. As the results claim to show, globalization indeed
promotes growth. The dimensions most robustly related with growth refer to actual economic flows
and restrictions in developed countries. Although less robustly, information flows also promote
growth whereas political integration has no effect. While our analysis does not necessarily side with
these arguments, it is necessary to emphasize that there is an urgent need in public health for further
solid empirical studies on these subjects and realizing that large sections of the science, claiming that
it developed the greatest professional competence for issues such as inequality and globalization,
start from a consensus, which is completely different from the one, emerging in public health.
All the original variables see at URL: http://www.hichemkaroui.com/?p=2017 (date accessed:
20.05.2014).
Arno Tausch and Almas Heshmati
271
The very idea of ‘smart development’ was first proposed by Dennis Meadows and has not been really followed up to now in social science ever since
(Meadows 1992). In the face of the huge usage of this term in the international
media, such a statement is perhaps surprising, but our verdict corresponds to
the clear bibliographical evidence on the base of such indices as ‘ISI Web of
Knowledge’4 or ‘Cambridge Scientific Abstracts/Proquest’.5
To present a theory or competing theories of ‘smart public health’ is virtually impossible, because there has been no measurement, let alone accounting
of its cross-national successes and failures in the literature up to now. We really
had to start research into this issue from ‘scratch’.
Of particular interest in the context of our research is the effect of migration. As it is well-known, migration is part and parcel of what social sciences
but also international politics and international law nowadays call the ‘four
freedoms’ of ‘capitalism’ (i.e. ‘market economies’), besides the freedom of
goods, services, and capital. A particular earlier flagship survey of the hitherto
existing migration theories came to the pessimistic conclusion that migration
theories up to that time were either advanced to explain the initiation of international migration or put forth to account for the persistence of migration across
space and time (Massey et al. 1993). Massey et al. suggested that, because they
are specified at such different levels of analysis, the theories are not inherently
logically inconsistent. As Taylor pointed out in his later, summarizing policy
statement on the state of migration theory for the United Nations in 2006, indeed it would be foolish to exclude migration from any future discourse about
global development, but that existing hard-core evidence on how migration
really affects the development process is limited (Taylor 1999, 2006).
This is all the more surprising, since the number of international migrants
has increased more or less linearly over the past 40 years, from an estimated
76 million in 1965 to 188 million in 2005. The flow of international migrant
remittances has increased more rapidly than the number of international migrants, from an estimated US$ 2 billion in 1970 to US$ 216 billion in 2004.
Nearly 70 % of all remittances go to less-developed countries (LDC). Remittances were equivalent to 78 % of the total value of exports in El Salvador and
108 % in Nicaragua. Worker remittances are especially affecting the less developed sending countries by the multiplier effect, well-known in economics:
$1 of remittances from international migrants may create $2–$3 or more of new
income in migrant-sending areas. One person's spending is another person's
income. Even if all income in remittance-receiving households is spent on consumption, remittances may stimulate investments by the other households
whose incomes go up (Taylor 2006: 9). This optimistic view about worker re4
5
URL: http://wokinfo.com/ (Date accessed: 20.05.2014).
URL: http://www.csa.com/ (Date accessed: 20.05.2014).
272
Labour Migration and ‘Smart Public Health’
mittances is also supported in the well-received comparative international study
by Ziesemer (2009).
Migration is thus seen in many social scientific approaches as a win-win
situation (United Nations 2009; Williamson 2002). For several observers,
among them Hatton and Williamson (2009), the ‘current hysteria’ about inward
migration in many industrialized countries has no real basis. For them,
the Third World has been undergoing an emigration life cycle since the 1960s,
and, except for Africa, emigration rates have remained about equal or were
even declining since a peak in the late 1980s and the early 1990s. The current
economic crisis will serve only to accelerate those trends. Sanderson (2010)
was one of the first consistent research attempts to bring in migration as a determining variable of social well-being. Contemporary levels of international
migration in less-developed countries are raising new and important questions
regarding the consequences of immigration for human welfare and well-being.
However, there is little systematic cross-national evidence of how international
migration affects human development levels in migrant-receiving countries in
the less-developed world. The Sanderson paper addressed this gap in the literature by assessing the impact of cumulative international migration flows on the
human development index, the composite, well-known UNDP measure of aggregate well-being. A series of panel data models are estimated using a sample
of less-developed countries for the period, 1970–2005. The results indicate that
higher levels of international migration are associated with lower scores on the
human development index, net of controls, but that the effect of international
migration is relatively small.
Methods
To estimate the effects of migration on ‘smart public health’, we used a freelyavailable new cross-national comparative data set, which is publicly available
on the Internet without any restrictions.6 This electronic data set offers Microsoft EXCEL data and a list of the international standard sources, and
a codebook in PDF format. It also offers an EXCEL file with the combined
UNDP type development performance index, on which this study rests.
Each of these indicators (infant mortality, female survival probability of
surviving to age 65, the United Nations Development Programme (UNDP)
Human Development Index (HDI), average life expectancy (years) and life
satisfaction (0–10) was standardized according to the well-known practice of
the United Nations Human Development Programme on a scale, ranging from 0
(worst value) to 1 (best value) according to the formula:
max
Z ij ( X ij X min
X min
(Eq. 1)
j ) /( X j
j ),
6
URL: http://www.hichemkaroui.com/?p=2017 (Date accessed: 20.05.2014).
273
Arno Tausch and Almas Heshmati
where Xij is indicator j of country i and Zij its normalized counterpart and Xmin
and Xmax are sample minimum and maximum values of indicator j. Our final
index of public health performance is based on the simple means of the standardized component indices:
Indexi
J
j 1
w j Z ij ,
(Eq. 2)
where wj are weights assigned to each of the J indicators, in this case equal
weights, w = 1, is employed. Our performance scale of public health is then
compared with the environmental destruction, which a society causes in maintaining its development level. We rely here on data about ecological footprint,
which measures how much land and water area a human population requires to
produce the resource it consumes and to absorb its carbon dioxide emissions,
using prevailing technology.7 Ecological Footprint is usually measured in global hectares. Existing time series nowadays allow us to grasp the extent of the
accelerating environmental constraints, facing our globe.8
The standardized residual (SR) values of Table 1 – our final performance
scale of ‘smart public health’, measuring how much of infant mortality reduction, female survival to age 65, a good Human Development Index, a high average life expectancy and a good life satisfaction are achieved at a minimum
ecological footprint and are computed as observed minus predicted development outcomes, Z, divided by the square root of the residual mean square, :
(Eq. 3)
SRi (Z i Zˆ i ) / ̂
.
High positive outliers imply a very high smart public health performance,
while countries below the fitted trend line are the countries with a low smart
public health performance. Having established a residual-based smart public
health indicator family, we now can look more realistically at the cross-national
determinants of smart public health performance (see Table 1). We are aware
about the limitations of our approach but we think that our estimates cover the
wide range of existing international data in the field. Even with different components of our indicator, the results would not dramatically differ.
Table 1. Performance of countries in respect with smart public health
Country
1
Jamaica
Philippines
7
Smart
public
health
2
1.780
1.745
Rank
3
1
2
Country
4
France
Belgium
Smart
public
health
5
0.132
0.119
Rank
6
71
72
URL: http://www.footprintnetwork.org/en/index.php/GFN/page/glossary/ (Date accessed: 20.05.
2014).
8
URL: http://www.happyplanetindex.org/learn/download-report.html (Date accessed: 20.05.2014).
274
Labour Migration and ‘Smart Public Health’
1
Cuba
Sri Lanka
Costa Rica
Vietnam
Dominican
Republic
Indonesia
Colombia
Moldova
Guatemala
El Salvador
2
1.707
1.699
1.670
1.650
1.488
3
3
4
5
6
7
1.480
1.404
1.211
1.204
1.180
8
9
10
11
12
Morocco
Georgia
Tunisia
Armenia
Tajikistan
Peru
Argentina
Egypt
Jordan
1.164
1.162
1.143
1.129
1.110
1.105
1.084
1.053
1.033
13
14
15
16
17
18
19
20
21
China
Ecuador
Albania
Honduras
Malaysia
0.893
0.874
0.870
0.866
0.853
22
23
24
25
26
Bangladesh
Algeria
Syria
Kyrgyzstan
Brazil
Nicaragua
India
Trinidad and
Tobago
0.846
0.840
0.798
0.789
0.783
0.756
0.754
0.750
27
28
29
30
31
32
33
34
4
5
0.100
0.058
0.043
0.037
0.029
6
73
74
75
76
77
Australia
Iceland
Hungary
Norway
United Arab
Emirates
Iran
Paraguay
United Kingdom
Ireland
Canada
Denmark
Portugal
Latvia
Hong Kong, China
New Zealand
Cambodia
Azerbaijan
Congo
Bosnia & Herzegovina
Greece
Guyana
Kuwait
Czech Republic
Lebanon
Senegal
Togo
Madagascar
0.025
0.024
0.015
0.001
–0.003
78
79
80
81
82
–0.012
–0.014
–0.017
–0.044
–0.066
–0.085
–0.088
–0.094
–0.106
83
84
85
86
87
88
89
90
91
–0.114
–0.117
–0.152
–0.242
–0.270
92
93
94
95
96
–0.273
–0.297
–0.328
–0.337
–0.339
–0.378
–0.423
–0.445
97
98
99
100
101
102
103
104
Turkey
Poland
Ukraine
Bolivia
Spain
275
Arno Tausch and Almas Heshmati
1
Belize
Saudi Arabia
Luxembourg
Chile
Thailand
Bhutan
Nepal
Pakistan
Panama
Laos
Venezuela
Croatia
Malta
Netherlands
Mexico
Bulgaria
Singapore
2
0.732
0.718
0.713
0.697
0.670
0.619
0.583
0.567
0.555
0.519
0.484
0.480
0.470
0.439
0.407
0.398
0.386
3
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
Germany
Korea
(Republic of)
Haiti
Uzbekistan
Slovakia
Switzerland
United States
Myanmar
Romania
Sweden
Austria
Lithuania
Cyprus
Finland
Japan
Italy
Yemen
0.385
0.376
52
53
0.349
0.315
0.312
0.288
0.281
0.274
0.274
0.273
0.242
0.229
0.214
0.196
0.193
0.173
0.145
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
4
Belarus
Ghana
Uruguay
Russia
Malawi
Mauritania
Macedonia
Kazakhstan
Djibouti
Benin
Kenya
Mongolia
Guinea
Estonia
South Africa
Cameroon
Congo (Dem.
Rep. of)
Uganda
Rwanda
5
–0.489
–0.560
–0.574
–0.645
–0.646
–0.733
–0.760
–0.797
–0.853
–0.921
–0.966
–1.043
–1.047
–1.091
–1.156
–1.220
–1.249
6
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
–1.262
–1.277
122
123
Tanzania
Nigeria
Burundi
Sudan
Zambia
Mozambique
Ethiopia
Chad
Angola
Mali
Zimbabwe
Sierra Leone
Niger
Burkina Faso
Central African
Rep.
–1.455
–1.463
–1.480
–1.516
–1.545
–1.545
–1.593
–1.749
–1.811
–1.889
–1.956
–2.032
–2.104
–2.120
–2.382
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
276
Labour Migration and ‘Smart Public Health’
1
Slovenia
Israel
2
3
4
0.138
0.135
69
70
Namibia
Botswana
5
6
–2.457
–3.052
139
140
Notes: Public health performance is measured by a combined UNDP-type index of infant mortality, female survival probability of surviving to age 65, the United Nations
Development Programme (UNDP) Human Development Index (HDI), average life expectancy (years) and life satisfaction (0–10). The data for the standardized performance
indicators are given in the data sheet ‘Smart development Heshmati Tausch Final UNDP
type indicators 2011’, the energy efficiency indicators are found in the file ‘Data for
energy efficiency analysis May 2011’ (see Tausch 2010). The codebook of this data file
lists the data definitions and sources.
Our standard comparative cross-national data operationalize standard economic, sociological and political science knowledge in international development accounting. We compare the predictive power of all these standard predictors, using standard ordinary least squares (OLS) stepwise regression procedures, based on IBM SPSS XVIII, weeding out the relevant from the irrelevant
predictors of smart public health. The final model is based on standard forward
OLS multiple regression with the most significant predictors from the prior,
preliminary weeding out exercise.
The independent variables, used in our research to explain performance
along this new international scale of smart public health in the first decade of
the new Millennium, range from standard social science cross national development accounting explanatory variables, measuring the dimensions of feminism, demography, economic freedom, geography, dependency and world systems theories, to migration, convergence effects of poorer countries growing
more rapidly than richer countries, Muslim population shares and membership
of a country in the Organization of Islamic Cooperation, military expenditures
and military personnel rates, human capital formation, and participation in European economic and monetary integration, thus reflecting contemporary social
science and public health research practice of cross-national development accounting.9
The independent variables are (arranged in alphabetical order) as follows
(Table 2).
9
For a recent exhaustive argumentation about drivers and bottlenecks of global development see
Tausch et al. (2012).
Arno Tausch and Almas Heshmati
277
Table 2. The potential societal drivers and bottlenecks of smart public
health
% women in government, all levels
% world population
2000 Economic Freedom Score
Absolute latitude
Annual population growth rate, 1975–
2005 (%)
Comparative price levels (US = 1.00)
Foreign savings rate
FPZ (free production zones) employment as % of total population
Immigration – Share of population
2005 (%)
ln GDP per capita
ln GDP per capita ^2
Membership in the Organization of
Islamic Cooperation (OIC); Muslim
population share per total population
Military expenditures per GDP
Military personnel rate ln (MPR+1)
MNC outward investments (stock) per
GDP; MNC PEN – stock of Inward
FDI per GDP; MNC PEN: DYN
MNC PEN 1995–2005
Net international migration rate,
2005–2010
Openness-Index, 1990 (export-share
per GDP + import-share per GDP)
Population density
Public education expenditure per
GNP; UNDP education index
Worker remittance inflows as % of
GDP
Years of membership in EMU, 2010,
Years of membership in the EU, 2010
The choice of a country to be included in the final analysis (175 countries) was
determined by the availability of a fairly good data series for these independent
variables (if not mentioned otherwise, UNDP data for the middle of the first
decade of the new millennium). In the final regressions, we applied the ‘list
wise deletion of missing values’ routine (i.e. only entering countries with complete data into the statistical analysis, in total 115).
The statistical design of our study is thus based on the usual, SPSS XVIII
ordinary least square standard regression analysis of the ‘kitchen sink type’ of
economic growth and economic, social and political performance.
Results
Table 2 shows the estimation results for the drivers and bottlenecks of ‘smart
public health’. Which are the countries best combining the task of a maximum
of ‘public health’ with a minimum of ecological footprint per capita? Our model explains 29.9 % of the total variance of ‘smart public health’, and is based on
the analysis of the 115 countries with complete data; the F-value is 13.183 and
the error p of the entire equation is 0.000, and constitutes the best available
estimate from our independent variables. The constant, which is significant, has
a value of –1.657. The drivers of ‘smart public health’ are the share of a country's population in world population, indicating the relative size of a nation,
the UNDP education index, measuring the levels of education in a given country, and worker remittance inflows as percent of GDP. The main bottleneck of
278
Labour Migration and ‘Smart Public Health’
‘smart public health’ is constituted by the crowding-out effect of public education expenditures on human development.
Table 3. OLS regression results of drivers and bottlenecks of smart
public health (dependent variable is SR)
B (unstandardized
Standard
regresIndependent Variable
error
sion
coefficient)
Constant
–1.657
0.348
% world population
0.055
0.029
Public education expendi- –0.097
0.042
ture per GNP
UNDP education index
2.437
0.430
Worker remittance inflows
0.044
0.010
as % of GDP
Memorandum item: statis- Adj. R^2
Df.
tical properties of the
equation
29.900
114
t-value
(Student's
test)
Error
probability
0.152
–0.196
–4.760
1.894
–2.283
0.000
0.061
0.024
0.478
0.352
5.666
4.461
0.000
0.000
F
Error prob.
of the entire
equation
0.000
Beta
13.183
Conclusion
Our residuals-based reformulation of smart public health realistically captures
the trade-off between Global Ecological Footprint per capita and development
performance and offers us a better idea about smart public health performance
at different stages of socio-economic development.10 Our results show that traditional indicators of economic globalization and also inequality have little influence on combined smart public health performance, but that hitherto neglected elements of social science theories, such as migration, gain in importance. Also such factors as the demographic weight of a country and scale effects of public health provision, and education cannot be overlooked. In contrast to most of the current thinking on the issue, we can show that levels
of public education expenditures crowd out health performance, while levels of
achieved education, measured by the UNDP education index, have a beneficial
10
The inclusion of the UNDP-standardized equality score (= performance in avoiding a high ratio of
income differences between the richest 20 % and the poorest 20 %) only has a minor effect on our
results: for the 106 countries with complete data. The equality score achieves an error probability of
13.5 %. As expected, equality has a positive effect on smart public health, but the effect is far
smaller than existing approaches would suggest.
Arno Tausch and Almas Heshmati
279
effect on ‘smart public health’. True enough, we have to state that worker remittances redistribute global well-being and the achievement of good public
health outcomes at relatively low ecological resource use to the countries of the
‘global South’ and away from the rich democracies of the OECD.
We are aware that our answers to the questions raised in this article might
be incomplete. But we hope to have provided at least some preliminary guiding
posts for further research on this important subject how the four economic freedoms affect smart public health and to have shown that primarily not inequality, but migration matters for public health. If we have expressed this perspective sufficiently clear, then our essay already achieved its aim. Further research
might concentrate on such issues as ‘smart infant mortality reduction’ or ‘smart
life expectancy’.
References
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9
Is Geography ‘Dead’ or ‘Destiny’
in a Globalizing World?
A Network Analysis
and Latent Space Modeling Approach
of the World Trade Network
Anthony Howell
Abstract
Drawing on advancements made in network analysis, statistical modeling and
computer science, this paper employs latent space modeling techniques to explore the role of geography in the global trade economy. Latent space models
postulate that the probability of a link between pairs of actors depends on the
distance between them in unobserved Euclidean social space and on observed
covariates. Using probabilistic models, I investigate the effect that distance has
on influencing trade ties in social space, while also controlling for several covariates, including region-based homophily (a proxy for regionalization), transitivity and country wealth. The findings are posited within the ‘Geography is
Dead’ thesis and reveal that the distance-destroying result attributed to globalization may be over-estimated in the global trade economy.
Keywords: network analysis, latent space model, world trade network, geography, regionalization, globalization.
1. Introduction
Since Toffler (1970) first argued that place is no longer an important determinant due to the evolution of transport and communication systems, numerous
scholars have speculated the ‘death of geography’, giving rise to a heated debate (Ohmae 1990, 1995; Friedmann 1995). O'Brien (1992) proclaimed that the
globalization era equates to ‘the end of geography’, because geographical location no longer matters for economic development due to the increasing rate of
globalization. In this context, globalization is defined as ‘the deepening integration of global economic activity facilitated by the rapid development of information and communications technology and the underlying trend towards liberalization in trade and investment’ (Staples 2007: 99).
History & Mathematics: Trends and Cycles 281–299
281
282
Is Geography ‘Dead’ or ‘Destiny’ in a Globalizing World?
Despite the ‘geography is dead’ claims, many notable (economic) geographers emphasize the critical role of geography in trade, as well as in innovation,
knowledge and development (Krugman 1993; Yeung 1998; Massey 1984,
1999; Morgan 2004). It is well known that the effects of globalization are not
distributed uniformly throughout the global economy, and there are place- and
region-based variations that require a geographical lens in order to understand
issues of unequal development (Warwick 2005). Moreover, the growing forms
of regionalization shed further evidence that geography does matter for trade
and economic development. Regionalization is defined here as a process,
‘whereby economic interaction, such as flows of goods and capital, increase
faster among countries within a particular geographical area than between those
countries and others outside the area’ (Moore 2007: 36).
In the present paper, I apply latent space modeling – developed by Hoff
et al. (2002) – to test the ‘geography is dead’ thesis. Hoff et al. (2002) postulate
that the probability of a link between pairs of actors depends on the distance
between them in unobserved Euclidean social space and on observed covariates. Using the latent space modeling approach, I investigate the effect that distance has on trade ties in latent space, while also controlling for several covariates, including region-based homophily (a proxy for regionalization), transitivity and country wealth.
Stochastic models can be used to identify the specific processes that have
led the network to its particular configuration. Both the gravity model and
the exponential random graph model (ERGM) are possible approaches to test
the relationship between geography and trade. Aside from weak theoretical
backing, another main shortcoming with these approaches is that they assume
independence among all trade linkages between country pairs. In reality, it is
very likely that there is inherent dependency between ties (Shortreed et al.
2006). For example, if South Africa and Brazil are trade partners, and China
and Brazil are trade partners, then it is more likely that South Africa and China
are trade partners then it is if these previous trade relationships did not exist.
By implementing proxies to take into account second- and third-order dependences in the network, the latent space model is one method to deal with
this dependency.
This paper attempts to add to the growing literature on the World Trade
Network (WTN), as well as to test the ‘death of geography’ thesis, by statistically analyzing the role of geography and trade integration using latent space
stochastic models. To carry out these objectives, I estimate several simple latent
space models to capture the relationship between distance and the likelihood of
two countries establishing a trade partnership in the WTN, while also taking
into account higher order dependencies in the network. Results from the analysis support regionalization, in favor of the ‘geography is destiny’ thesis (Dieter
2007), implying that proponents of the ‘geography is dead’ overestimate the
distance-destroying effects of globalization on the global trade economy.
Anthony Howell
283
The outline of this paper is as follows. In the subsequent section, I provide
a brief background on relevant network analysis studies. In Section 3, I discuss
issues related to building, specifying and representing the trade network. In
Section 4, I provide an overview of the main network statistics and network
properties commonly used to infer patterns in the trade network. Specifically,
I consider connectivity, centrality, clustering and hierarchy, as well as homophily and transitivity. In Section 5, I specify several latent space models and
test the principles of propinquity, homophily and transitivity. Lastly, Section 6
concludes with some final remarks.
2. Background
Due to advancements in physics and computer science, network analysis is increasingly relied upon to study the world trade network and is a powerful tool
that can be used to reveal topological properties, as well as the underlying
structure of the trade network (Fagiolo et al. 2009; Reyes et al. 2007, 2010).
For instance, network analysis applications of the world trade network (WTN)
have most notably addressed two major questions: (1) does the trade network
follow a core-periphery structure (Clark 2008, 2010; Kali and Reyes 2007); and
(2) do global elites tend to trade among themselves and what are the effects of
international trade on economic growth (Bhattacharya et al. 2008; Serrano
2008; Fagiolo et al. 2009).
Although comparatively underdeveloped, network analysis has also been
employed to investigate the role of geography in the global trade economy.
Kim and Shin (2002) argue that network analysis can naturally be extended
from dependency/world-systems theory to test the globalization vs. regionalization thesis that indirectly tests the role of geography by determining whether
countries in the network are globalizing or regionalizing (Aggarwal and Koo
2005; Kim and Shin 2002; He and Deem 2010).
Findings from network analysis contribute to the debate over whether regionalization is a stepping stone or stumbling block to globalization (Bhagwati
et al. 1999). On the one hand, some scholars believe that regionalization is
a transitory step that some countries pursue to become more competitive on the
global market, eventually promoting globalization and rendering geography
unimportant. On the other hand, other scholars suggest that regionalization impedes globalization by hurting the welfare of non-member countries and leading to inefficient production strategies that may work at the regional scale but
not at the global scale.
For instance, Kastelle et al. (2006) provides evidence that the ‘movement
of trade, capital and people is a geographically heterogeneous and historically
episodic process and can be interpreted to support regionalization rather than
globalization’. The authors' finding is significant because it highlights the power of geography to influence trade outcomes; even in an ever-increasing global-
284
Is Geography ‘Dead’ or ‘Destiny’ in a Globalizing World?
ized world, countries still pursue regional trade integration policies with nearby
countries.
Conversely, Kim and Shin (2002) argue that globalization and regionalization are not necessarily competitive, but complementary processes. From 1959–
1996, the authors show that the WTN became globalized (overall network density increased significantly), while it also became regionalized (intraregional
density also significantly increased). Based on their findings, the authors suggest that regionalization does not jeopardize globalization; rather the two processes are complimentary and can coincide with one another.
While the authors' findings have far reaching implications into the effects of
regionalization and globalization on the global economy, the findings are predicated merely on descriptive statistics, in this case, a network statistic called node
degree. Node degree measures the probability of a randomly chosen vertex to
have k-connections to other vertices and provides a summary of a node's overall
activity.11 The problem with this network statistic, like any other descriptive
statistic, is that no statistical model is used to control for other potential intermediating variables that may influence the outcome of a trade tie being established.
Most of the literature on the WTN only examines the network's summary
statistics to track topological changes, and few attempts are made to statistically
analyze the trade network using stochastic models (notable exceptions are Garlaschelli and Loffredo 2005; Garlaschelli et al. 2007). Fitting statistical models
to networks, in general, is still in its infancy stages due to the complexity of
modeling networks and the high level of computation that is required (Hunter
and Handcock 2005). It is not surprising, therefore, that the WTN literature
has only recently begun to be modeled; despite the complicated nature of
the WTN, pertinent topological properties of the global trade system can and
should be extracted through modeling the system as a network (Serrano
2008).
3. The Network Data: Specification and Representation
Bilateral trade data are extracted from the United Nations COMTRADE database. Data for GDP per capita and the trade/GDP share are extracted from Penn
World Table 6.2 (for a country listing, see Appendix). In the trade network,
countries represent nodes and the links between two countries are their shared
imports and exports. If a trade tie is not present, then yij = 0. The data offer information on both exports and imports, however, I use only import data because previous scholars suggest that these figures are more accurate than export
figures (Kim and Shin 2002).
1
Node degree is discussed in greater detail in Section 4.
Anthony Howell
285
A network can be set up as some combination of binary/weighted, directed/undirected and static/longitudinal. For the purposes of this research,
I build a binary, undirected and static network. These specifications are chosen
for the following reasons: (1) Squartini et al. (2011) specify various combinations of the network and find that the projections made by the binary matrix are
maximally informative and should be the focus of subsequent models of trade;
(2) the number of in and out ties are highly correlated, and in accordance with
Fagiolo et al. (2009) and Serrano and Boguna (2003), the WTN is sufficiently
symmetric to use an undirected analysis; and (3) while the descriptive statistics
may change as new countries are incorporated into the network and trade relationships are established and/or strengthened, it is likely that the underlying
processes that generate the network are likely to be stable over time (Schiavo
et al. 2010). To avoid the complexities of using longitudinal data, it is suffice to
select a stochastic model for a single year, 2008, to examine the statistical
properties of the WTN.
Network Representation
Graph theory, advanced by Harary and his collaborators (Harary 1959; Harary
et al. 1965), is used to inform much of what we know about how networks
work. A graph is a network model consisting of dichotomous (binary) relations.
The network can be represented with the following graph notation:
G = (V, E)
(Eq. 1)
where V is a vertex set, V = {υ1, …, υ2}, and in the undirected graph, E {(υi, υj) :
: υi, υj V}. In the undirected case, if country i exports to country j or country j exports to country i, then yij = 1. Countries represent vertices, and edges
between any two countries (υi, υj) exist if at least one million U.S. dollars in
trade is transacted during the year in observation. The one million U.S. dollar
threshold is common in the WTN literature (Kim and Shin 2002) and is selected in order to focus on significant trade relationships that shape the network.
I set Y to be the adjacency matrix for the random graph G. Yij is a binary
random variable which indicates the state of the i, j edge. The Pr (Y↓ij = y↓ij) is
the probability of the Yij edge state. I can express yij in terms of the WTN as
a dichotomous outcome:
1 if ( i , j ) trade volume $1 million US .
(Eq. 2)
yij =
0 otherwise
The density of a network is the proportion of present ties to the maximum
possible lines in a graph. A gXg nodal graph can be computed as:
i , j yij
.
(Eq. 3)
g ( g 1)
The density for the WTN in 2008 is .59, which means based on the number
of nodes, trade ties represent approximately 59 per cent of the total possible.
286
Is Geography ‘Dead’ or ‘Destiny’ in a Globalizing World?
There are 7,177 mutual ties in 2008, but 2,799 asymmetric trade ties. Germany,
the U.S., and China are the biggest traders averaging around US $8 billion to
each of its trading partners. Almost 40 per cent of countries export something
to almost every other country, and every country exports to at least 20 other
countries, indicating that the trade network is very concentrated.
Table 1. Network statistics for 2008
2008
Countries Reporting Trade
Graph Density
Total number of dyad trade ties
Total number of asymmetric trade
ties
Countries making up 50 % of exports
190
.59
7 177
2 799
9
Source: Author's calculations using COMTRADE database on reported trade 2008.
4. Network Summary Measures: Definitions
and Descriptive Statistics
Each network statistic attempts to explore the underlying structure of the network along one of the four major dimensions: connectivity, assortativity, clustering and centrality. Within each dimension, various node level statistics can
be employed to quantify individual positions in the network and describe the
local neighborhood. For example, node degree (ND) and node strength (NS) are
network statistics used to measure node connectivity. ND is used when dealing
with a binary network, and is the fractional count of trading partners a country
has relative to all possible trade links in the network. NS is used when dealing
with weighted networks, and measures the intensity of these trade links.
Both statistics calculate the number of direct ties coming in and going out
of a node and represent how connected a country is within a trade network.
High degree positions are influential in the network, and at the same time, may
be vulnerable to other actors' influence. These statistical measures are used in
the empirical studies to offer evidence for or against increasing globalization.
If the statistics increase in value, they show the globe is becoming smaller or
more integrated over time.
The average nearest neighbor degree (ANND) and average nearest neighbor
strength (ANNS) are the most common network statistics to test assortativity.
They measure the number of trading partners and the intensity (volume of trade)
of a given country's trading partners. For example, if country A has 20 trading
partners and each of those 20 countries trades with 20 other countries,
ANND/ANNS gives ND/NS statistics for each of country A's trading partners.
These two statistics are commonly employed to assess whether certain group-
Anthony Howell
287
ings of countries tend to trade with well- or less-connected countries. For example, ANND/ANNS can be used to test whether a ‘rich club phenomenon’ has
emerged in the WTN.
The binary clustering coefficient (BCC) and the core clustering coefficient
(CCC) are statistics for clustering. The BCC is a ratio that counts the number of
triangles that exist compared to the total number of triangles that are possible in
the network. CCC measures the trade intensity of these triangles. These statistics
offer a perspective on the multi-lateralism vs. bilateralism debate. Clearly, if the
statistics increase over time, the WTN is strengthening multi-lateral ties, whereas if the statistic is decreasing, it is associated with a rise in bilateralism.
Lastly, the centrality dimension has probably received the most attention in
the network analysis because of its explanatory power of describing the hierarchy that exists within the network. The betweenness (BET) and the random
walk betweenness centrality (RWBC) measures are the most commonly employed statistic for the centrality dimension and are based on reach and flow
mediation. Both statistics quantify the ability of the ego-node to influence other
vertices in the network. The higher is the measure for a country, the higher is
the degree of influence that country has on the WTN. Most often, this measure
has been found to show a core-periphery hierarchy in the WTN, thus strengthening the position of world-systems perspective.
In addition to network statistics, homophily is an important feature in this
study of social networks and helps to explain why we observe a particular type
of network. The principle of homophily is predicated on the fact that people with
similar characteristics will have a higher rate of contact between them than dissimilar people (Louch 2000; McPherson et al. 2001). One can scale this principle
up to include, organizations, countries, regions, and so forth. In the present context, I am interested in whether homophily by region exists. That is, do regions
delineated by geographical proximity and historical reference tend to trade more
among themselves relative to ‘outsiders’ in other regions that do not share a similar degree of cultural and historical shared experience? While there are many
different ways to delineate regions, the most basic source of homophily is space
(McPherson et al. 2001), so it makes intuitive sense to group countries based on
geographic proximity (refer back to the Appendix for a country listing by region).
Transitivity is another main feature found within networks. Transitivity is
a statistics that measures the degree of network integration. Balance theory predicts that people should adjust their relations until the network becomes stabilized around a pattern where all dyadic ties are largely transitive, that is triadic.
This social phenomenon tends to be explained in terms of triadic relationships
and by the adage ‘a friend of a friend is a friend’ (Krivitsky et al. 2009). Balance theory predicts that if ties exist between country A and country B and
country B and country C, then country A and country C have a strong propensity to develop a tie. A triangle is defined to be any set f(i; j); (j; k); (k; i)g of
three edges (Morris et al. 2008).
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Is Geography ‘Dead’ or ‘Destiny’ in a Globalizing World?
Descriptive Network Statistics: Connectivity, Centrality and
Homophily
Mathematically, the node degree measures the probability of a randomly chosen
vertex to have k-connections to other vertices and provides a summary of a node's
overall activity. The number of incoming ties is called in-degree, expressed as the
sum of incoming ties over the number of actors in the network minus 1. In-degree
ties will equal out-degree ones, expressed as
Ci ni gj1 x ji
.
(Eq. 4)
g 1
Histograms of the node degree show that the distribution of trading partners is right-skewed, meaning that most countries in the network have a small
number of trading partners but a smaller number of countries, referred to as
‘hubs’, have a comparatively larger number of trading partners (see Fig. 1).
Fig. 1. Node degree distribution for the world trade network
289
Anthony Howell
Along the second dimension, centrality measures the quantity of walks that
pass through the ego-node, that is betweenness. Betweenness (BET) is the tendency for an ego-node to reside on the shortest paths between third parties, that is,
to serve as a bridge between two other nodes.
Betweenness relies on the concept of geodesic distance, which is the
shortest path between two nodes, i and j. Betweenness can be quantified and
expressed as:
g n
j k ik i
g jk
(Eq. 5)
Cb ni
g 1g 2 .
2
gjk is the number of j, k geodesics (the shortest path between j, k) and gik (ni)
is the number of j, k geodesics that include i. High betweenness positions are
associated with the term ‘broker’. In the network literature, a ‘broker’ is an actor that mediates between third parties who are not directly tied. Both the node
degree and betweenness measures are standardized and are compared to the
theoretical maximum number of edges possible for that graph, values ranging
from 0 to 1.
Another centrality measure that is less commonly explored in the world
trade network is the eigenvalue centrality (EC). This measure quantifies the
position of the actor in terms of the sum of the centralities of its neighbors, attenuated by a scaling constant (). Eigenvector centrality can be expressed numerically as:
C D ni
1
x C n .
g
j 1
ij
D
j
(Eq. 6)
Actors with high eigenvector centrality are those with many central neighbors. This centrality measure is often overlooked by the previous articles on the
WTN, which is bizarre considering this statistics is ideally suited to test coreperiphery relations, a major focus point for the WTN analyses in the past.
Table 2 reports the statistics for a selective number of measures, including
connectivity (ND) and centrality (BET, EC) by region. The findings reveal the
most connected countries within regions, as well as compare the degree of influence across regions. For example, NAFTA and East Asian countries are the
most connected and central/influential regions in the global economy. Despite
the high connectivity and centrality scores for the United Kingdom, Germany
and France, the EU consists of many small Eastern European countries not very
well connected, thereby lowering overall average scores for the EU. SAA and
the Arab league are the least connected and least central regions in the global
economy.
290
Is Geography ‘Dead’ or ‘Destiny’ in a Globalizing World?
Table 2. Connectivity and Centrality Measures by Region and Select
Countries
Region
1
NAFTA (n = 3)
USA
CAN
MEX
EU 2 (n = 40)
UKG
GFR
FRN
East Asia (n = 5)
JPN
China
ROK
ECE (n = 11)
RUS
UKR
BLR
ASEAN (n = 10)
THI
MAL
INS
SAA (n = 9)
IND
PAK
BNG
Arab League (n = 17)
SAU
ISR
UAE
Pacific Islands (n = 13)
AUL
AUS
NEW
Latin America (31)
BRA
ARG
RUM
African Union (50)
SAF
EGY
ND
2
279.3
346
284
208
210.3
344
340
338
246
342
332
310
156.2
278
276
194
191.4
304
298
292
136.7
314
262
196
155.4
234
232
218
80
294
266
220
132.9
294
244
242
106.3
280
228
BET
3
218.9
439.39
186.2
31.2
103.8
522.9
376.9
304.3
177.7
477.7
270.8
177.21
27.4
104
109
39.5
78.5
233.7
170.4
144.4
45.6
222.7
107.6
57.68
24.4
90.2
65.3
62.1
38.04
246.7
114.12
120.7
21.2
175.2
65.3
69.4
11.2
131.2
49.5
EC
4
.107
.121
.11
.09
.084
.12
.121
.11
.094
.12
.121
.11
.079
.11
.12
.082
.079
.113
.113
.112
.058
.116
.102
.082
.068
.093
.095
.09
.033
.11
.106
.09
.059
.11
.101
.1
.049
.109
.096
291
Anthony Howell
Within East Asia, China has only 10 fewer trading partners than Japan (i.e.
connectivity), yet its BET centrality score is almost half as big as Japan's. This
distinction between connectivity and centrality is a key feature of network
analysis. It reveals that although China is increasing the number of its trading
partners and becoming better connected with the global economy, its actual
influence in the network in terms of trade remains limited relative to Japan.
Japan, along with the UK, and the USA have the highest BET centrality score,
representing the brokers in the network; China, on the other hand, is plotted
much lower than any of these three countries (see Fig. 2).
To gain a better understanding on whether homophily by region is present
in the WTN, I present the mixing matrix for each region (Table 3). The mixing
matrix presents the count of trade relationships cross-tabulated by the region of
the two countries involved. If a strong presence of homophily is present, then
there would be large values along the diagonal relative to off-diagonal values.
Based on the fact that the diagonal values in the matrix do not tend to be higher
than the off-diagonal values, countries do not appear to be overwhelmingly
trading within their particular region; homophily by region does not appear to
be a major factor.
500
UKG
JPN
GFR
NTH
300
FRN
CHN
ITA
200
AUL
BEL
SPN
IND
CAN
BRA
AUS
100
Betweenness
Measure
Betweeness Measure
400
USA
ROK
POR
MAL
DEN
GRC
INS
NOR
NEW
PAK
IRE
THI
SAFSIN
SWD TUR
SWZ
TAW
UKR
FIN
RUS
SAU
POL
RUM
CZR
HUNISR
UAE YUG
TUN
BNG
DRV
EGY
VEN
CDICOL
BLR BUL
PHI
ALG
LEBLUX MEXMOR
CHL CYP
SLO
SLV
PER
KEN
TRI
IRN
ZIM
NIG
JAM
SEN SRI
EST GHA HON
CUBDOM
ECU
MLT
CAO COS
MAS
OMA
LAT
LIB
BAH
BAR
URU
KZK
KUW
JOR
CRO
SYR
YEM
MYA
PANPRK
ZA
SAL
MLD
LIT
MAC
AZE
TOG
ICE
GUA
QAT
MZM
GUY
TAZ
MAW
ANG
GUI
GRG
FJI
CON
UZB
SUD
TAJ
TKM
NIC
LBR
BEN
BFO
BHM
GAB
BOL
DMA
UGAVAN
ALB
MAA
KYR
GAM
ETH
CEN
DRC
SUR
SVG
SIE
SLU
PNGRWA
MLI
NEP
MAG
NIRPAL
AFG
ARM BHU
HAI IRQKBI
BLZ
BOS
BOT
SWA TON
TUV
STP
SEY
SKN
SNM
SOL
SOM
MNC
MON
MSI
PAR
NAM
NAU
AAB
AND
LAO
LES
LIE
MAD
GRN
GNB
FSM
EQG
ERI
COMDJI
CHA
CAP
BRU
BUI
CAM
0
ARG
0
50
100
Index
Fig. 2. Centrality score by country
150
292
Is Geography ‘Dead’ or ‘Destiny’ in a Globalizing World?
Table 3. Mixing matrix by region
1
1
2
3
4
5
6
7
8
9
10
11
3
104
3
12
21
23
18
40
19
81
92
2
104
590
37
144
302
250
168
388
141
599
893
3
3
37
NA
5
11
10
7
16
7
27
43
4
12
144
5
7
38
37
25
52
23
99
123
5
21
302
11
38
47
48
43
71
27
98
106
6
23
250
10
37
48
40
51
93
43
128
194
7
18
168
7
25
43
51
16
62
29
62
118
8
40
388
16
52
71
93
62
83
44
142
247
9
19
141
7
23
27
43
29
44
13
80
81
10
81
599
27
99
98
128
62
142
80
243
259
11
92
893
43
123
106
194
118
247
81
259
251
There are two caveats to this interpretation. First, marginal totals can be misleading and do not statistically test for the presence of homophily (this will be
carried out in the modeling section below). The trade network is also very
complex and strict interpretations of homophily are not always straight forward.
For example, the largest value in the matrix is between Europe (region 2) and
Africa (region 11). Due to the colonization era, African and European countries
still maintain a strong, client-like relationship in many cases. Second, there are
likely some misleading results due to the way countries are grouped. While
there is no ‘right’ way to group countries into regions, defining China (region 4) as its own region has some drawbacks in certain cases, since its value
along the diagonal is 0, and the data only cover international trade. Therefore, it
is not possible to see China's intra-trade relationships and how it compares to
other countries' international trade within a particular region.
The number of triangles found in the network area is a proxy for measuring
the transitivity. Of the 7,177 ties in the network, the number of triangles is surprisingly large – 157,645. This number is far larger than what would be expected by chance and offers initial evidence that the trade network has a high
degree of transitivity. This is significant because it reveals the dyadic trade dependencies among countries supporting the use of a latent space modeling approach.
5. Latent Space and Latent Position Model: Is Geography
Dead?
Latent space models have replaced block-modeling as the primary approach to
study issues of propinquity, the tendency of spatially proximate vertices to be
tied. In other words, latent space models are used to determine the role of geography in the international trade context, and can help examine whether the trade
network is globalizing or regionalizing. If proponents of globalization who
suggest ‘geography is dead’ are correct in their assertion, then the results
of the latent space model will confirm that distance does not play a significant
293
Anthony Howell
role in influencing the probability that a trade tie is established between country
i and country j.
In order to test the role of geography in determining the probability two
countries (i, j) form a trade relationship, I specify several latent space models.
Based on the presence of homophily indicated by the descriptive statistics,
there is evidence that propinquity – the probability of a link between two actors
is a function of the distance between them in an unobserved latent space – exists in the trade network.
The latent position model assumes a conditional independence approach to
modeling. Let {zi} be the positions of the actors in the social space Rk and {xi, j}
denote the observed characteristics that are dyad-specific. That is the presence
or absence of a trade tie between two countries is independent of all other ties
in the system, given the unobserved positions in social space of the two individuals:
P(Y|Z, X, θ) = P(yi, j | zi, zj, xi, θ),
(Eq. 7)
where X and xi and xi, j are observed characteristics that are pair-specific and
vector-valued and θ and Z are parameters and positions to be estimated (Hoff
et al. 2002). I use logistic regression to parameterize Eq. 3.
i , j log odds yi , j 1 zi , z j , xi , j , , .
(Eq. 8)
i , j xi , j zi z j
,
(Eq. 9)
where the log odds ratio for two actors j and k, equidistant from i, is
B , xi , j xi , k . I estimate i, j using the log-likelihood of a conditional independlog P Y
ence model, expressed as
i j
i , j
i , j yi , j log 1 e
,
(Eq. 10)
where is a function of parameters and unknown positions. As such, I use
maximum-likelihood to estimate . Model degeneracy is a serious problem that
frequently occurs when dealing with networks. If a model is degenerate then
the terms in the model are grossly unsuitable at describing the underlying processes that form the observed network. That is, even under the maximum likelihood coefficients in the model, the observed network is so unlikely to occur
that the model cannot even be properly estimated (Goodreau et al. 2008).
To check for issues of degeneracy, I carry out an MCMC estimation procedure
for each model that I estimate. The results show that the model statistics do not
diverge from the mean, meaning that the models are not degenerate and the
maximum likelihood estimates are reliable.
I specify several simple latent space models to test the role of distance and
region-based homophily. Table 4 reports the coefficients generated from the
latent space models. Model 1 only examines the role of distance in establishing
a trade partner. The coefficient on EDGES is highly significant and positive,
indicating that larger distances increase the likelihood of two countries estab-
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Is Geography ‘Dead’ or ‘Destiny’ in a Globalizing World?
lishing a tie. This finding is bizarre and at odds with predictions made by gravity models that predict trade decreases as a function of distance. In Models 2
and 3, I give additional measures to control for underlying structures within the
network that may affect whether a trade tie is established.
Table 4. Latent space models (d = 2)
Edges
Latentcov (homoregion)
Triangle
Nodecov.GDP
Model 1
2.56***
Model 2
–5.73***
26.25***
Model 3
–6.21***
27.20***
1.84***
Model 4
–6.13***
27.81***
2.02***
1.42***
A good model is the one that accounts for a country's tendency for assortative
mixing, which is based on the notion of homophily (Goodreau et al. 2008). In
the present context, I want to account for assortative mixing that may occur for
countries that belong to a particular region. If assortative mixing is present,
then countries within the same region have a greater probability of forming a tie
relative to countries in other regions.
Model 2 introduces Homoregion, a covariate that accounts for homophily.
In this model, I find the sign of the EDGES coefficient switches from negative
to positive, confirming the conventional relationship between trade and distance. In other words, the likelihood of two countries forming a tie decreases as
distance between countries in latent space increases. The coefficient on Homoregion is very large and statistically significant. This finding indicates that
countries classified into the same regional grouping will be more likely to form
a trade tie within their own region than with countries from other regional
groupings, in support of the regionalization thesis. Model 3 adds Triangle to
take into account the transitive nature of the network. The significant, positive
coefficient for Triangle confirms that if two countries i, j, have a mutual trading
partner, m, then the likelihood that countries i, j begin to trade increases.
In addition to controlling for network statistics, Model 4 adds real per capita GDP, Nodecov.GDP as an additional covariate to control for the effect of
wealth on countries forming a tie. The positive, statistically significant coefficient produced by the wealth covariate reveals the hierarchical structure of the
network, meaning that rich countries tend to trade disproportionately among
themselves.
6. Conclusion
The findings presented in this paper suggest that regionalization is a particularly important strategy pursued by countries in the global economy. The integration of regional blocs, along with the proliferation of regional trade agreements (RTAs) promote regionalization and have emerged as individual countries attempt to mitigate the new economic and security vulnerabilities (unregulated capital flows, human and drug trafficking, transnational terrorist net-
Anthony Howell
295
works, disease, etc.) brought about by globalizing forces that undermine individual states' territorial sovereignty. The process of regionalization signals that
‘geography is destiny’ (Dieter 2007: 11), as opposed to ‘geography is dead’.
The results of the descriptive analyses in this report agree with other previous works. The WTN network has a high density, the node degree has a high
right-skew, trade partners of well-connected countries are less interconnected
relative to those of poorly connected ones, and countries holding many trade
partners are on average connected with countries holding relatively few countries. The latent space model tests directly the role of space in determining the
likelihood of whether or not a tie will be established. When controlling for regional homophily and other covariates, the Euclidean distance – calculated in
social space – is returned negative, significant, and large in magnitude. This
result supports findings in the gravitas literature on trade and reaffirms that the
probability that trade ties are established decreases as distance increases. Lastly, the latent space models add an additional dimension of analysis of the WTN
by controlling for network dependencies, and reveals that region-based homophily – the proxy for regionalization – has a large and significant influence on
trade outcomes, even more so than a country's wealth.
Despite the complicated nature of the WTN, pertinent topological properties of the global trade system are extracted through modeling the system as
a network, and are used to show the significance of geography in influencing
trade outcomes. Understanding the structure of the global trade network has
implications for research across numerous social science disciplines trying to
examine the effects of geography on economic integration and internationalization. Future areas of research can extend the latent space model applied in this
paper to examine the evolutionary role of geography over time. Although evidence reported in this paper suggests that geography maintains a crucial role in
the trade network, it is indeterminate whether geography's impact on trade ties
is increasing or decreasing over time.
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Appendix
190 countries are placed into 11 regions. These regions are based on presentday trading blocs and/or geographical location. Several regions combine two or
more economic trading blocks that span a certain geographic region. For example, the EU, EFTA and Central European FTA member countries are all categorized as one European region based on their geographical proximity. Similarly,
UNASUL, Caribbean Community and the Central American Integration System member countries are all categorized as Latin America.
Regional Groupings
NAFTA (Region 1)
CAN
MEX
USA
Europe (Region 2)
ALG
AND
ANG
ARG
ARM
AUL
AUS
AZE
BAH
BAR
BEL
BEN
BFO
BHM
BHU
BLR
BLZ
BNG
BOL
BOS
BOT
BRA
BRU
BUI
BUL
CAM
CAN
CAO
CAP
CDI
CEN
CHA
CHL
CHN
COL
COM
CON
COS
CRO
CUB
East Asia (Region 3)
(Also Region 4)
JPN
MON
PRK
ROK
TAW
CHN
Eurasian Economic
Community
(Region 5)
ARM
AZE
BLR
GRG
KYR
KZK
RUS
TAJ
TKM
UKR
UZB
ASEAN (Region 6)
BRU
CAM
DRV
INS
LAO
MAL
DRV
MYA
PHI
SIN
THI
South Asia Association
(Region 7)
AFG
BHU
BNG
IND
MAD
NEP
PAK
SOL
SRI
299
Anthony Howell
Arab League (Region 8)
BAH
EQG
IRN
IRQ
ISR
JOR
KUW
LEB
MOR
OMA
PAL
QAT
SAU
SUD
SYR
UAE
YEM
Pacific Islands
(Region 9)
AAB
AUL
AUS
DMA
FJI
FSM
KBI
NAU
NEW
PNG
TON
TUV
VAN
Latin America (Region 10)
ARG
BAR
BHM
BLZ
BOL
BRA
BRA
CHL
COL
COS
CUB
DOM
ECU
GRN
GUA
GUI
GUY
HAI
HON
JAM
MSI
NIC
PAN
RUM
SAL
SKN
SLU
SUR
SVG
TRI
URU
VEN
African Union
(Region 11)
ANG
BEN
BFO
BOT
BUI
CAO
CAP
CDI
CEN
CHA
COM
CON
DJI
DRC
EGY
ERI
ETH
GAB
GAM
GHA
GNB
KEN
LBR
LES
LIB
LIE
MAG
MAS
MAW
MLI
MZM
NAM
NIG
NIR
PAR
PER
RWA
SAF
SEN
SEY
SIE
SOM
STP
SWA
TAZ
TOG
TUN
UGA
ZAM
ZIM
10
The British-Italian Performance
in the Mediterranean from the Artillery
Perspective
Kent R. Crawford and Nicholas W. Mitiukov
Abstract
The Italian defeat in the Second World War was a consequence of its failure to
dominate the central Mediterranean. In the numerous works that address the
issue, scholars tend to see reasons of a political nature, shortcomings in
the organization and planning by the Italian Navy, indecisive political leadership, and so on. But all agree that technically the Italian fleet was superior to
British ships deployed in the Mediterranean area, and in this regard the defeat
of the Italians is seen as paradoxical. In this paper, the authors explore the
theory that the poor showing of the Italian navy may have resulted from the
errors of the political, military and technical leadership in the prewar period,
in particular in the performance of the Italian naval artillery.
Keywords: Mediterranean history, naval history, Italy, Great Britain, historical reconstruction.
Introduction
In recent years the phrase ‘technical innovation’ has been widely used in the
literature or for various purposes. But nevertheless, there is an undeniable connection between social evolution and technical innovation. Probably, one can
find the most original presentation of this relationship in Theory of Cultural
Circles by Fritz Graebner (Methode der Ethnologie; see Graebner 1911). When
analyzing ancient and medieval data, it is easy to notice that progress in technical areas, especially in military technology, could give the possessors of these
innovations a decisive advantage over other nations, contribute to the conquest
and exploration of new territories, and insure a certain domestic tranquility.
Also there is no doubt that the level of innovation is ‘cumulative’; each subsequent military innovation is much more effective than the previous one. Nor is
there any doubt that a continual innovation became the key to survival. For
instance, in the twelfth century, Saladin's Moslems perfected the horse archer
regarding it as the ultimate weapon. Thereafter, the innovation in the military
History & Mathematics: Trends and Cycles 2014 300–313
300
Kent R. Crawford and Nicholas W. Mitiukov
301
sphere virtually ceased, and the Muslim states thus missed out on the developments in gunpowder weapons.
The twentieth-century data brought about some changes in this coherent
theory. It turned out that the nature of technical innovations varies, which is
most clearly demonstrated by the evolution of naval artillery. Because of the
high cost, hardly anyone, even the richest state, could afford to evolve artillery
by trial and error or aesthetics, but had to develop and strictly adhere to a certain doctrine, referred to in the literature as ‘technology policy’. For example,
advances in development of propellant powders and artillery materiel in the
beginning of the twentieth century was applied to create a new generation of
artillery for high muzzle velocities and therefore, better ballistic performance.
And it became possible to design artillery with the performance of the previous
generation, but much easier and simpler to produce, and hence less expensive.
In this case, there seems to be a continuing conformity with the ‘cultural circles’, though this is an illusion. It was just the high cost and complexity of the
twentieth-century artillery technology that turned out to be a trap in innovation.
If the underlying facts and theories for a particular technology policy decision
subsequently prove to have been incorrect, the resulting material must still be
used until it can be replaced, with corresponding performance issues. Making
a wrong choice in policy has serious and costly consequences.
To illustrate the effect of such a highly subjective characteristic as ‘technology policy’ at the macro-level, one needs merely to look at the combat operations in the Mediterranean theater of the Second World War. The most characteristic feature are the operation in 1940–1943, the period of active participation in the war at sea in Italy. In the late 1920s and 1930s, Italy had been virtually isolated from the influence of external military innovation, primarily German and American. And in point of fact, the Italian ordnance technology had its
origins in the British firms such as Armstrong/Elswick and Vickers in the late
nineteenth century, which continued through and immediately following the
Great War, after which the source ‘dried up’ and left the Italians to their own
devices. So, in a general sense, their ordnance of the Second World War predominately reflected the Italian policy decisions.
Perhaps, more than any other form of combat, naval warfare is dominated
by technology. For example, the naval engagements of the Russo-Japanese War
(1904–1905) may be viewed in terms of French and French influenced technology versus British technology. In a like manner, the combat in the 1940–1943
period compares the products of Italian versus British technology. At stake was
control of the central Mediterranean, necessary to provide the ability to supply
and reinforce the military forces in North Africa.
Historical Note
The naval war in the Mediterranean Sea from 1940 to 1943 is still the subject of
much controversy, revolved not so much about what actually happened, but
302
The British-Italian Performance in the Mediterranean
rather why the campaign proceeded the way it did, and the various engagements
so unsatisfactory for the Italian Regia Marina. There are many theories, and
this paper and model explore one of them.
The Regia Marina. The strategic situation of the Italian military in 1940
was the one of dominating the central Mediterranean, from roughly Algiers to
Tripoli. And this was improved considerably in the spring of 1941 with the
conquest of Greece and Crete, which extended their presence as far as Benghazi, with a combination of air power and naval power.
The main power of the Regia Marina was four extensively re-built and
thoroughly modernized fast battleships from the Great War. More properly,
these should probably be considered as battle-cruisers due to their high speed
and relatively light armor protection. Four very powerful modern fast battleships of the Littorio class, two of which would join the fleet in 1940, and the
other two scheduled for completion in 1942. In the event, only Roma would be
completed on time, with Impero still fitting out slowly in September 1943
(Gardiner 1980).
These were backed by seven heavy cruisers armed with 8-in (203-mm)
guns, completed between 1928 and 1933, and twelve light cruisers armed with
6-in (152-mm) completed between 1931 and 1937. Twelve extremely fast unarmored scout cruisers were laid down in 1939, but only three were completed
before the Italian surrender.
Sixty well armed destroyers, launched between 1925 and 1943, and sixty
five torpedo boats, which could also be classified as destroyer escorts or corvettes, were launched between 1937 and 1943.
The Regia Marina had adopted a high velocity / heavy projectile combination for their naval guns, first used with the 12-in (304.8-mm) guns of 1909. This
would provide good range and good armor penetration. With the modern guns, it
was quickly apparent that the dispersion pattern was too great, so the muzzle velocity was reduced without completely fixing the problem. The Table below gives
the original MV and the reduced MV, with comments as applicable.
Table 1. Ballistic information of Italian guns
Gun
381 mm / 50
203.2 mm / 50
203.2 mm / 53
Original MV (m/s)
870
905
960
Reduced MV (m/s)
850
840
900
152.4 mm / 53
120 mm / 50
1000
950
850
920
Notes
With new lighter shell
With original heavy
shell
The 320-mm / 43.8 (bored out 304.8-mm / 46) were quite good. With a muzzle
velocity of 830 m/s, their shooting was good and the initial patterns were very
tight; so tight, in fact, that they were adjusted to be larger. The 6-in / 55 (152.4-mm)
Kent R. Crawford and Nicholas W. Mitiukov
303
had a muzzle velocity of 910 m/s, which was left unchanged. The new 135-mm /
45 (5.3-in) had a muzzle velocity of 825 m/s and shot well. Doctrine called for
firing by turret with a several second interval. For a three turreted ship, the order would be A, C, B. For a four turreted ship it would be A, D, and C and B
together. Cruisers with twin turret mounts would be A, D, C, B.
Fire Control was one of the RM's strong points, and their equipment and
system were excellent. While they were late developing radar, they had fully
developed the concept of the Fire Control Central, which featured the Director,
computing machinery, inclinometers, follow-the-pointer gear, and range finders, all of a very high quality. They had also developed the concept of scartometry, by means of which the fall of shot was ranged with a stereoscopic
range finder and the results compared to the calculated gun range. This would
measure the variance and provide the correction. Problems with Italian gunnery
cannot be blamed on their fire control suite (O'Hara 2009).
The Royal Navy. Great Britain had a vastly larger navy than Italy. But
they also had many commitments for their finite resources, which included
keeping a viable force at each end of the Mediterranean, so they were perpetually numerically inferior to the Regia Marina.
The main strength of the RN in 1940 consisted of the five Queen Elizabeth
class battleships, four of which had fought at Jutland in 1916. Two of them had
been reconstructed and modernized, while the other two had not been, and remained little improved. The fifth, the famous Warspite, which had been reconstructed to a slightly lesser extent than the other two, engaged Italian warships
on several occasions. There were also the four surviving Revenge class, two of
which had been at Jutland. They had not been modernized, and were decidedly
inferior at modern battle ranges. The two ‘Treaty’ battleships completed the
battle line. The new fast battleship King George V joined the fleet in 1940.
There were additionally the battle-cruisers Hood, Renown and Repulse, the last
two very lightly protected and under-armed. However, Renown had been thoroughly reconstructed and modernized, and was often attached to Force H out of
Gibraltar (Gardiner 1980).
The Royal Navy also had many modern heavy and light cruisers and destroyers. Losses had been heavy, especially around Crete. Thus the make-up of
these light forces changed frequently throughout the period.
British naval guns were of good quality. The performance was moderate,
so they were often theoretically out ranged by their opponents, though not so in
reality. In fact, Warspite scored one of the two longest range hits during the
war. Their projectiles, however, were first rate, and always seem to have performed well. Doctrine was for fairly tight patterns with ‘half’ salvos.
The RN's fire control was one of their strong suits. They were well ahead
in the development of radar, and all the cruisers and capital ships had elaborate
equipments for solving the gunnery problem. All the un-reconstructed ships
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The British-Italian Performance in the Mediterranean
were fitted with the Dreyer Fire Control Table Mk. V, or as modified over the
inter-war years. The new ships and those that had been reconstructed were fitted with the Admiralty Fire Control Table (AFCT), which was a post-Great
War development, as did most of the modern cruisers.
The Royal Navy was not ‘flashy’ in its ships and guns. Rather, they sought
consistency and high quality throughout. It should be remembered that the
brand new, untried and not even properly worked up Prince of Wales scored
against Bismarck in spite of equipment breakdowns and other problems with
the gun turrets.
None of the engagements between the heavy ships was fought to a conclusion, and all were at long range. Neither side has a significant advantage in fire
control. This is to say that the RN advantage of radar would have been offset by
the RM's scartometry. The RM enjoyed, on the whole, the advantage of more
powerful guns. This, however, meant nothing in view of the overly large dispersion patterns.
Research
Marc Antonio Bragadin's The Italian Navy in World War II (Bragadin 1997) is
bewildering. Their ‘greatest’ victory was Pantellaria, in which a British destroyer and several transports were sunk. But given the correlation of the forces
involved, they should have exterminated the entire convoy to the last vessel!
And the ‘super fast’ Italian ships would never catch the much slower British
vessels; Bartilomeo Colleoni, supposedly capable of 40 kts, was savaged by
HMAS Sydney, which on her best day made only 32 kts.
How could it be that with the larger fleet, magnificent artillery and welltrained crews the Italian Fleet suffered one shattering defeat after another? Let
us try to look at the problem through the prism of naval guns.
For the purposes of comparison, we shall select three artillery systems that
were nearly analogous between the two navies: the 381-mm (15'') main guns of
the battleships, 203-mm (8'') guns of the heavy cruisers, and the 152-mm (6'') of
the light cruisers. The performance of each is summarized below.
Table 2. Characteristics of British and Italian guns (Campbell 1985)
Caliber
Model
Shell weight,
kg
Muzzle velocity, m/s
152/50
203/50
381/42
152/53
203/53
381/50
Mk XXIII
Mk VIII
Mk I
Model 1926
Model 1927
Model 1934
50.8
116.1
871.0
47.5
125.3
885.0
841
855
752
1000
955
850
Form factor to
the Law of
1943
1.08
1.03
1.27
1.09
1.09
0.89
Kent R. Crawford and Nicholas W. Mitiukov
305
The technique and functions for ballistic calculations was presented in sufficient detail on the pages of Warship International in the article by William
Jurens (1984). Many of the functions are of an empirical character, and thus
differ a little bit for each country. So in Russia the definitions of a standard
atmosphere were set forth in the Russian State Standard 4401–78, which defined the character of temperature variations, density, viscosity, and air pressure
at altitude functions. These are the functions used for this analysis. And for the
laws of resistance the following were applied:
– Law of Siacci (for shells of a form similar to the standard Type 1);
– The Law of 1930 (similar to Type 8);
– The Law of 1943 (similar to Type 7).
In this case for the definition of the form factor of a shell, the Law of 1943
was employed. From Table 2, it is evident that the British and Italians have
used shells with almost identical ballistic properties. However, here there is
nothing unusual, as the British influence on Italian ordnance was really significant. Up to the end of WWI, the guns of the Italian fleet were made under license to designs from the firms of Armstrong (EOC) and Vickers. And as
a matter of fact, subsequent gun developments were modern versions of those
designs. This connection, by the way, shows rather exponential comparison of
the form factors for shells of the main guns of the leading maritime states. For
example, for guns of about 127-mm (5'') which were introduced into the inventories during the 1920–1930s, as the main guns for destroyers, the values are as
follows (using the Law of Siacci):
Table 3. Characteristics of destroyers' guns of the world
System
State
120/45 Mk I, Mk II
130/40 Model 1924
127/45 SK C/34
120/50 Model 1926
120/45 Type 3
130/50 B 13
127/38 Mk 12
Britain
France
Germany
Italy
Japan
USSR
USA
Muzzle
velocity, m/s
814
725
830
950
825
870
762
Shell
weight,
kg
22.70
34.85
28.00
23.15
20.41
33.40
25.04
Range for
elevation, m
14,450 (30)
18,700 (35)
17,400 (30)
22,000 (45)
16,000 (33)
25,730 (45)
15,300 (35)
Form factor
to the Siacci's Law
0.82
0.60
0.66
0.62
0.66
0.52
0.73
From the above table, taken from Tony DiGiulan's contributions to the Warships1 website (www.warships1.com), the ballistics of guns of the main European states and Japan were at approximately the same level. It is interesting to
note, however, that the Soviet shell had the best ballistic form. But this should
not be surprising, as the attention given to ballistics in the USSR, which resulted in the M.1928 pattern projectiles, is well known now. Stalin even took
a personal interest in the development program, which produced gun systems
equal or superior to all foreign designs in all main parameters save one – barrel
306
The British-Italian Performance in the Mediterranean
life. This unfortunately cancelled out all of their virtues, as the Effective Full
Charge life of the gun was equal to the capacity of the magazine!
The American and British guns have the worst ballistics form, but this cannot be the only criterion, since doctrine required the more universal application
of both anti-surface and anti-air capabilities.
But to return to the Anglo-Italian conflict in the Mediterranean, it is well
known that the hit probability is determined in large part by the angle in descent of a shell, known as the Danger Space. Steve McLaughlin (2001) defined
this relationship as:
Danger space = Target width + Target height / Tangent of Angle of Descent.
It follows, therefore, that the lower the angle of descent, the greater the hit
probability, which is the rationale behind the use of high velocity guns. Fig. 1
reflects this parameter of the major British and Italian guns.
As is depicted in Fig. 1, at all battle ranges the angle of descent of the Italian shells is less than that of their British opposite number. Indeed, at ranges up
to 16,000 m, the angle of descent of the Italian 203-mm shell is less than that of
the British 381-mm!
Fig. 1. Comparison of angle of incidences of shells1
If comparison were only limited to the size of the danger space, than the Italians
should have enjoyed a considerable advantage. This makes the results of the gun
1
For all figures: circle are 152-mm guns, square are 203-mm, rhombus are 381-mm guns; white for
British systems, black for Italian systems.
Kent R. Crawford and Nicholas W. Mitiukov
307
battles quite paradoxical. Therefore, as a second step we must try to estimate the
values of the ballistic corrections. A technique for obtaining such values would be
to determine the effect of corrections in an elevation angle: the variation of an elevation angle is applied, which affects the range. Thus, for each degree of deviation
either way, the shell either falls short or flies over by a certain number of meters.
Other corrections produce a similar result. The unique exception is a variation of
the atmospheric density and pressure, the values of which are generally included in
the Range Tables. The given technique was approved by the authors on the basis of
Range Tables (see TS-146 1971) for the 122-mm Soviet howitzer, model 1938, and
has given satisfactory convergence.
1) Correction of elevation angle – its physical sense is sensitivity of the
gun to the roll of the ships (see Fig. 2). Though Fire Control Suites were common before the War, the very sensitive instruments that appeared only afterwards had effect as if the ship were on an even keel, the consequences of roll
being eliminated insofar as the guns were concerned. But in the absence of such
systems, the divergence between the British and Italian guns is most obvious in
the performance of the 381-mm guns. Dispersion of the Italian shells was almost 1.5–2 times greater! This means that in the presence of virtually any wave
activity at sea (which is almost always), the British would have on average
twice as many hits as would the Italians!
Fig. 2. The correction on an elevation angle
308
The British-Italian Performance in the Mediterranean
2) Correction for the mass of the shell – sensitivity of the gun to the
‘know-how’ of shells (see Fig. 3). As is known, the more developed manufacturing processes warrant obtaining smaller tolerances. Thus, dispersion due to
variation of the mass of the shell is lower, as the shells are more uniform. However, as Jack Greene and Alessandro Massignani (see Greene and Massignani
1998) have pointed out in their The Naval War in the Mediterranean 1940–
1943, manufacturing tolerances in the production of the Italian shells were
overly large on the one hand, as was the weight control of the propellant used
in bagged charges.
The Table below shows the changes in range caused by a mere one per
cent variance in shell weight and propellant charge weight.
Table 4. Changes in range caused by a per cent variance in shell
weight and propellant charge weight
Condition
Range with 0 % increase
1 % increase in charge
1 % decrease in charge
1 % increase in shell wt.
1 % decrease in shell wt
1 % increase in both
1 % decrease in both
1 % increase in charge &
1 % decrease in shell wt
1 % decrease in charge &
1 % increase in shell wt
Shell weight
(kg.)
MV (m/s)
885
885
885
893.85
876.15
893.85
876.15
876.15
870
874.34
865.64
865.68
874.38
870
870
878.74
Range at 15-deg. elevation
(meters)
26,420
26,640
26,201
26,289
26,552
26,507
26,332
26,772
893.85
861.34
26,070
So even though it may have been possible for the Italians to have adjusted for
the variations in shell weight, which were often labeled on the projectile and
allowed for in the Range Tables, the variation in the propellant charges could
not. Thus the Italians were laboring under an additional burden with regard to
dispersion.
3) Correction for atmospheric pressure (see Fig. 4). In this area, the
change in condition would affect both sides, with neither obtaining a material
advantage. Thus, the value of this correction is not so great, as atmospheric
pressure varies rather slowly, which allows for its rather exact measure.
Kent R. Crawford and Nicholas W. Mitiukov
Fig. 3a. The correction on a mass for 152-mm shells
Fig. 3b. The correction on a mass for 203-mm shells
309
310
The British-Italian Performance in the Mediterranean
Fig. 3c. The correction on a mass for 381-mm shells
Fig. 4. The correction on atmospheric pressure
Kent R. Crawford and Nicholas W. Mitiukov
311
4) The correction for atmospheric density actually displays sensitivity of
the gun to meteorological conditions, as the presence of rain or snow results in
increased density of the air (see Fig. 5). This correction, as opposed to atmospheric pressure, is rather difficult to take into account. Sudden rain or snow
showers (the latter not common in the Mediterranean), or fog, would have
a detrimental effect on ballistic performance. But in this regard, the opponents
approximately correspond to each other, with neither obtaining an advantage.
5) Corrections in initial (muzzle) velocity caused by variations in the condition of the charges (see Fig. 6). These include charge temperature. Within
a range of tolerance, accounted for in the Range Tables, a higher temperature
would result in a higher initial velocity, and a lower temperature – in a lower
velocity. Other factors are not so predictable. The very conditions of storage
can negatively affect the charges, and could result in a breakdown of the chemical
components, while excess moisture would reduce burning efficiency. In our
opinion, the Italians had a slight advantage in this area.
Fig. 5. A correction for air density
312
The British-Italian Performance in the Mediterranean
Fig. 6. The correction on initial velocity
On the face of it, the British Royal Navy has an advantage over the Italians in
only one area of correction, but it is the most important and significant. What
does this mean? In the theoretical sense, the smaller danger space of the lower
velocity British guns would imply that only the most careful preparations and
calculations would counter the Italian advantage in hit probability. However,
the ballistic effects of roll are less for the British than for the Italians, and therefore correspondingly easier to correct. The worse is the sea state, the greater is
the British advantage in this respect. It is interesting that, empirically, the Italian gunnery performance should have improved as a result of their reducing the
muzzle velocity of their guns. The effect would have been to decrease the danger space, on the one hand, but to enjoy a corresponding decrease in the dispersion caused by the roll of the ship, on the other.
Conclusion
It is interesting to note that both the Royal Navy and the Regia Marina came to
similar conclusions based on the empirical evidence of combat, and over the
Kent R. Crawford and Nicholas W. Mitiukov
313
course of the war demonstrated an inclination to favor reduced muzzle velocities. Such reductions could be ten per cent or more, giving, for example, the
Italian 152-mm cannon a new muzzle velocity of 850 m/s from its original of
1000 m/s.
We are aware of the fact that such measures can only attempt a ‘cure for
the disease’, but in any case do not answer the question of the ‘severity of the
disease’. The British guns, of course, demonstrated much less sensitivity to roll,
but also a marked inferiority in other areas of performance, that they stood to
gain little or nothing from further reductions in muzzle velocity.
Thus, the choice of any one or two specifications as a marker for the evolution of a ‘cultural community’ can give the illusion of progress, but paradoxically lead to misunderstanding of the deep historical processes that affect the
synergistic relationship of many parameters (Crawford et al. 2005).
References
Bragadin M. A. 1997. The Italian Navy in WW II. 2 vols. Ekaterinburg: Zerkalo. In
Russian (Бра а и
. А. И а ья
ф
В
е. 2- .
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р : З р а ).
Campbell J. 1985. Naval Weapons of World War Two. Annapolis, MD: Naval Institute
Press.
Crawford K. R., Mitiukov N. W., and Mokrousov S. A. 2005. On Confrontation between England and Italy in the Mediterranean during the WW II. Istoriya korablya
2: 50–54. In Russian (Кра
р К. ., и
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а
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р и
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ир
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а я 2: 50–54).
Gardiner R. (Ed.) 1980. Conway's All the World's Fighting Ships, 1922–1946. New
York: Mayflower Books.
Graebner F. 1911. Methode der Ethnologie. Heidelberg: Carl Winter.
Greene J., and Massignani A. 1998. The Naval War in the Mediterranean, 1940–1943.
London: Chatham Publishing.
Jurens W. R. 1984. Exterior Ballistics with Microcomputers. Warship International 1:
49–72.
McLaughlin S. 2001. Predreadnoughts vs. Dreadnought: Action off Cape Sarych, 18
November 1914. In Preston A. Warship 2001–2002, pp. 117–140. London: Conway
Maritime Press.
O'Hara, V. P. 2009. Struggle for the Middle Sea. Annapolis, MD: Naval Institute Press.
ТS-146. 1971. Range Tables TS-146. Moscow: Voenizdat. In Russian ( а ицы
р ь ы
-146. .:
и а ).
11
The Shield of Islam? Islamic Factor of
HIV Prevalence in Africa*
Alisa R. Shishkina, Leonid M. Issaev,
Konstantin M. Truevtsev, and Andrey V. Korotayev
Abstract
HIV first appeared in West-Central Africa, then spread to the South, East and
West and, at the same time, had hardly reached North Africa. A possible explanation of this pattern can be the role of Islam that pays particular attention to
the prevention of extramarital sexual relations. In addition, one can mention
that the circumcised men suffer from HIV significantly less frequently than the
non-circumcised. Against such background, we had certain grounds to expect
that Islamic societies would have lower levels of HIV prevalence than nonIslamic. Our cross-cultural tests have supported this hypothesis. The data have
been analyzed with power-law regression. We have found a significant (p < .001)
and really strong (r = – .747) negative power-law correlation between percentage of Muslims and the HIV prevalence in African countries. Of course,
one should take into account that the stigma attached to HIV is also much
higher among Muslims and so, the Muslims tend to be tested, identified and
monitored at lower numbers than those from other religious and cultural backgrounds, which implies that further in-depth research is necessary in order to
detect the real relationship between variables in question.
Keywords: HIV prevalence, Africa, power-law correlation, Muslims, extra-
marital sexual relations, circumcision.
The HIV (Human Immunodeficiency Virus) first appeared in West-Central
Africa, then spread to the South, East and West and, at the same time, had hardly reached North Africa. In the last decade of the twentieth century an acquired
immunodeficiency syndrome (AIDS) caused by the HIV became a critical issue
of socio-economic and demographic development of the Third World, and,
especially, in Africa. By 2000, three quarters of 22 million of deaths from
AIDS in the world were reported from Africa (United Nations 2001). The origin of HIV is still a matter of scientific debate, although there are many suppo*
This article is an output of a research project implemented as part of the Basic Research Program
at the National Research University Higher School of Economics (HSE) in 2014.
History & Mathematics: Trends and Cycles 2014 314–321
314
Alisa R. Shishkina et al.
315
sitions about its West-Central African origins (Garenne and Zwang 2008; Preston and Alcabes 2001). Examining the emergence and diffusion of HIV in
Central Africa, one should pay particular attention to ‘the historical association
between soldiers, prostitute contact and the spread of sexually-transmitted diseases in countries which have recently experienced civil war’ (Cliff and
Shallman-Raynor 1992). Some geneticist associate the emergence of circumstances facilitating the HIV diffusion with the advent of colonialism and the
growth of large colonial African cities leading to social changes, including
a higher degree of disorder in sexual relations, the spread of prostitution, and
the concomitant emergence of a high frequency of genital ulcer disease (such as
syphilis) in the population of nascent colonial cities (De Sousa et al. 2010).
The epidemic started in Africa around the late 1970s and early 1980s. According to one version, some African monkeys are carriers of the virus, but they
do not become sick with AIDS. As a result of contacts between people and infected monkeys or their bites the virus could get into the human body. Virologists have found that a simian immunodeficiency virus (SIV) which is observed
among West African monkeys is genetically similar to a weakly contagious
form of the AIDS and could be considered as its precursor (Moore 2004). HIV-1
and HIV-2 viruses are believed to have originated in West and Central Africa
and transferred (a process known as zoonosis) from monkeys to humans. HIV-1
first appeared in southern Cameroon through the evolution of simian immunodeficiency virus (SIVcpz) which infects wild chimpanzees (HIV-1 descends
from SIVcpz endemic in the chimpanzee subspecies Pan troglodytes troglodytes) (Gao, Bailes et al. 1999; Keele and van Heuverswyn et al. 2006). Next
of kin HIV-2 is SIVsmm, a virus of sooty mangabeys (Cercocebus atys), Old
World monkeys in West Africa (from southern Senegal to western Ivory Coast)
(Reeves and Doms 2002).
Thus, there are all grounds to make a conclusion about cross-species
(chimpanzee-to-human) transmissions of AIDS in African region. Paul M.
Sharp and his associates mention that M, N, and O – different groups of HIV-1
virus – represent three distinct cross-species transmissions of HIV-1cpz, evidently pointing to Western Equatorial Africa as the territory where they occurred (Sharp, Bailes et al. 2001). Sharp insists that the common ancestor of
HIV-1 group M existed before 1940 already infecting humans at that point.
The transmission of the virus became possible only in the latter half of the
twentieth century due to the changes in population structure and behavior in
Africa during the twentieth century and perhaps medical interventions that provided the opportunity for rapid human-to-human spread of the virus (Chitnis
and Rawls et al. 2000).
The first epidemic of HIV/AIDS is believed to have occurred in Kinshasa,
the Democratic Republic of Congo, in the 1970s. Later, HIV has been carried
to Eastern Africa (Kenya, Uganda, Tanzania, etc.) from its eastern equatorial
316
Islamic Factor of HIV Prevalence in Africa
origin and has gained rapid transmission rates due to labor migration, sexually
transmitted diseases (Iliffe 2006) and the prevalence of sex workers as well
(Piot et al. 1987). The spread of HIV into Western Equatorial Africa continued
further in the 1980s, although it did not reach the proportions of East African
states. In this decade HIV had been identified in all countries of West Africa. In
the middle of the 1980s the virus spread into the rural areas of South Africa
through traders, migrants, soldiers or mostly by truck drivers (New Scientist
1987). By the end of the decade Malawi, Zambia, Mozambique, Botswana and
Zimbabwe were enveloped by the epidemic that acquired devastating nature in
the general population. It is thought that HIV in South Africa had been mostly
homosexually transmitted (Hiza 1988). HIV prevalence in South African states
continued to increase in the 1990s at the same time as in some parts of East
Africa it stabilized or even declined (Mayanja 1999). Note, however, that the
HIV diffusion in the northern direction was much less successful. As a result
the HIV diffusion pattern looks now as an inversed pattern of the diffusion of
Islam in the African continent (see Figs 1 and 2).
Fig. 1. Share of Muslims in total population of African countries (%)
Alisa R. Shishkina et al.
317
Fig. 2. HIV prevalence in African countries in 2009
There are certain features in Islam (which we well spell out in the final part of
the present article) that would inhibit the diffusion of the AIDS epidemic;
hence, there are certain grounds to expect that Islamic societies would have
lower levels of HIV prevalence than non-Islamic. Our cross-national tests have
supported this hypothesis.
The data on prevalence of HIV have been taken from the World Development Indicators database (Washington: World Bank, 2012); the data on percentage of Muslims in the population of respective countries are from the Pew
Research Center (The Future of the Global Muslim Population. Pew Research
Center, 2011. URL: http://pewresearch.org/pubs/1872/muslim-population-projec
tions-worldwide-fast-growth). The data have been analyzed through a powerlaw regression analysis.
The cross-country association between share of Muslims in total population of African countries and HIV prevalence in 2009 is shown in Fig. 3.
318
Islamic Factor of HIV Prevalence in Africa
Fig. 3. Cross-sectional relationship between share of Muslims in total
population of African countries and HIV prevalence in 2009
(double logarithmic scale with fitted power-law regression line)
The power-law correlation between the two variables has turned out to be in the
predicted direction, rather strong (r = – 0.64; R2 = 0.412) and significant beyond any doubt (p << 0.0001). It was obtained with the least squares method
through a power-law regression analysis; the best fit is produced by the following power-law equation:
H = 8.03 × M – 0.454,
where H is HIV prevalence in a country, M is share of Muslims in the population of a respective country.
Thus, we believe that one of the possible explanations of the pattern of
HIV diffusion in Africa can be connected with the role of Islam, which pays
particular attention to the prevention of extramarital sexual relations. Unlike
Christianity, which also decries the extramarital sexual relations, Islam not only
condemns them, but punishes. This is primarily due to the close relationship
between legal and religious precepts of Islam, a religious basis of Islamic law.
This is a fact confirmed by the analysis of Muslim law as a system of existing
legal norms (Sykiyainen 2007a, 2007b). First of all, we speak about common
origins of all regulations of Islam. Thus, al-Qur’an and al-Sunnah are recognized as the main sources of Islamic law; they are based on the divine revelation and consolidate basic foundations of faith, rules of worship and morality,
generally determining the content of Islamic law in the legal sense.
Alisa R. Shishkina et al.
319
Its focus on the realization of the ideals of Islam as a religious system, the
inclusion of a number of religious cult rules explain why Islamic law is often
rightly called the quintessence, the main part of Islam, the most clear expression of Muslim ideology (David 1967). In particular, the ‘concept of interest’
coming out of focus of law to defend the five core values, among which the
first is given to religion, is important to understand not only the general ideological framework, but also a number of legal features of Islamic law (Zayyed
1966–1967). Students of Islamic Law generally point its two characteristic and
interdependent features: the religious origin (‘the divine nature’), and the close
relationship of legal orders with Muslim dogma, morals and religious law of
Islam in general. Famous modern specialists in the Islamic Law, such as Muhammad Moussa Youssuf and Subhi Mahmasani note that Islamic law is religious in origin and faithful people consider it as a divine revelation (Moussa
1952). On the base of universal nature of Islam and its regulatory requirements, it
is concluded that Islam is both ‘faith and state’, and Islamic Law (fiqh) is not only
a law itself, but a religion as well (Mahmasani 1952). A similar point of view is
expressed by many famous specialists in the Islamic Law. Thus, Joseph Schacht
notes that Islamic law is characterized by the dualism of religion and state
(Schacht 1966). According to R. Charle, Islamic law is primarily a religion, and
then – a state and culture (Charle 1959). Islam is a religion of law, and Islamic
law nature is not rational, but religious (divine), – emphasizes Rene David (David
1967). This is not applicable to Christianity where the Canon law could not become an imperative norm and, respectively, a part of current legislation.
Thus, we can summarize that the essential feature of Islamic law is in close
dependence of its norms implementation on religious consciousness. At the
same time, this approach helps to identify another important feature of sociopsychological mechanism of Islamic law implementation which explains the
high efficiency of its regulatory effect on the behavior of Muslims who, in
practice, in many cases refer to the norms of Islamic law as religious precepts.
This is not typical for Canon law. As a consequence, Christian Canon law, in
contrast to the Muslim law, could not be a part of the current legislation, including that in African countries.
Islam not only condemns extramarital sexual relations (zinā), but considers
it as a serious crime (hadd) like, for example, crimes against the Ummah and
infringement of the Allah rights (al-Qur’ān 4: 19–22; 7: 32; 25: 68–69; 17: 32;
al-Bukhārī 2475, 6878; Muslim 57/100, 1676/25; Ibn Mājah 4019; al-Manhaj
2/40). This is due to the fact that this kind of law breaking impinges on the basis of the Islamic Ummah – the family, and therefore should be punished to the
fullest extent of the law. It is no accident that adultery and extramarital sexual
relations are governed by the criminal law, not the Muslim family law in Africa
(Al-Riahi 2011; Sykiyainen 2007a, 2007b).
Obviously, we should remember regarding this point that there exist some
kind of disjuncture between religious law and beliefs and practices (see, e.g.,
Korotayev 2000, 2004). We can suppose that the Muslims who follow the reli-
320
Islamic Factor of HIV Prevalence in Africa
gious doctrine, and also pronouncedly worship and confirm to the rules actually
have lower risk of HIV infection.
In addition, one can mention that the circumcised men suffer from HIV
significantly less frequently than the non-circumcised, whereas the circumcision is practiced very consistently by the African Muslims (but, of course, not
only African). Thus, some of epidemiological studies have shown that in highrisk sub-Saharan Africa the male circumcision that is performed for different
reasons including religious, ritual, cultural, and medical, is often associated
with a reduced risk of HIV infection (Bloemenkamp and Farley 2002). Although
in some cases there in no sufficient evidence, the proposition about protective
effect of male circumcision against HIV infection becomes more and more
popular day by day, and it is regarded as one of the more powerful reducers of
infection risk (Harmon 2011; Short 2006; Bonner 2007).
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Contributors
David G. Anderson is an archaeologist in the department of anthropology at the University of Tennessee, Knoxville, who specializes in Southeastern archaeology. His
professional interests include exploring the development of cultural complexity in
Eastern North America, maintaining and improving the nation's CRM program, teaching and writing about archaeology, and developing technical and popular syntheses of
archaeological research. He is the project director of the on-line Paleoindian Database
of the Americas. Anderson has conducted field work and led field projects in many
locations in the Eastern United States, as well as projects in the Southwest and the
Caribbean. His work is documented in over 200 publications, some 30 technical monographs, and 7 books. Anderson has received a number of professional awards from
his colleagues, including the Excellence in Cultural Resource Management Research
Award from the Society for American Archaeology (1999), the Dissertation Prize
from the Society for American Archaeology (1991), and the first C. B. Moore Award
for Excellence in Southeastern Archaeological Studies by the Lower Mississippi Valley Survey / Southeastern Archaeological Conference (1990). In 2006 he was elected
President-elect of the Southeastern Archaeological Conference and served as President of that organization from 2008 to 2010. He has served as President of the South
Carolina Council of Professional Archaeologists (1992–1993), The Tennessee Council for Professional Archaeology (2006–2007), and the Archaeological Society of
South Carolina (1998–1999), and as an officer or board member in a number of state,
regional, and national professional organizations.
David C. Baker is an Assistant Professor in Big History at the University of Amsterdam
and an editor for the Paris Basin in the cliodynamics SESHAT project. He did his
PhD under David Christian in Sydney, and works frequently on projects in population
dynamics, cultural evolution, and the wider application of Universal Darwinism to
complexity studies. He is currently script-writing for a Big History Youtube series
that is funded by the Gates Big History Project and is going to be released on the
channel Crashcourse later in 2014. E-mail: david.baker1@students.mq.edu.au.
Kent Rand Crawford, Master in History, Doctor of Science, Professor of Natural History. He educated in the United States, he spent much of the past ten years traveling
and visiting colleagues in the United Kingdom, Spain and Russia. Now retired, he
lives and works in Costa Rica, where he continues his forty plus years study of Naval
Ordnance. He is the author about 50 scholarly publications, including such monographs as Identification of the Parameters of Naval Artillery (in co-authorship with
N. W. Mitiukov, Prague, 2013).
Sergey Gavrilets is a Distinguished Professor at the Department of Ecology and Evolutionary Biology and the Department of Mathematics at the University of Tennessee,
Knoxville, as well as an Associate Director for Scientific Activities at the National Institute for Mathematical and Biological Synthesis (NIMBioS) in Knoxville. He obtained his PhD in Physics and Mathematics from the Moscow State University in
the USSR in 1987. He subsequently worked at the Vavilov Institute of General GenetHistory & Mathematics: Trends and Cycles 2014 322–327
322
Contributors
323
ics in Moscow, the Institute National de la Recherche Agronomique in Toulouse,
France, and the University of California at Davis, USA, before moving to Knoxville
in 1995. He has received the President's Award from the American Society of Naturalists (1999) and the Guggenheim Fellowship (2008). He has published a monograph
on the mathematical theory of speciation (in 2004) and over 100 papers. His current
research interests are in speciation, human origins, and human social and societal evolution. E-mail: gavrila@utk.edu.
Leonid E. Grinin is Research Professor and the Director of the Volgograd Center for
Social Research, as well as the Deputy Director of the Eurasian Center for Big History
& System Forecasting, Senior Research Professor at the Institute for Oriental Studies
of the Russian Academy of Sciences in Moscow and Leading Research Fellow of the
Laboratory for Destabilization Risk Monitoring of the National Research University
Higher School of Economics. He is the Editor-in-Chief of the journal Age of Globalization (in Russian), as well as a co-editor of the international journals Social Evolution & History and the Journal of Globalization Studies. Dr. Grinin is the author of
more than 400 scholarly publications in Russian and English, including twenty six
monographs. These monographs include Philosophy, Sociology, and the Theory of
History (2007, in Russian); Productive Forces and Historical Process (2006, in Russian); State and Historical Process (3 vols, 2009–2010, in Russian); Social Macroevolution: World System Transformations (2009, in Russian; with A. Korotayev); Macroevolution in Biological and Social Systems (2008, in Russian; with A. Markov and
A. Korotayev); Global Crisis in Retrospective: A Brief History of Upswings and Crises (2010, in Russian; with A. Korotayev); The Evolution of Statehood: From Early
State to Global Society (2011); The Cycles of Development of Modern World System
(2011, in Russian; with A. Korotayev and S. Tsirel); From Confucius to Comte:
The Formation of the Theory, Methodology and Philosophy of History (2012, in Russian); Macrohistory and Globalization (2012); Cycles, Crises, and Traps of the Modern World-System (2012, in Russian; with A. Korotayev).
Tony Harper is an independent researcher with interests in the pattern of urbanization
over time and the implications of that pattern. He was a teacher at the faculty of New
Trier High School for thirty-three years, during the last eleven of which he developed
a strong interest in the application of math models to the study of human history. Tony Harper was twice invited by Andrey Korotayev to take part in the conference ‘Hierarchy and Power in the History of Civilizations’, has recently presented at the Big
History conference at Dominican University in San Rafael, California, and is continuing to do research in the relationship between urbanization and deurbanization.
E-mail: ajdharper@gmail.com.
Almas Heshmati is currently Professor of Economics at Jönköping University, Sweden,
and Sogang University, South Korea. He held similar positions at the Korea University, Seoul National University, and University of Kurdistan Hawler. His research interests include applied microeconomics, globalization, development strategy, efficiency, productivity and growth with application to manufacturing and services. In
addition to more than 120 scientific journal articles he has published books on the EU
Lisbon Process, global inequality, East Asian manufacturing, Chinese economy, technology transfer, information technology, water resources, landmines, power generation, development economics and economic growth. He is also Kurdish Board mem-
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ber of the World Kurdish Congress (South Korea). E-mail: almas.heshmati@
gmail.com.
Anthony Howell is currently a Doctoral Candidate at the Geography Department at
UCLA and holds advanced degrees in both Statistics (UCLA – 2012) and Geography
(Michigan State University – 2009). Trained as a statistician, urban-economic geographer and China specialist, Anthony's research combines applied statistical approaches
with the aid of GIS techniques and mapping of spatial relationships to develop new
empirically-driven theoretical frameworks that are capable of informing social and
economic policy. His dissertation research, supported by a 2012–2013 Fulbright
scholarship, is a microeconomic analysis that presents new, critical information highlighting the short- and long-run impacts of Chinese industrial policy on innovation,
knowledge spillovers and firm performance. Prior to enrolling at UCLA, Anthony
Howell attended Michigan State University for both undergraduate and graduate studies. At MSU, he participated in 9 study/research abroad programs that provided diverse opportunities to study Spanish and Chinese languages, volunteer with orphans
and the disabled, intern, and carry out research projects in countries ranging from
Mexico to Ireland, Czech Republic, United Arab Emirates and China. In summer
2006, Anthony Howell participated in an undergraduate research opportunity that took
him for the first time to China, where he examined rural-urban migration patterns at
the Chinese Academy of Sciences in Beijing. The culmination of his experiences in
China were life-changing, both personally and professionally. Since 2006, Anthony
has accumulated two-years of experience living in China, dedicating much of his time
to language acquisition, and researching issues related to migration, inequality and regional growth.
Leonid M. Issaev is a Senior Lecturer of the General Politics Department at the National Research University Higher School of Economics, Researcher at the Laboratory
for Sociopolitical Destabilization Risks Monitoring (National Research University
Higher School of Economics), and Member of Scientific Council of the Russian Association of Political Science. He graduated from the Faculty of Applied Political Science, the National Research University ‘Higher School of Economics’ and the University of Cairo. He had internship at the headquarters of the League of Arab States in
Cairo. He is an author of more than 60 scientific publications, including the monograph Egyptian Turmoil of the 21st Century (Moscow: Librokom, 2012, co-authored
with A. R. Shishkina), Syria and Yemen: Unfinished Revolutions (Moscow: Librokom, 2012, in collaboration with A. R. Shishkina), System Monitoring of Global and
Regional Risks: The Arab World After the Arab Spring (Moscow: Librokom/URSS,
2013; ed., together with A. V. Korotayev and A. R. Shishkina), and System Monitoring
of Global and Regional Risks. Central Asia: New Challenges (Moscow: Librokom/
URSS, 2013, ed., together with B. A. Akayeva, A. V. Korotayev and A. R. Shishkina).
Andrey V. Korotayev is Head of the Laboratory for Destabilization Risk Monitoring of
the National Research University Higher School of Economics, Senior Research Professor of the International Laboratory for Political Demography of the Russian Presidential Academy of National Economy and Public Administration, Senior Research
Professor of the Oriental Institute and Institute for African Studies, Russian Academy
of Sciences, as well as a Professor at the Faculty of Global Studies of the Moscow
State University. He is the author of over 300 scholarly publications, including such
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325
monographs as Ancient Yemen (1995), World Religions and Social Evolution of
the Old World Oikumene Civilizations: A Cross-Cultural Perspective (2004), Introduction to Social Macrodynamics: Compact Macromodels of the World System
Growth (2006), and Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends (2006). At present, together with Askar Akaev and Sergey Malkov, he
coordinates the Russian Academy of Sciences Presidium Project ‘Complex System
Analysis and Mathematical Modeling of Global Dynamics’. He is a laureate of the
Russian Science Support Foundation in ‘The Best Economists of the Russian Academy of Sciences’ Nomination (2006).
Sergey Yu. Malkov is a Senior Research Fellow of the Institute of Economics of the
Russian Academy of Sciences and a Professor of the Department of Applied Mathematics of the Russian State Social University. He is an author of more than 200 scientific publications, including such monographs as, for example, Modeling of SocioPolitical and Economic Dynamics (Moscow: Russian State Social University, 2004)
and Social Self-Organization and Historical Process. Possibilities of Mathematical
Modeling (Moscow: Librokom/URSS, 2009). E-mail: S@Malkov.org.
Alexander V. Markov is Acting Head of the Department of Biological Evolution at
Moscow State University and Senior Research Fellow of the Institute for Paleontology of the Russian Academy of Sciences. He is the author of more than 140 scientific
publications in zoology, paleontology, evolution theory, historical dynamics of biodiversity, and in other fields of evolutionary biology, including monographs: Morphology, Systematics and Phylogeny of Sea Urchins of the Schizasteridae Family (1994);
Quantitative Laws of Macroevolution: Experience of Systematic Approach Use for the
Analysis of Supraspecific Taxons (1998; with E. B. Neymark); Macroevolution in Biological and Social Systems (2008; with Leonid Grinin, Andrey Korotayev), Hyperbolic Growth in Biological and Social Systems (2009; with Andrey Korotayev).
Dr. Markov is a member of the Editorial Board of Journal of General Biology, an author of numerous popular science publications, the founder and author of the research
and education portal ‘Problems of Evolution’. E-mail: http://www.evolbiol.ru.
Nicholas W. Mitiukov is Professor in Engineering, Docent, Corresponding Member of
Real Academia de la Mar (Spain), Corresponding Member of the Academy of Military Science (Russia), Professor of Izhevsk State Technical University, Professor
of Kama Institute of Humanitarian and Engineering Technologies. He is the author of
over 500 academic publications, including such monographs as The SpanishAmerican War in the Pacific Ocean (in 3 volumes, St. Petersburg, 2005–2007), Simulation Modeling in Military History (Moscow, 2007, 2nd ed., Moscow, 2010), Ballistics of Arrows according to the Archeological Data (in co-authorship with
A. V. Korobeinikov, Izhevsk, 2007, 2nd ed., Moscow, 2014), Identification of the Parameters of Naval Artillery (in co-authorship with K. R. Crawford, Prague, 2013).
Sergey A. Nefedov is Senior Fellow at the Institute of History and Archaeology, Ural
Branch of the Russian Academy of Sciences, Professor of Ural Federal University. He
is the author of over 200 scholarly publications, including such monographs as Demographic and Structural Analysis of the Socio-Economic History of Russia (2005),
Factor Analysis of the Historical Process. History of the Orient (2008), Secular Cycles (2009, with P. Turchin), History of Russia. Factor Analysis (in 2 vols, 2010–
2011). Sergey Nefedov is the winner of the ‘Social Thought’ (2008, 2011), besides he
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Contributors
received the award named after the academician Rychkova (2011). In 2009–2011, he
gave an interdisciplinary research program ‘Russian Historical Dynamics: Factors,
Models, Predictions’. Е-mail: hist1@yandex.ru.
Arno Tausch is an Austrian citizen and in his academic functions he is Adjunct Professor (Universitätsdozent) of Political Science at Innsbruck University, Department of
Political Science. Currently, he is also Associate Professor of Economics, Corvinus
University, Budapest, and Lecturer of International Development, Vienna University.
He authored or co-authored 82 articles in peer-reviewed journals and 16 books in
English, 2 in French, and 8 books in German. His publications include a number of
essays for leading economic and foreign policy think tanks in nine countries, and for
the Jean Monnet Institutes of the European Union in three European Union countries.
E-mail: arno.tausch@yahoo.de.
William R. Thompson is Distinguished Professor and Donald A. Rogers Professor of
Political Science at Indiana University. His recent books include The Arc of War: Origins, Escalation and Transformation (2011, with Jack S. Levy), How Rivalries End
(2013, with Karen Rasler and Sumit Ganguly), and Transition Scenarios: China and
the United States in the Twenty-first Century (2013, with David P. Rapkin). E-mail:
wthompso@indiana.edu.
Konstantin M. Truevtsev, Associate Professor of the General Politics Department at
the National Research University Higher School of Economics, Senior Fellow at the
Laboratory for Sociopolitical Destabilization Risks Monitoring (National Research
University Higher School of Economics). He is an author of more than 60 scientific
publications, including the monographs Political System of Modern Russia (Moscow:
HSE, 2004); 2011 – a New Wave of the Democratisation? (Moscow: HSE, 2011).
E-mail: hrrc@mail.ru.
Kentaro Sakuwa is working on his PhD dissertation in the Political Science Department at Indiana University.
Alisa R. Shishkina is a Junior Research Fellow at the Laboratory for Sociopolitical
Destabilization Risks Monitoring, National Research University Higher School of
Economics. Alisa Shishkina is an author of more than 20 scientific works, including
monographs Egyptian Turmoil of the XXI Century (Moscow: Librokom, 2012, coauthored with L. M. Issaev), Syria and Yemen: Unfinished Revolutions (Moscow: Librokom, 2012, in collaboration with L. M. Issaev), The Arab World in the Digital
Age: Social Media as a Form of Political Activity (Moscow: Librokom/URSS, 2014,
co-authored with L. M. Issaev), System Monitoring of Global and Regional Risks:
The Arab World after the Arab Spring (Moscow: Librokom/URSS, 2013, ed., together
with A. V. Korotayev and L. M. Issaev), and System Monitoring Global and Regional
Risks. Central Asia: New Challenges (Moscow: Librokom/URSS, 2013, ed., together
with B. A. Akayeva, A. V. Korotayev, and L. M. Issaev). Her sphere of scientific interests includes human rights, democratic transition, political processes in the modern
world, sociocultural development, media studies, and the risks of social and political
instability. E-mail: alisa.shishkina@gmail.com.
Peter Turchin was trained as a theoretical biologist, but during the last fifteen years he
has been working in the field of historical social science that he and his colleagues
call Cliodynamics (http://cliodynamics.info/). His research interests lie at the intersec-
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327
tion of sociocultural evolution, historical macrosociology, economic history and cliometrics, mathematical modeling of long-term social processes, and the construction
and analysis of historical databases. More specifically, he investigates two broad and
interrelated questions: What general mechanisms explain the collapse of historical
empires? And how did large-scale states and empires evolve in the first place? What
are the social forces that hold together huge human conglomerates, and under what
conditions they fail? Turchin uses the theoretical framework of cultural multilevel selection to address these questions. Currently his main research effort is directed at coordinating SESHAT – a massive historical database of cultural evolution that will be
used in empirical tests of theoretical predictions coming from various social evolution
theories. Turchin has published over 100 articles in peer-reviewed journals, including
over ten in Nature, Science, and PNAS. His publications are frequently cited and in
2004 he was designated as ‘Highly cited researcher’ by ISIHighlyCited.com. Turchin
has authored five books. The most recent include Secular Cycles (with Sergey Nefedov, Princeton, 2009), War and Peace and War (Plume, 2005), and Historical Dynamics: Why States Rise and Fall (Princeton 2003). Turchin is Editor-in-Chief of
Cliodynamics: The Journal of Theoretical and Mathematical History. His blog is on
the Social Evolution Forum. Web page (with a link to publications and CV):
http://cliodynamics.info/Turchin.html.
History and Mathematics
Guidelines for Contributors
Preparation of manuscripts. Articles should generally be no longer than 100,000
symbols. The paper's abstract should not exceed 150 words. A separate sheet should
give the author's brief CV (up to 250 word). A list of keywords should be supplied. Figures of good quality should be submitted as separate files.
Bibliographical references should be given in parentheses in standard author-date
form in the body of the text: (Duffy, Morrison, and Macdonald 2002; Crumley 1987:
164–165; 1995: 4; 2001; Claessen 1985: 196–198, 201, 207; 2000, 2002; Chu et al.
2003: 29).
Examples of references in text:
‘In a larger population there will be proportionally more people lucky or smart
enough to come up with new ideas’ (Kremer 1993: 685); according to Rothmaler (1976:
127–129).
A complete list of references cited, arranged alphabetically by author's surname,
should be typed at the end of the article along the following lines:
A) Journal articles:
Schaffer W. M. 1985. Order and Chaos in Ecological Systems. Ecology 11(1): 103–109.
B) Edited volumes:
Frank A. G., and Gills B. K. (Eds.) 1993. The World System: Five Hundred Years of
Five Thousand? London: Routledge.
C) Contributions to edited volumes:
Humphrey N. K. 1976. The Social Function of Intellect. Growing Points in Ethology /
Ed. by P. P. G. Bateson and R. A. Hinde, pp. 303–317. Cambridge: Cambridge
University Press.
D) Monographs:
Berryman A. A. 1981. Population Systems: A General Introduction. New York, NY:
Plenum Press.
E) Internet resource:
a) If the site does not mention the publication date:
Chase-Dunn C., and Hall T. D. 1999. The Chesapeake World-System. URL: http://
www.wsarch.ucr.edu/archive/papers/c-d&hall/asa99b/asa99b.htm.
b) If possible, put the publication date:
U.S. Bureau of the Census. 2008. World Population Information. URL: http://www.
census.gov/ipc/www/world.html. Date accessed: 24.02.2008.
Quotations. Single inverted commas should be used except for quotations within
quotations, which should have double inverted commas. Quotations of more than
60 words should be set off from the text with an extra line of space above and below,
and typed without inverted commas.
The articles are to be sent to the following email addresses:
Leonid Grinin lgrinin@mail.ru
Andrey Korotayev akorotayev@mail.ru
‘History and Mathematics’ homepage on our website: http://www.sociostudies.
org/almanac/ham/