Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth
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Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth by Andrey Korotayev, Artemy Malkov, and Daria Khaltourina. Moscow: URSS, 2006.
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.
Contents |
[edit] 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
[edit] From the review by Robert Bates Graber
From the review by Robert Bates Graber (Professor Emeritus 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)): 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, 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" (p. 104).
[edit] 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 ob-served. 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 in-volve 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 practi-cally 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 dy-namics, 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 con-cerns growing life standards, and not vitally important needs). Thus, the demo-graphic 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 it-self 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 weak-ness 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 gen-erate highly deterministic macrolevel behavior (e.g., Chernavskij 2004).
As has already been mentioned in the Introduction, to describe the behavior of a few dozen gas molecules in a closed vessel we need very complex mathe-matical models, which will still be unable to predict the long-run dynamics of such a system due to an inevitable irreducible chaotic component. However, the behavior of zillions of gas molecules can be described with extremely simple sets of equations, which are capable of predicting almost perfectly the macrodynamics of all the basic parameters (and just because of chaotic behavior at the microlevel).
Our analysis suggests that a similar set of regularities is observed in the human world too. To predict the demographic behavior of a concrete family we would need extremely complex mathematical models, which would still predict a very small fraction of actual variation due simply to inevitable irreducible chaotic components. For systems including orders of magnitude higher numbers of people (cities, states, civilizations), we would need simpler mathematical models having much higher predictive capacity. Against this background it is hardly surprising to find that the simplest regularities accounting for extremely large proportions of all the macrovariation can be found precisely for the largest possible social system – the human world.
This, of course, suggests a novel approach to the formation of a general theory of social macroevolution. The approach prevalent in social evolutionism is based on the assumption that evolutionary regularities of simple systems are significantly simpler than the ones characteristic of complex systems. A rather logical outcome of this almost self-evident assumption is that one should first study the evolutionary regularities of simple systems and only after understanding them move to more complex ones. We believe this misguided approach helped lead to an almost total disenchantment with the evolutionary approach in the social sciences as a whole.
