Cover of Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth
Human society is a complex nonequilibrium system that changes and develops constantly.
Complexity, multivariability, and contradictoriness 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 predominant within the academic community,
especially among those who specialize in the Humanities and who confront directly
in their research all 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.
This book discusses general regularities of the World System growth.
It is shown that they can be described mathematically in a rather accurate
way with rather simple models.
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).
Artemy Malkov is Research Fellow of the Keldysh Institute for Applied Mathematics, Russian Academy of Sciences from where he received his PhD. His research concentrates on the modeling of social and historical processes, spatial historical dynamics, genetic algorithms, cellular automata. He has authored over 35 scholarly publications, including such articles as "History and Mathematical Modeling" (2000), "Mathematical Modeling of Geopolitical Processes" (2002), "Mathematical Analysis of Social Structure Stability" (2004) that have been published in the leading Russian academic journals. He is a laureate of the 2006 Award of the Russian Science Support Foundation.
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).
Chapter 1. Macrotrends of World Population Growth
Chapter 2. A Compact Macromodel of World Population Growth
Chapter 3. A Compact Macromodel of World Economic and Demographic Growth
Chapter 4. A General Extended Macromodel of World Economic, Cultural, and Demographic Growth
Chapter 5. A Special Extended Macromodel of World Economic, Cultural, and Demographic Growth
Chapter 6. Reconsidering Weber: Literacy and "the Spirit of Capitalism"
Chapter 7. Extended Macromodels and Demographic Transition Mechanisms
Appendix 1. World Population Growth Forecast (2005-2050)
Appendix 2. World Population Growth Rates and Female Literacy in the 1990s: Some Observations
Appendix 3. Hyperbolic Growth of the World Population and Kapitza's Model
From the review by Robert Bates Graber
From the review by Robert Bates Graber (Professor Emeritаus of Anthropology, Division of Social Science, Truman State University)
of "Introduction to Social Macrodynamics" (Three Volumes. Moscow: URSS, 2006) (published in Social Evolution & History. Vol. 7/2 (2008): 149-155):
This interesting work is an English translation, in three brief volumes, of an
amended and expanded version of the Russian work published in 2005. 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 Macromodels of the World System Growth". 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, conаsidered 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" (p. 104).
(pages 105-111 of the original)
Let us start the conclusion to the first part of our introduction to social
macrodynamics with one more brief consideration of the employment of
mathematical modeling in physics.
The dynamics of every physical body is influenced by a huge number of factors.
Modern physics abundantly evidences this. Even if we consider such a simple
case as a falling ball, we inevitably face such forces as gravitation, friction,
electromagnetic forces, forces caused by pressure, by radiation, by anisotropy
of medium and so on.
All these forces do have some effect on the motion of the considered body. It is
a physical fact. Consequently in order to describe this motion we should
construct an equation involving all these factors. Only in this case may we
"guarantee" the "right" description. Moreover, even such an equation would not
be quite "right", because we have not included those factors and forces which
actually exist but have not been discovered yet.
It is evident that such a puristic approach and rush for precision lead to
agnosticism and nothing else. Fortunately, from the physical point of view, all
the processes have their characteristic time scales and their application
conditions. Even if there are a great number of significant factors we can
sometimes neglect all of them except the most evident one.
There are two main cases for simplification:
1. When a force caused by a selected factor is much stronger than all the other forces.
2. When a selected factor has a characteristic time scale which is adequate to
the scale of the considered process, while all the other factors have significantly
different time scales
The first case seems to be clear. As for the second, it is substantiated by the
Tikhonov theorem (1952). It states that if there is a system of three differential
equations, and if the first variable is changing very quickly, the second changes
very slowly, and the third is changing with an acceptable characteristic time
scale, then we can discard the first and the second equations and pay attention
only to the third one. In this case the first equation must be solved as an
algebraic equation (not as a differential one), and the second variable must be
handled as a parameter.
Let us consider some extremely complicated process, for example,
photosynthesis. Within this process characteristic time scales (in seconds) are
1. Light absorption: ~ 0.000000000000001.
2. Reaction of charge separation: ~ 0.000000000001.
3. Electron transport: ~ 0.0000000001.
4. Carbon fixation: ~ 1 – 10.
5. Transport of nutrients: ~ 100 – 1000.
6. Plant growth: ~ 10000 – 100000.
Such a spread in scales allows constructing rather simple and valid models for
each process without taking all the other processes into consideration. Each
time scale has its own laws and is described by equations that are limited by the
corresponding conditions. If the system exceeds the limits of respective scale,
its behavior will change, and the equations will also change. It is not a defect of
the description – it is just a transition from one regime to another.
For example, solid bodies can be described perfectly by solid body models
employing respective equations and sets of laws of motion (e.g., the mechanics
of rigid bodies); but increasing the temperature will cause melting, and the
same body will be transformed into a liquid, which must be described by
absolutely different sets of laws (e.g., hydrodynamics). Finally, the same body
could be transformed into a gas that obeys another set of laws (e.g., Boyle's
It may look like a mystification that the same body may obey different laws and
be described by different equations when temperature changes slightly (e.g.,
from 95ºС to 105ºC)! But this is a fact. Moreover, from the microscopic point of
view, all these laws originate from microinteraction of molecules, which remains
the same for solid bodies, liquids, and gases. But from the point of view of
macroprocesses, macrobehavior is different and the respective equations are
also different. So there is nothing abnormal in the dynamics of a complex
system could have phase transitions and sudden changes of regimes.
For every change in physics there are always limitations that modify the law of
change in the neighborhood of some limit. Examples of such limitations are
absolute zero of temperature and velocity of light. If temperature is high
enough or, respectively, velocity is small, then classical laws work perfectly, but
if temperature is close to absolute zero or velocity is close to the velocity of
light, behavior may change incredibly. Such effects as superconductivity or
space-time distortion may be observed.
As for demographic growth, there are a number of limitations, each of them
having its characteristic scales and applicability conditions. Analyzing the
system we can define some of these limitations.
Growth is limited by:
1. RESOURCE limitations:
1.1. Starvation – if there is no food (or other resources essential for vital
functions) there must be not growth, but collapse; time scale ~ 0.1 – 1 year;
conditions: RESOURCE SHORTAGE.
This is a strong limitation and it works inevitably.
1.2. Technological – technology may support a limited number of workers;
time scale ~ 10–100 years;
conditions: TECHNOLOGY IS "LOWER" THAN POPULATION.
This is a relatively rapid process, which causes demographic cycles.
2.1. Birth rate – a woman cannot bear more than once a year;
time scale ~ 1 year;
condition: BIRTH RATE IS EXTREMELY HIGH.
This is a very strong limitation with a short time scale, so it will be the only rule
of growth if for any possible reasons the respective condition (birth rate is
extremely high) is observed.
2.2. Pubescence – a woman cannot produce children until she is mature;
time scale ~ 15–20 years;
conditions: EARLY CHILD-BEARING.
This condition is less strong than 2.1., but in fact condition 2.1. is rarely
observed. For real demographic processes limitation 2.2. is more important
than 2.1. because in most pre-modern societies women started giving birth very
soon after puberty.
3.1. Infant mortality – mortality obviously decreases population growth;
time scale ~ 1–5 years;
condition: LOW HEALTH PROTECTION.
Short time scale; strong and actual limitation for pre-modern societies.
3.2. Mobility – in preagrarian nomadic societies woman cannot have many
children, because this reduces mobility; time scale: ~3 years;
condition: NOMADIC HUNTER-GATHERER WAY OF LIFE.
3.3. Education – education increases the "cost" of individuals; it requires many
years of education making high procreation undesirable. High human cost
allows an educated person to stand on his own economically, even in old age,
without the help of offspring. These limitations reduce the birth rate;
time scale: ~25–40 years;
condition: HIGHLY DEVELOPED EDUCATION SUBSYSTEM.
All these limitations are objective. But each of them is ACTUAL (that is it must
be included in equations) ONLY IF RESPECTIVE CONDITIONS ARE OBSERVED.
If for any considered historical period several limitations are actual (under their
conditions) then, neglecting the others, equations for this period must involve
their implementation. According to the Tikhonov theorem, the strongest factors
are the ones having the shortest time scale. HOWEVER, factors with a longer
time scale may "start working" under less severe requirements, making short-
time-scale factors not actual, but POTENTIAL. Let us observe and analyze the
I. pre-agrarian societies;
II. agrarian societies;
III. post-agrarian societies.
We shall use the following notation:
– atypical – means that the properties of the epoch make the conditions
– actual – means that such conditions are observed, so this limitation is actual
and must be involved in implementation;
– potential – means that such conditions are not observed, but if some other
limitations are removed, this limitation may become actual.
I. Pre-agrarian societies (limitation statuses):
1.1. – ACTUAL
1.2. – ACTUAL
2.1. – potential
2.2. – ACTUAL
3.1. – ACTUAL
3.2. – ACTUAL
3.3. – atypical
II. Agrarian societies (limitation statuses):
1.1. – ACTUAL
1.2. – ACTUAL
2.1. – potential
2.2. – ACTUAL
3.1. – ACTUAL
3.2. – atypical
3.3. – potential
III. Post-agrarian societies (limitation statuses):
1.1. – atypical
1.2. – potential/ACTUAL
2.1. – potential
2.2. – potential
3.1. – atypical
3.2. – atypical
3.3. – ACTUAL
With our macromodels we only described agrarian and post-agrarian societies
(due to the lack of some necessary data for pre-agrarian societies). According
to the Tikhonov theorem, to describe the DYNAMICS of the system we should
take the actual factor which has the LONGEST time-scale (it will represent
dynamics, while shorter scale factors will be involved as coefficients – solutions
of algebraic equations).
So epoch [II] is characterized by 1.2, and [III] by 3.3. ([III] also involves 1.2,
but for [III] resource limitation 1.2 is much less essential, because it concerns
growing life standards, and not vitally important needs). Thus, the demographic
transition is a process of transition from II:[1.2] to III:[3.3].
Limitation 3.3 at [III] makes biological limitations unessential but potential
(possibly, in the future, limitation 3.3 could be reduced, for example, through
the reduction of education time due to the introduction of advanced educational
technologies, thereby making [2.2] actual again; possibly cloning might make
[2.1] and [2.2] obsolete, so there would become apparent new limitations).
In conclusion, we want to note that hyperbolic growth is a feature which
corresponds to II:[1.2]; there is no contradiction between hyperbolic growth
itself and [2.1] or [2.2]. Hyperbolic agrarian growth never does reach the birth-
rate, which is close to conditions of [2.1]. If it was so, hyperbola will obviously
convert into an exponent, when birth-rate comes close to [2.1] (just as physical
velocity may never exceed the velocity of light) – and it would not be a weakness
of the model, just common sense.
It would be just [1.2] → [2.1, 2.2].
But actual demographic transition [1.2] → [3.3] is more drastic than this
[1.2] → [2.1, 2.2]!
[3.3] is reducing the birth-rate much more actively, and it may seem strange:
the system WAS MUCH CLOSER TO [2.1] and [2.2] WHEN IT WAS GROWING
SLOWER – during the epoch of [II]! (This is not nonsense, because slower
growth was the reason of [2.1] and [3.1]).
As for the "after-doomsday dynamics", if there is no resource or spatial
limitation (as well as [3.1]), then [2.1] and [2.2] will become actual. If they are
also removed (through cloning, etc.), then there will appear new limitations.
But if we consider the solution of C/(t0 – t) just formally, the after-doomsday
dynamics makes no sense. But this is "normal", just as temperature below
abso-lute zero, or velocity above the velocity of light, makes no sense.
Thus, as we have seen, 99.3–99.78 per cent of all the variation in demographic,
economic and cultural macrodynamics of the world over the last two millennia
can be accounted for by very simple general models.
Actually, this could be regarded as a striking illustration of the fact well known
in complexity studies – that chaotic dynamics at the microlevel can generate