Finite-time singularity in the dynamics of the world population, economic and financial indices

Abstract

Contrary to common belief, both the Earth's human population and its economic output have grown faster than exponential, i.e., in a super-Malthusian mode, for most of the known history. These growth rates are compatible with a spontaneous singularity occuring at the same critical time 2052 ± 10 signaling an abrupt transition to a new regime. The degree of abruptness can be infered from the fact that the maximum of the world population growth rate was reached in 1970, i.e., about 80 before the predicted singular time, corresponding to approximately 4% of the studied time interval over which the acceleration is documented. This rounding-off of the finite-time singularity is probably due to a combination of wellknown finite-size effects and friction and suggests that we have already entered the transition region to a new regime. In theoretical support, a multivariate analysis coupling population, capital, R&D and technology shows that a dramatic acceleration in the population during most of the timespan can occur even though the isolated dynamics do not exhibit it. Possible scenarios for the cross-over and the new regime are discussed. IntroductionBoth the world economy as well as the human population have grown at a tremendous pace especially during the last two centuries. It is estimated that 2000 years ago the population of the world was approximately 300 million and for a long time the world population did not grow significantly, since periods of growth were followed by periods of decline. It took more than 1600 years for the world population to double to 600 million and since then the growth has accelerated. It reached 1 billion in 1804 (204 years later), 2 billion in 1927 (123 years later), 3 billion in 1960 (33 years later), 4 billion in 1974 (14 years later), 5 billion in 1987 (13 years later) and 6 billion in 1999 (12 years later). This rapidly accelerating growth has raised sincere worries about its sustainability as well as concerns that we humans as a result might cause severe and irreversible damage to eco-systems, global weather systems etc [6,22]. At, what one may say the other extreme, the optimists expect that the innovative spirit of mankind will be able to solve the problems associated with a continuing increase in the growth rate [15,46]. Specifically, they believe that the world economic development will continue as a successive unfolding of revolutions, e.g., the Internet, bio-technological and other yet unknown innovations, replacing the prior agricultural, industrial, medical and information revolutions of the past. Irrespective of the interpretation, the important point is the presence of an acceleration in the growth rate. Here, it is first shown that, contrary to common belief, both the Earth human population as well as its economic output have grown faster that exponential for most of the known history and most strikingly so in the last centuries. Furthermore, we will show that both the population growth rate and the economic growth rate are consistent with a spontaneous singula...

Superexponential long-term trends in information technology

“…Note that here we are talking about a mathematical singularity (division by zero) of the kind described for example in von Foerster, Mora, and Amiot (1960); Meyer and Vallee (1975); Kremer (1993); Johansen and Sornette (2001);Bettencourt, Lobo, Helbing, Kühnert, and West (2007). This is different from the "technological singularity" discussed by various authors (Vinge 1993;Kurzweil 2005;Yudkowsky 2007) 5 .…”

Scale Relativity and Fractal Space-Time: Theory and Applications

“…It has been shown that such a behaviour provides a very satisfactory and possibly predictive model of the time evolution of many critical systems, including earthquakes and market crashes ( [122] and references therein). More recently, it has been applied to the analysis of major event chronology of the evolutionary tree of life [19,85,86], of human development [14] and of the main economic crisis of western and precolumbian civilizations [44,85,50,45]. One can recover log-periodic corrections to self-similar power laws through the requirement of covariance (i.e., of form invariance of equations) applied to scale differential equations [75].…”

“…The adjusted critical time T c and scale ratio g are indicated for each lineage [19,85,86]. [19,85,86], long time scale evolution of western and other civilizations [85,86,45], world economy indices dynamics [50], embryogenesis [14], etc... Thus emerges the idea that this behaviour typical of temporal crisis could be extremely widespread, as much in the organic world as in the inorganic one [122].…”

“…Examples of such a predictivity (or retropredictivity) are: (i) the retroprediction that the common Homo-Pan-Gorilla ancestor (expected, e.g., from genetic distances and phylogenetic studies), has a more probable date of appearance at ≈ −10 millions years [19]; its fossil has not yet been discovered (this is one of the few remaining 'missing links'); (ii) the prediction of a critical date for the long term evolution of human societies around the years 2050-2080 [85,50,86,45]; (iii) the finding that the critical dates of rodents may reach +60 Myrs in the future, showing their large capacity of evolution, in agreement with their known high biodiversity; (iv) the finding that the critical dates of dinosaurs are about −150 Myrs in the past, indicating that they had reached the end of their capacity of evolution (at least for the specific morphological characters studied) well before their extinction at −65 Myrs; (v) the finding that the critical dates of North american Equids is, within uncertainties, consistent with the date of their extinction, which may mean that, contrarily to the dinosaur case, the end of their capacity of evolution has occured during a phase of environmental change that they have not been able to deal with by the mutation-selection process; (vi) the finding that the critical date of echinoderms (which decelerate instead of accelerating) is, within uncertainties, the same as that of their apparition during the PreCambrianCambrian radiation, this supporting the view of the subsequent events as a kind of "scale wave" expanding from this first shock.…”

Fifty years to prove Malthus right

“…We ask to what extent models that are premised on a constant global K as in Suweis et al (3) agree with an alternative class of carrying capacity models on predicting the timing for unsustainable global population growth. In particular, factors that symbolize innovation and adaptation lead to K representations that are not constant (4,5) but may depend on a dynamic population size.…”