Mathematical models of world-system development

Korotayev, Andrey; Malkov, Sergey

doi:10.4324/9780203863428.ch4_5

Cited by 15 publications

(27 citation statements)

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“…It appears to be a dynamic relationship. The development of the education system stimulates economic growth (especially in underdeveloped countries), while growth of GDP per capita, in its turn, stimulates the development of education, as it leads to a significant growth of resources that can be allocated for the development of this system and hence to increase the level of education of the population (see, for example, Barro, 1991; Barro & Sala-i-Martin, 1995; Benos & Zotou, 2014; Korotayev, 2009; Korotayev & Khaltourina, 2010; Korotayev, Malkov, & Khaltourina, 2006, 2007; Sadovnichij, Akaev, Korotayev, & Malkov, 2016; Sala-i-Martin, 1997).…”

Section: Discussionmentioning

confidence: 99%

GDP Per Capita and Protest Activity: A Quantitative Reanalysis

Korotayev

Bilyuga

Шишкина

2017

Cross-Cultural Research

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Our research suggests that the relation between GDP per capita and sociopolitical destabilization is not characterized by a straightforward negative correlation; it rather has an inverted U-shape. The highest risks are typical for the countries with intermediate values of GDP per capita, not the highest or lowest values. Thus, until a certain value of GDP per capita is reached, economic growth predicts an increase in the risks of sociopolitical destabilization. This positive correlation is particularly strong (r = .94, R 2 = .88) and significant for the intensity of antigovernment demonstrations. This correlation can be observed in a very wide interval (up to 20,000 of international 2014 dollars at purchasing power parities [PPPs]). We suggest that it is partially accounted for by the following regularities: (a) GDP growth in authoritarian regimes strengthens the pro-democracy movements, and, consequently, intensifies antigovernment demonstrations; (b) in the GDP per capita interval from the minimum to $20,000, the growth of GDP per capita correlates quite strongly with a declining proportion of authoritarian regimes and a growing proportion of intermediate and democratic regimes; and, finally, (c) GDP growth in the given diapason increases the level of education of the population, which, in turn, leads to a higher intensity of antigovernment demonstrations.

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Section: Discussionmentioning

confidence: 99%

GDP Per Capita and Protest Activity: A Quantitative Reanalysis

Korotayev

Bilyuga

Шишкина

2017

Cross-Cultural Research

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“…This impression became even stronger when the equation describing the planetary macroevolution acceleration pattern turned out to be identical with the equation that was found by Heinz von Foerster in 1960 to describe in an extremely accurate way the global population growth acceleration pattern between 1 and 1958 CE. I had some grounds to expect that the planetary macroevolutionary acceleration in the last 4 billion years could be described by a single hyperbolic equation quite accurately, because our earlier research found that both biological and social macroevolution could be described by rather similar simple hyperbolic equations (Korotayev 2005(Korotayev , 2006a(Korotayev , 2006b(Korotayev , 2007a(Korotayev , 2007b(Korotayev , 2008(Korotayev , 2009(Korotayev , 2012(Korotayev , 2013Khaktourina et al 2006;Korotayev, Malkov, Khaltourina 2006a, 2006bMarkov, Korotayev 2007Markov, Anisimov, Korotayev 2010;Korotayev, S. Malkov 2012;Korotayev, Markov 2014Grinin, Markov, Korotayev 2013Korotayev, A. Malkov 2016;Zinkina, Shulgin, Korotayev 2016;Korotayev, Zinkina 2017), but I NOTE: black markers correspond to empirical estimates of the world population by McEvedy and Jones (1978) for 1000-1950 and UN Population Division (2018) for 1950-1970. The grey curve has been generated by von Foerster's Eq.…”

Section: On the Formula Of Acceleration Of The Global Evolutionary Dementioning

confidence: 99%

“…Earth between each pair of "biospheric revolutions" increased about the same number of times (somewhere around 2.8). It should be noted that this is not in bad agreement with many mathematical models of hyperbolic growth of the world poulation 41 , as such models tend to consider the hyperbolic growth of the world population as a result of the functioning of the positive feedback mechanism of the second order between demographic growth and technological development, when technological development (most vividly manifested precisely as "biospheric revolutions" -e.g., the Neolithic Revolution, or the Industrial Revolution) significantly accelerated the growth rate of the population, which (by virtue of the principle "the more people, the more inventors" 42 ) 41 See, e.g., Korotayev, Malkov, Khaltourina 2006a, 2006bTaagepera 1976;Kremer 1993;Podlazov 2000Podlazov , 2001Podlazov , 2002Tsirel 2004;Korotayev, Malkov, Khaltourina 2006a;Korotayev, S. Malkov 2012;Korotayev 2012Korotayev , 2013Korotayev, A. Malkov 2016;Grinin, Markov, Korotayev 2013 42 As Kremer puts it, "high population spurs technological change because it increases the number of potential inventors… In a larger population there will be proportionally more people lucky or smart enough to come up with new ideas" (Kremer 1993: 685-686). Kremer rightly notes that"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.…”

Section: (11)mentioning

confidence: 99%

The 21st Century Singularity and its Big History Implications: A re-analysis

Korotayev

2018

JBH

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The idea that in the near future we should expect "the Singularity" has become quite popular recently, primarily thanks to the activities of Google technical director in the field of machine training Raymond Kurzweil and his book The Singularity Is Near (2005). It is shown that the mathematical analysis of the series of events (described by Kurzweil in his famous book), which starts with the emergence of our Galaxy and ends with the decoding of the DNA code, is indeed ideally described by an extremely simple mathematical function (not known to Kurzweil himself) with a singularity in the region of 2029. It is also shown that, a similar time series (beginning with the onset of life on Earth and ending with the information revolution-composed by the Russian physicist Alexander Panov completely independently of Kurzweil) is also practically perfectly described by a mathematical function (very similar to the above and not used by Panov) with a singularity in the region of 2027. It is shown that this function is also extremely similar to the equation discovered in 1960 by Heinz von Foerster and published in his famous article in the journal "Science"-this function almost perfectly describes the dynamics of the world population and is characterized by a mathematical singularity in the region of 2027. All this indicates the existence of sufficiently rigorous global macroevolutionary regularities (describing the evolution of complexity on our planet for a few billion of years), which can be surprisingly accurately described by extremely simple mathematical functions. At the same time it is demonstrated that in the region of the singularity point there is no reason, after Kurzweil, to expect an unprecedented (many orders of magnitude) acceleration of the rates of technological development. There are more grounds for interpreting this point as an indication of an inflection point, after which the pace of global evolution will begin to slow down systematically in the long term.

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“…The main mathematical models of hyperbolic growth in the world population (Taagapera 1976(Taagapera , 1979Kremer 1993;Cohen 1995;Podlazov 2004;Tsirel 2004;Korotayev 2005Korotayev , 2007Korotayev , 2008Korotayev , 2009Korotayev , 2012Korotayev, Malkov, et al 2006a: 21-36;Golosovsky 2010;Korotayev and Malkov 2012) are based on the following two assumptions:…”

Section: The Von Foerster Et Al Equation ⁄mentioning

confidence: 99%

On Similarities between Biological and Social Evolutionary Mechanisms: Mathematical Modeling

Гринин¹,

Марков

Korotayev³

2013

CDN

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In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. This is more or less identical with the working of the collective learning mechanism. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure, suggesting the presence within the biosphere of a certain analogue of the collective learning mechanism. We discuss how such positive feedback mechanisms can be modelled mathematically.

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Mathematical models of world-system development

Cited by 15 publications

References 0 publications

GDP Per Capita and Protest Activity: A Quantitative Reanalysis

GDP Per Capita and Protest Activity: A Quantitative Reanalysis

The 21st Century Singularity and its Big History Implications: A re-analysis

On Similarities between Biological and Social Evolutionary Mechanisms: Mathematical Modeling

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