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).

Contents

Acknowledgements

Introduction

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

Conclusion

Appendices

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

Bibliography

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).

Conclusion

(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

as follows:

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

law, etc.)

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. BIOLOGICAL

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. SOCIAL

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

following epochs:

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

practically impossible;

– 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