1.The overall population trend in the 1^{st}–18^{th} centuries CE in Egypt is suggested to be upward, rather than downward.

2.On
the other hand, the carrying capacity of land appears to have grown in
medieval Egypt considerably higher than population, whereas the
population growth was significantly slower than throughout the Old
World System (outside the Middle East).

Daria Khaltourina

3.We
believe this phenomenon could be at least partly accountedfor by the
mechanisms of political-demographic cycles typical for Egypt (and
apparently for the other countries of the Islamic Middle East),on the one hand, and by the very different mechanisms in the other major
regions of Eurasia, on the other.

4.Medieval Egyptian political-demographic cycles had a rather short length (approximately 90 years).

5.During the relatively short medieval Egyptian political-demographic cycles, population simply had not enough time to reach the carrying capacity of land. Political-demographic collapses took place well before the population reached the carrying capacity level, and medieval Egypt suffered from underpopulation rather than overpopulation. The population of medieval Egypt fluctuated well below the carrying capacity.

6.Thus the political-demographic cycle models that connect demographic collapses with the ecological niche saturation and that describe rather well political-demographic dynamics of pre-Modern China do not appear appropriate for medieval Egypt.

7.Hence, it might not be a coincidence that the mathematical model that appears to be more appropriate for describing the political-demographic dynamics of medieval Egypt than the rest of the models is the one (Turchin 2003: 131–7) that was developed in an attempt to formulate in a mathematical form some part of the theory of `Abd al-Rahmān Ibn Khaldūn (1332–1406) who spent a substantial part of his life specifically in medieval Egypt.

8.Turchin (2003) developed two "Ibn Khaldūn models", within which political-demographic collapses are produced not by actual overpopulation, but rather by elite overpopulation. Elite overproduction can take place in a generally underpopulated country (or at least in a country whose population is still significantly below the saturation level). Hence, these models suggest a direction within which the political-demographic dynamics of medieval Egypt could be adequately described.

9.However, in a few points these models fail to describe adequately the political-demographic dynamics of medieval Egyptian.

10.Though Turchin's models were no doubt inspired by Ibn Khaldūn's treatise, Turchin moved rather far from the original Ibn Khaldūn's theory in the process of the model development, and thus, not so much of it survived in the final versions of the models. We believe that in order to produce a mathematical model describing the medieval political-demographic dynamics in a more accurate way it makes sense to try to follow Ibn Khaldūn's theory more closely.

11.Ibn Khaldūn's observations on the role of climatic fluctuations as an important factor of political-demographic dynamics appear of special interest. By taking them into consideration it is possible to develop the basic mathematical model that describes the medieval Egyptian political-demographic dynamics more accurately.

12.As in Turchin's extended model, in our basic model the increase of the natural elite growth rate leads to a decline in the length of the political-demographic cycles, whereas its decrease results in the lengthening of those cycles. Thus, it turns out to be possible to produce the model that describes rather adequately the basic features of medieval European political-demographic dynamics through the decrease by 4 times of the "Egyptian" natural elite growth rate coefficient (which would correspond to the strictly monogamous reproduction context typical for all the medieval European Christians, including the elites).

13.One of the main simplifying assumptions of our basic model is that the technologically determined carrying capacity of land is assumed to be constant. In reality, of course, it was not a constant, but a variable with a pronounced long-term upward trend dynamics. This trend is conditioned by technological innovations whose intensity also tends to grow. This way this variable is treated in our extended model, which makes it possible to investigate numerically the influence of the "secular cycle" structure on the "millennial" economic and demographic trends.

14. Our extended model also takes into account the "Boserupian" effect – such that relative overpopulation creates powerful stimuli for generating and introducing innovations that raise the carrying capacity of land (Boserup 1965).

15.Our numerical investigation of this model suggests that within the "European" ("monogamous") versions of the model subsistence technologies do tend to develop faster than they do within the "Egyptian" ("polygynous") versions. The comparison of population at cycle peaks indicates that within the "Egyptian" model population tends to approach the ceiling of the carrying capacity of land to a much smaller degree than is observed within the "European" version of the model. It is highly remarkable that within the "Egyptian" model a significant increase in the carrying capacity could take place without a parallel demographic growth; what is more, for considerable periods of time the growth of carrying capacity can be accompanied by a certain population decline, which appears to have been actually observed for certain parts of the medieval Egyptian history.

16.The closest fit with the actually observed long-term political-demographic dynamics of Egypt in the 1^{st} – 18^{th} centuries CE is observed when we bring our model closer to the Egyptian history realities and take into consideration the fact that during the period covered by the present part of our monograph we observe the transition from strictly monogamous elites to elites who practiced polygyny in a rather extensive way. This model provides a mathematical description of the phenomenon that has been detected through the analysis of the economic-demographic dynamics of Egypt in the 1^{st} – 18^{th} centuries: significant increases in the carrying capacity of land were accompanied by a comparatively insignificant population growth. Thus, our models suggest possible ways to account for this phenomenon.

Korotayev A., Khaltourina D. Introduction to Social Macrodynamics:

Human
society is a complex nonequilibrium system that changes and develops
constantly. Complexity, multivariability, and contradictions of social
evolution lead researchers to a logical conclusion that any
simplification, reduction, or neglect of the multiplicity of factors
leads inevitably to the multiplication of error and to significant
misunderstanding of the processes under study. The view that any simple
general laws are not observed at all with respect to social evolution
has become totally dominant within the academic community, especially
among those who specialize in the Humanities and who confront directly
in their research the manifold unpredictability of social processes. A
way to approach human society as an extremely complex system is to
recognize differences of abstraction and time scale between different
levels. If the main task of scientific analysis is to detect the main
forces acting on systems so as to discover fundamental laws at a
sufficiently coarse scale, then abstracting from details and deviations
from general rules may help to identify measurable deviations from
these laws in finer detail and shorter time scales. Modern achievements
in the field of mathematical modeling suggest that social evolution can
be described with rigorous and sufficiently simple macrolaws.

The
first book of the {it Introduction (Compact Macromodels of the World
System Growth}. Moscow: URSS, 2006) discusses general regularities of
the World System long-term development. It is shown that they can be
described mathematically in a rather accurate way with rather simple
models. In the second book ({it Secular Cycles and Millennial Trends}.
Moscow: URSS, 2006) the authors analyze more complex regularities of
its dynamics on shorter scales, as well as dynamics of its constituent
parts paying special attention to «secular» cyclical dynamics. It is
shown that the structure of millennial trends cannot be adequately
understood without secular cycles being taken into consideration. In
turn, for an adequate understanding of cyclical dynamics the millennial
trend background should be taken into account.

In this book the authors analyze the interplay of trend and cyclical dynamics in Egypt and Subsaharan Africa.

Contents

Acknowledgements

Introduction: Secular Cycles and Millennial Trends

Part I: Secular Cycles and Millennial Trends in Egypt

Chapter 1.

General Trends of Egyptian Demographic Dynamics in the 1st -- 18th Centuries CE

Chapter 2.

Some Features of Medieval Egyptian Political-Demographic Cycles

Chapter 3.

`Abd
al-Rahman ibn Khaldun's Sociological Theory as a Methodological Basis
for Mathematical Modeling of Medieval Egyptian Political-Demographic
Dynamics

Chapter 4.

Basic Model of Medieval Egyptian Political-Demographic Dynamics

Chapter 5.

Extended Model of Medieval Egyptian Political-Demographic Dynamics

Chapter 6.

Secular Cycles and Millennial Trends in Egypt: Preliminary Conclusions

Part II: Cyclical and Trend Dynamics in Postcolonial Tropical Africa

Appendix: Cyclical Dynamics and Mechanisms of Hyperbolic Growth

Bibliography

Acknowledgements

First and foremost, our thanks go to the Institute for Advanced
Study, Princeton. Without the first author's one-year membership
in this Institute this book could hardly have been written. We
are especially grateful to the following professors and members
of this institute for valuable comments on the first sketches of
this monograph: Patricia Crone, Nicola Di Cosmo, John Shepherd,
Ki Che Angela Leung, and Michael Nylan. We would also like to
express our deepest gratitude to Elizabeth Sartain, Eleonora
Fernandez and Nelly Hanna of the Arabic Studies Department,
American University in Cairo, for their invaluable help and
advice. We are also grateful to the Russian Science Support
Foundation and the Russian Foundation for Basic Research for
financial support of this work (projects ## 06--06--80503 and
04--06--80225).

We would like to express our special gratitude to Robert Graber
(Truman State University), Victor de Munck (State University of
New York), Gregory Malinetsky and Sergey Podlazov (Institute for
Applied Mathematics, Russian Academy of Sciences), Diana
Pickworth (Aden University, Yemen), Antony J.Harper (New Trier
College), Ahren La Londa (Beloit College), Duran Bell, Donald
Saari, and Douglas R.White (University of California, Irvine)
for their invaluable help and advice.

We would also like to thank our colleagues who offered us useful
comments and insights on the subject of this book: Ferida
Atsamba and Vitalij Meliantsev (Institute of Asia and Africa,
Moscow State University), Leonid Borodkin (Historical
Informatics Laboratory, Moscow State University), Igor
Sledzevski and Dmitri Bondarenko (Institute for African Studies,
Russian Academy of Sciences), Robert L.Carneiro (American
Museum of Natural History, New York), Henry J.M.Claessen
(Leiden University), Dmitrij Chernavskij (Institute of Physics,
Russian Academy of Sciences), Georgi and Lubov Derlouguian
(Northwestern University, Evanston), Leonid Grinin (Center for
Social Research, Volgograd), Alexander Kadyrbaev (Oriental
Institute, Russian Academy of Sciences), Natalia Komarova
(University of California, Irvine), Sergey Nefedov (Russian
Academy of Sciences, Ural Branch, Ekaterinburg), Nikolay Kradin
(Russian Academy of Sciences, Far East Branch, Vladivostok),
Eginald Mihanjo and Abillah H.Omari (Centre for Foreign
Relations, Dar es Salaam), Rifat Pateev (Russian Cultural Centre
in Tanzania), and Peter Turchin (University of Connecticut,
Storrs). We would also like to thank Tatiana Shifrina, the
Director of "Khalturka-Design" Company, for the design of the
cover of this monograph.

Needless to say, faults, mistakes, infelicities, etc.,
remain our own responsibility.

About the authors

Andrey Korotayev is Director and
Professor of the "Anthropology of the East" Center, Russian
State University for the Humanities, Moscow, as well as Senior
Research Fellow of the Institute for Oriental Studies and the
Institute for African Studies of the Russian Academy of
Sciences. He also chairs the Advisory Committee in
Cross-Cultural Research for "Social Dynamics and Evolution"
Program at the University of California, Irvine. He received his
PhD from Manchester University, and Doctor of Sciences degree
from the Russian Academy of Sciences. He is author of over 200
scholarly publications, including Ancient Yemen (Oxford
University Press, 1995), Pre-Islamic Yemen (Harrassowitz
Verlag, 1996), Social Evolution (Nauka, 2003), World
Religions and Social Evolution of the Old World Oikumene
Civilizations: a Cross-Cultural Perspective (Mellen, 2004),
Origins of Islam (OGI, 2006). He is a laureate of the
Russian Science Support Foundation Award in "The Best Economists
of the Russian Academy of Sciences" nomination (2006).

Daria Khaltourina is Research Fellow of the Center for
Regional Studies, Russian Academy of Sciences (from where she
received her PhD) and Associate Professor at the Russian Academy
for Civil Service. Her research concentrates on complex social
systems, countercrisis management, cross-cultural and
cross-national research, demography, sociocultural anthropology,
and mathematical modeling of social processes. She has authored
over 40 scholarly publications, including such articles as
"Concepts of Culture in Cross-National and Cross-Cultural
Perspectives" (World Cultures 12, 2001), "Methods of
Cross-Cultural Research and Modern Anthropology" (Etnograficheskoe obozrenie 5, 2002), "Russian Demographic
Crisis in Cross-National Perspective" (in Russia and the
World. Washington, DC: Kennan Institute, forthcoming). She is a
laureate of the Russian Science Support Foundation Award in "The
Best Economists of the Russian Academy of Sciences" nomination
(2006).

Review

Review
of Andrey Korotayev, Artemy Malkov, and Daria Khaltourina, Introduction
to Social Macrodynamics (Three Volumes). Moscow: URSS, 2006.

Robert Bates Graber
Professor Emeritus of Anthropology Division of Social Science Truman State University

(published in Social Evolution & History. Vol. 7 (2008). Issue 2. Forthcoming)

This
interesting work is an English translation, by the authors and in three
brief volumes, of an amended and expanded version of their Russian work
published in 2005. Andrey Korotayev is Director of the "Anthropology of
the East" Center at the Russian State University for the Humanities;
Artemy Malkov is Research Fellow of the Keldysh Institute for Applied
Mathematics; and Daria Khaltourina is Research Fellow of the Center for
Regional Studies. By way of full disclosure, I should state that I have
enjoyed not only making the acquaintance of the first and third authors
at professional meetings, but also the opportunity to offer comments on
earlier versions of some parts of this English translation. In terms
coined recently by Peter Turchin, the first volume focuses on
"millennial trends," the latter two on "secular cycles" a century or
two in duration.

The
first volume's subtitle is Compact Models of the World System Growth
(CMWSG hereafter). Its mathematical basis is the standard hyperbolic
growth model, in which a quantity's proportional (or percentage) growth
is not constant, as in exponential growth, but is proportional to the
quantity itself. For example, if a quantity growing initially at 1
percent per unit time triples, it will by then be growing at 3 percent
per unit time. The remarkable claim that human population has grown,
over the long term, according to this model was first advanced in a
semi-serious paper of 1960 memorably entitled "Doomsday: Friday, 13
November, A.D. 2026" (von Foerster, Mora, and Amiot, 1960). Admitting
that this curve notably fails to fit world population since 1962,
chapter 1 of CMWSG attempts to salvage the situation by showing that
the striking linearity of the declining rates since that time,
considered with respect to population, can be identified as still
hyperbolic, but in inverse form. Chapter 2 finds that the hyperbolic
curve provides a very good fit to world population since 500 BCE. The
authors believe this reflects the existence, from that time on, of a
single, somewhat integrated World System; and they find they can
closely simulate the pattern of actual population growth by assuming
that although population is limited by technology (Malthus), technology
grows in proportion to population (Kuznets and Kremer). Chapter 3
argues that world GDP has grown not hyperbolically but quadratically,
and that this is because its most dynamic component contains two
factors, population and per-capita surplus, each of which has grown
hyperbolically. To this demographic and economic picture chapter 4 adds
a "cultural" dimension by ingeniously incorporating a literacy
multiplier into the differential equation for absolute population
growth (with respect to time) such that the degree to which economic
surplus expresses itself as population growth depends on the proportion
of the population that is literate: when almost nobody is literate,
economic surplus generates population growth; when almost everybody is
literate, it does not. This allows the authors' model to account nicely
for the dramatic post-1962 deviation from the "doomsday" (hyperbolic)
trajectory. It also paves the way for a more specialized model
stressing the importance, in the modern world, of human-capital
development (chapter 5). Literacy's contribution to economic
development is neatly and convincingly linked, in chapter 6, to Weber's
famous thesis about Protestantism's contribution to the rise of modern
capitalism. Chapter 7 cogently unravels and elucidates the complex role
of literacy male, female, and overall in the demographic transition. In
effect, the "doomsday" population trajectory carried the seeds of its
own aborting:

the
maximum values of population growth rates cannot be reached without a
certain level of economic development, which cannot be achieved without
literacy rates reaching substantial levels. Hence, again almost by
definition the fact that the [world] system reached the maximum level
of population growth rates implies that . . . literacy [had] attained
such a level that the negative impact of female literacy on fertility
rates would increase to such an extent that the population growth rates
would start to decline (CMWSG: 104).

The
second volume is subtitled Secular Cycles and Millennial Trends (SCMT
hereafter). Chapter 1 stresses that demographic cycles are not, as
often has been thought, unique to China and Europe, but are associated
with complex agrarian systems in general; and it reviews previous
approaches to modeling such cycles. Due to data considerations, the
lengthy chapter 2 focuses on China. In the course of assessing previous
work, the authors, though writing of agrarian societies in particular,
characterize nicely what is, in larger view, the essential dilemma
reached by every growing human population:

In
agrarian society within fifty years such population growth [0.6 percent
per year] leads to diminishing of per capita resources, after which
population growth slows down; then either solutions to resource
problems (through some innovations) are found and population growth
rate increases, or (more frequently) such solutions are not found (or
are not adequate), and population growth further declines (sometimes
below zero) (SCMT: 61-62).

(Indeed,
for humans, technological solutions that raise carrying capacity are
always a presumptive alternative to demographic collapse; therefore,
asserting or even proving that a particular population "exceeded its
carrying capacity" is not sufficient to account logically for the
collapse of either a political system or an entire civilizations.)
Interestingly, the authors find evidence that China's demographic
cycles, instead of simply repeating themselves, tended to increase both
in duration and in maximum pre-collapse population. In a brief chapter
3 the authors present a detailed mathematical model which, while not
simulating these trends, does simulate (1) the S-shaped logistic growth
of population (with the effects of fluctuating annual harvests smoothed
by the state's functioning as a tax collector and famine-relief
agency); (2) demographic collapse due to increase in banditry and
internal warfare; and (3) an "intercycle" due to lingering effects of
internal warfare. Chapter 4 offers a most creative rebuttal of recent
arguments against population pressure's role in generating
pre-industrial warfare, arguing that a slight negative correlation, in
synchronic cross-cultural data, is precisely what such a causal role
would be expected to produce (due to time lags) when warfare frequency
and population density are modeled as predator and prey, respectively,
using the classic Lotka-Volterra equations. Chapter 4 also offers the
authors' ambitious attempt to directly articulate secular cycles and
millennial trends. Ultimately they produce a model that, unlike the
basic one in chapter 3, simulates key trends observed in the Chinese
data in chapter 2:

the
later cycles are characterized by a higher technology, and, thus,
higher carrying capacity and population, which, according to Kremer's
technological development equation embedded into our model, produces
higher rates of technological (and, thus, carrying capacity) growth.
Thus, with every new cycle it takes the population more and more time
to approach the carrying capacity ceiling to a critical extent; finally
it "fails" to do so, the technological growth rates begin to exceed
systematically the population growth rates, and population escapes from
the "Malthusian trap" (SCMT: 130).

The
third volume is subtitled Secular Cycles and Millennial Trends in
Africa (SCMTA hereafter).It is divided into two parts, the first of
which is devoted to Egypt in the 1st through 18th centuries CE
(chapters 1-6); the second, to postcolonial tropical Africa (chapters
7-8). The first part argues that while Egypt's population probably
increased over the period in question, the increase was modest compared
to that of other agrarian societies. This modesty the authors ascribe
to the remarkable brevity of Egypt's political-demographic cycles,
which they estimate at averaging around ninety years little more than
half as long as China's. With such brief cycles, collapse repeatedly
occurred long before carrying capacities were approached. Strongly
inspired by Peter Turchin's work but hewing more closely to insights of
the anachronistic 14th-century cultural evolutionist Ibn Khaldun, the
authors find that these brief cycles can be modeled by including
climatic fluctuation and, especially, the rapid reproduction of
high-consumption elites due to polygyny. They estimate the annual
growth rate for Egyptian elites at 4 percent per year, the rate for
commoners (monogamous) at only 1 percent per year a recipe for rapid
political-demographic crisis and collapse, since elites of course
depend on the taxation of commoners!

The
second part of "Secular Cycles and Millennial Trends in
Africa" describes the impact of modernization on
political-demographic cycles. The authors find that low nutrition
predicts political instability and civil war in African nations; for
prevention, they recommend especially the diversification of national
economies, and the fostering of education to promote economic
development. Concerning the underlying causes of historical events,
they quote John Maynard Keynes writing in 1920:

The
great events of history are often due to secular changes in the growth
of population and other fundamental economic causes, which, escaping by
their gradual character the notice of contemporary observers, are
attributed to the follies of statesmen or the fanaticism of atheists
(quoted in SCMTA: 113). Some aspects of this work are easy to
criticize. The reporting of probabilities with sixteen zeros to the
right of the decimal point will strike as gratuitous those readers who
consider .001, .01, or even .05 sufficient to render randomness an
implausible explanation for a result, especially when, as here, the
danger of erroneously rejecting the null hypothesis (alpha or Type I
error) is clearly preferable to the premature truncation of inquiry
that could result from erroneous failure to reject the null (beta or
Type II error). More importantly, one would like to have seen more
attention given to the problems that attend using regression with
time-series data. Values in a variable's time series tend to be
affected by adjacent values ("autocorrelation"), a condition that
violates one of the assumptions underlying the ordinary-least-squares
model and that regularly results, for regressions on time itself (e.g.,
population plotted against time), in exaggerated R-squared magnitudes
and significance levels; similar exaggeration results for regressions
of a time-trending variable on one or more other time-trending
variables (e.g., population growth rate plotted against population).
The frequent appearance, in the book's graphs, of long runs of data
points on the same side of a theoretical line or curve is a symptom of
autocorrelation; and the book's regressions of trending variables on
other trending variables do not appear to have been protected from this
source of spuriousness by inclusion of time itself as an independent
variable in the regression equations. The hyperbolic curve, moreover,
is not systematically compared here with serious competitors. For these
reasons the hyperbolic curve's superiority, as a description of human
population history, remains by no means beyond question (cf. Cohen
1995: chapter 5 and appendix 6).

Important
questions remain, too, about the tenability of the Kuznets-Kremer
assumptions appealing as they are to some of us offered to
theoretically account for the hyperbolic model's applicability to human
population history. For example, the key assumption that technological
growth tends to keep pace with population growth appears problematic
enough to warrant perhaps greater caution than the authors express.
Also, one would like to see a better fit between the abstract global
model on one hand, and what we know about the growth rates for
particular populations on the other. Since particular populations
seldom sustain even exponential growth for very long, explaining
sustained hyperbolic growth globally apparently requires invoking the
spread, from population to population, of the demographic transition's
first phase (cf. CMWSG: 92-93; SCMTA: 116-117). This is for recent
centuries only; to cover the pre-industrial period, the authors posit
five somewhat intricate and interrelated mechanisms, one of which again
relies on diffusion (the "innovation diffusion" mechanism) (SCMTA:
140-141). It seems somewhat awkward, however, to rely so much on
diffusion from donor to recipient regional populations, sometimes over
considerable time periods, given that the Kuznets-Kremer assumptions
appear to ascribe the (apparently) hyperbolic shape of long-term global
population growth to direct and continuous interaction, within a single
world-system population, between a single technological base and a
single inventive potential (both seen as proportional, quantitatively,
to population itself).

While
the translation's English is often less than felicitous, it is quite
clear; the few typographical errors I noted were not of a kind to
create misunderstanding. The authors are to be commended, I think, for
putting most of the mathematics "up front" rather than tucked away in
appendices, as publishers are wont to urge. (There are technical
appendices three in CMWSG, two in SCMT, and one in SCMTA; but their
function is by no means to keep the text itself free of math.) Cultural
evolutionism is still near the beginning of the long process of
becoming a mathematical science; to that extent, the medium of this
book is, if perhaps not the message, certainly a message (Carneiro
2003: 285-286)!

Even
more generally, this work vigorously asserts the value of studying
social and cultural evolution as such. Noting the "almost total
disenchantment with the evolutionary approach in the social sciences as
a whole" (SCMT: 140), the authors perspicuously compare the resulting
stultification to the fate that "would have stricken physicists if a
few centuries ago they had decided that there is no real thing such as
gas, that gas is a mental construction, and that one should start with
such a simple' thing as a mathematical model of a few free-floating
molecules in a closed vessel" (SCMT: 140, note 6).

Thirty
years ago, Mark Nathan Cohen wrote, "It has been my observation that
simple hypotheses boldly defended are often the best teaching tools and
the best spurs to research" (Cohen 1977: ix) Aside from the
difficulties we all encounter, sooner or later, comprehending
mathematics (we differ only in when, not in whether, the difficulties
begin), this book's theses are simple; and they are nothing if not
"boldly defended"! In sum, this work deserves attention from anyone
interested in cultural evolutionism's scientific prospects, and close
study indeed by anyone hoping to contribute to this field's development
from a mathematical point of view.

REFERENCES

Carneiro, R. L.
2003. Evolutionism in Cultural Anthropology: A Critical History. Boulder, CO: Westview.

Cohen, J. E.
1995. How Many People Can the Earth Support? New York: W. W. Norton.

Cohen, M. N.
1977. The Food Crisis in Prehistory: Overpopulation and the Origins of Agriculture. New Haven, CT: Yale University Press.

Foerster, H. von, P. Mora, and L. Amiot
1960. Doomsday: Friday, 13 November, A.D. 2026. Science 132: 1291-1295.