History & Mathematics:

History & Mathematics:

Trends and Cycles

Volgograd: ‘Uchitel’ Publishing House, 2014. – 328 pp.
Edited by Leonid Grinin, Andrey Korotayev
ISBN 978-5-7057-4223-3
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).

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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.


Leonid E. Grinin
and Andrey V. Korotayev
Introduction. Modeling and Measuring Cycles, Processes, and Trends Full text

I. Long-Term Trends in Nature and Society
Leonid E. Grinin, Alexander V. Markov,
and Andrey V. Korotayev
Mathematical Modeling of Biological and Social Evolutionary Macrotrends Full text
Tony Harper The World System Trajectory: The Reality of Constraints and the Potential for Prediction Full text
William R. Thompson and
Kentaro Sakuwa
Another, Simpler Look: Was Wealth Really Determined in 8000 BCE, 1000 BCE, 0 CE, or Even 1500 CE? Full text

II. Cyclical Processes in Pre-industrial Societies
Sergey Gavrilets,
David G. Anderson,
and Peter Turchin
Cycling in the Complexity of Early Societies Full text
David C. BakerDemographic-Structural Theory and the Roman Dominate Full text
Sergey A. NefedovModeling Malthusian Dynamics in Pre-industrial Societies: Mathematical Modeling Full text

III. Contemporary History and Processes
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 Full text
Arno Tausch and
Almas Heshmati
Labour Migration and ‘Smart Public Health’ Full text
Anthony HowellIs Geography ‘Dead’ or ‘Destiny’ in a Globalizing World? A Network Analysis and Latent Space Modeling Approach of the World Trade Network Full text
Kent R. Crawford and
Nicholas W. Mitiukov
The British-Italian Performance in the Mediterranean from the Artillery Perspective Full text
Alisa R. Shishkina,
Leonid M. Issaev,
Konstantin M. Truevtsev,
and Andrey V. Korotayev
The Shield of Islam? Islamic Factor of HIV Prevalence in Africa Full text


Guidelines for Contributors