History & Mathematics: Analyzing and Modeling Global DevelopmentLeonid Efimovich Grinin, Victor C. De Munck, A. V. Korotaev |
Common terms and phrases
1st millennium BCE Andrey Korotayev Axial Age best-fit exponential model best-fit values Black markers correspond blow-up regime Calibrated decrease demographic transition Diagram empirical estimates Foerster Foerster's equation following equation grey solid line Hellemans hyper hyperbolic curve hyperbolic growth hyperbolic pattern hyperbolic trajectory inventions Khaltourina 2006a Korotayev Kremer Kremer's model Kuznets Largest Settlement least squares method Lineal literate population log.scale logarithmic scale long-term Macrodynamics Malkov mathematical analysis mathematical methods mathematical models McEvedy and Jones million Million B.C. Modelski Nefedov Note observed data overall parameters period Population Dynamics population growth rate production quadratic-hyperbolic model Simon Kuznets Simple Hyperbolic Model solid grey curve subsystem System technological development Technological Development Index technological growth rate tion Turchin U.S. Bureau Uncalibrated Grinin's Index Upper Paleolithic urban world literacy world population World Population Dynamics world population growth World System development World System population World System technological Younger Hyperbola Гринин Коротаев Малков Ред
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Page 56 - This implication flows naturally from the nonrivalry of technology... The cost of inventing a new technology is independent of the number of people who use it. Thus, holding constant the share of resources devoted to research, an increase in population leads to an increase in technological change
Page 56 - This implies that for any given level of technological development (7) there is "a unique level of population, n" that cannot be exceeded with the given level of technology (Kremer 1993: 685). Note that n can be also interpreted as the Earth carrying capacity, that is, the maximum number of people that the Earth can support with the given level of technology. However, as is well known, the technological level is not a constant, but a variable. And in order to describe its dynamics Kremer employs...
Page 43 - September marked the beginning of a new period in the history of the Russian Revolution ; and, very probably, of the world revolution.
Page 56 - ... increases above some steady state equilibrium level of per capita income, m, and decreases below it" (Kremer 1993: 685). Hence, with the decline of per capita income, the population growth will slow down and will become close to zero when the per capita income approaches m. Note that such a dynamics was actually rather typical for agrarian societies, and its mechanisms are known very well - indeed, if per capita incomes decline closely to m, it means the decline of nutrition and health status...
Page 54 - Macrodynamics we have tried to provide answers to this question and these answers are summarized below. However, before starting this we would like to state that our experience shows that most readers who are not familiar with mathematics stop reading books (at least our books) as soon as they come across the words - "differential equation".
Page 57 - Malthusian" demographic one will be denoted as "Malthusian-Kuznetsian". In general, we find this assumption rather plausible - in fact, it is quite probable that, other things being equal, within a given period of time, one billion people will make approximately one thousand times more inventions than one million people. This assumption is expressed by Kremer mathematically in the following way: — = bNT...
Page 55 - Earth could not support more than 10 million people, because the amount of naturally available useful biomass on this planet is limited, and the world population could only grow over this limit when the people started to apply various means to artificially increase the amount of available biomass, that is with the transition from foraging to food production. However, the extensive agriculture also can only support a limited number of people, and further growth of the world population only became...
Page 50 - R 2 can be regarded as a measure of the fit between the dynamics generated by a mathematical model and the empirically observed situation, and can be interpreted as the proportion of the variation accounted for by the respective equation. Note that 0.996 also can be expressed as 99.6%.
Page 59 - Retative poputation growth rate Note that the relationship between technological development and demographic growth cannot be analyzed through any simple cause-and-effect model, as we observe a true dynamic relationship between these two processes - each of them is both the cause and the effect of the other.
Page 57 - that population adjusts instantaneously to «" (1993: 685); he further combines technology and population determination equations and demonstrates that their interaction produces just the hyperbolic population growth (Kremer 1993: 685-6; see also Podlazov 2000, 2001, 2002, 2004; Tsirel 2004; Korotayev, Malkov, and Khaltourina 2006a: 21-36). Kremer's model provides a rather convincing explanation of why throughout most of human history the world population followed the hyperbolic pattern with the...