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Using mathematical modeling, we consider the phenomenon of singularity in the biological and social history. It is shown that hyperbolic trends in biological and social evolution can be explained by transitional processes that accompany the expansion of ecological niches due to periodically occurring revolutionary innovations. During these periods, strong positive feedbacks are actualized, leading to hyperbolic growth. However, this growth is then inhibited, and the system goes into a new qualitative state. Then, there is a relatively slow development of the updated system with a gradual accumulation of quantitative characteristics and a new innovative breakthrough. This cycle then repeats multiple times. In this regard, the system’s hyperbolic growth trends indicate the transitivity of its current state, while the time of singularity in this hyperbolic trend indicates the end of the transition process.

The authors quantitatively analyse the long-term dynamics of technological progress from 40,000 BCE and offer projections through the 22nd century. We provide one method to measure technological progress over that time period, using a simple hyperbolic equation, yt = C/(t0 – t), as our model. We define yt as the technological growth rate, measured as number of technological phase transitions per unit of time. Our method measures the worldwide technology dynamic growth with an accuracy of R2 = 0.99. We find the singularity date occurs in the early 21st century and expect a new powerful acceleration of technological development after the 2030s followed by a slow-down in the late 21st and early 22nd centuries. The authors discuss the role of global ageing as one of the main factors in both the technological acceleration and the subsequent deceleration.

In this chapter, we consider the process of technological progress presenting one of the options for measuring its speed throughout the entire historical process. We find that the general dynamics of accelerating technological growth over the past 40 thousand years can be described with amazing accuracy (R2 = 0.99) using the following simplest hyperbolic equation: yt = C/t0 − t, where yt is the technological growth rate measured as a number of technological phase transitions per unit of time. Although since 40,000 BP the speed of technological progress tended to generally increase, however, according to the theory of production principles on which we rely, the acceleration of technological progress had noticeable fluctuations. These fluctuations can be explained by the fact that technological development proceeded within the framework of super-long cycles. We show that, within these cycles, the phases of accumulation of basic breakthrough innovations are replaced by phases of rapid growth of improvements in basic innovations and their wide distribution. These fluctuations between cycle phases affect the pattern of acceleration of technological progress. Currently, there are a number of calculations of the point of singularity of the Big History and global evolution, which generally localize the singularity around the first half of the twenty-first century. The point of singularity in our calculations, if we rely only on historical time points, falls on 2018, that is, in principle, it fully fits the results of other studies. There is a fairly reasonable idea of slowing down a number of important social processes (such as demographic development, urbanization), including the speed of technological progress. Indeed, there are already some grounds for talking about signs of a slowdown in progress from the 1960 to 1970s. However, according to the theory of production principles, as already mentioned, there are strong fluctuations in the acceleration of technological progress. We assume that at the moment technological progress is in the fourth—the scientific and cybernetic—production principle. According to this theory, we expect a powerful acceleration of technological progress in the area between the 2030s and the 2070s. In this case, if we take into account the expected time points, the point of singularity, according to our calculations, is estimated to be around 2106. That is, with this method of calculation, we should first expect a new way of acceleration of technological progress, and then, its slowdown in the region of the end of the twenty-first century—the beginning of the 22nd. We also identify the social mechanism for such acceleration and deceleration: in the coming decades, the process of global ageing can cause technological acceleration first and change its direction, and then closer to the end of the present and the beginning of the next century, on the contrary, elderly society can be a brake on scientific-technological progress.

This paper proposes a methodological approach to analyzing the evolution of the stability of socioeconomic systems and to assessing the risk of their possible instability based on the use of mathematical modeling methods. In this paper, a basic model is presented, which allowsing us to describe the joint dynamics of processes in the economic, organizational, and socio psychological areas of the society. The model showsallows us to see at what parameters of the socioeconomic system its steady functioning is possible, and at which it is impossible. It is shown that the transition from its steady state to an its unsteady one is not smooth but rather occurs as a leap. This methodology is applied to the analysis of stability and change in the Egyptian socioeconomic system after 2010. 

This chapter discusses in some detail the possibility of the Singularity being a product of biased human perception described by the Weber–Fechner law. It is shown that though the Weber–Fechner effect can produce series with a hyperbolic shape, the hyperbolic acceleration pattern with the twenty-first century Singularity detected in Panov and Modis–Kurzweil series is explained first of all by the actual hyperbolic acceleration of the global megaevolution.

The article analyzes relative deprivation as a possible factor of sociopolitical instability during the Arab Spring events using the methods of correlation and multiple regression analysis. In this case, relative deprivation is operationalized in two ways: (a) through the indicator of subjective feeling of happiness on the eve of the events of the Arab Spring, and (b) through the scale of decrease of the subjective feeling of happiness on the eve of the events of Arab Spring. It is shown that the change in the level of subjective feeling of happiness between 2009 and 2010 is a powerful, statistically significant predictor of the level of destabilization in Arab countries in 2011. The next most powerful predictor is the mean value of the subjective feeling of happiness in the corresponding country for 2010. At the same time, the fundamental economic indicators we tested, while controlling for them, have turned out to be extremely weak and at the same time statistically insignificant predictors of the level of sociopolitical instability in the Arab countries in 2011.

Over a long period, the main intrigue within the current global contradiction has been the resistance of most of the world community to the growing egoism of the USA, which is not willing to consider other countries’ interests. This has become even more evident since Donald Trump’s rise to power, as the frontline of the contradictions has expanded since the USA continues to ignore the others’ interests. Trump’s 2016 campaign slogan, “Make America Great Again,” is direct evidence of the loss of the U.S.’s former leadership, and indicates that the situation in the world is going to heat up. Thus, it is important to consider the mater- ial basis of contemporary US power and whether it will allow America to be “great again” or not. The article analyzes seven (actual and potential) weaknesses of the USA—some of which, paradoxically, support its current power. But sooner or later these weaknesses will bring the USA to a crisis and topple it from its leading position. In the last part of the article, we show how we can speak of President Trump’s policy as an objective (though not terribly rational) reaction to changes in the World System and the weakening of the USA’s positions within it, linking his policies to the World System reconfiguration, with movement toward a new world order as a result. The novelty of the article is that the known problems of the USA are collected, systematized, their interrelations and mutual influences are shown, and forecasts made on this basis.

This article revisits the prediction, made in 2010, that the 2010–2020 decade would likely be a period of growing instability in the United States and Western Europe Turchin P. 2018. This prediction was based on a computational model that quantified in the USA such structural-demographic forces for instability as popular immiseration, intraelite competition, and state weakness prior to 2010. Using these trends as inputs, the model calculated and projected forward in time the Political Stress Indicator, which in the past was strongly correlated with socio-political instability. Ortmans et al. Turchin P. 2010 conducted a similar structural-demographic study for the United Kingdom. Here we use the Cross-National Time-Series Data Archive for the US, UK, and several major Western European countries to assess these structural-demographic predictions. We find that such measures of socio-political instability as anti-government demonstrations and riots increased dramatically during the 2010–2020 decade in all of these countries.

This book introduces a 'Big History' perspective to understand the acceleration of social, technological and economic trends towards a near-term singularity, marking a radical turning point in the evolution of our planet. It traces the emergence of accelerating innovation rates through global history and highlights major historical transformations throughout the evolution of life, humans, and civilization. The authors pursue an interdisciplinary approach, also drawing on concepts from physics and evolutionary biology, to offer potential models of the underlying mechanisms driving this acceleration, along with potential clues on how it might progress.  The contributions gathered here are divided into five parts, the first of which studies historical mega-trends in relation to a variety of aspects including technology, population, energy, and information. The second part is dedicated to a variety of models that can help understand the potential mechanisms, and support extrapolation. In turn, the third part explores various potential future scenarios, along with the paths and decisions that are required. The fourth part presents philosophical perspectives on the potential deeper meaning and implications of the trend towards singularity, while the fifth and last part discusses the implications of the Search for Extraterrestrial Intelligence (SETI). Given its scope, the book will appeal to scholars from various disciplines interested in historical trends, technological change and evolutionary processes. 

This introductory chapter discusses the overall place of the twenty-first-century Singularity within the overall Big History. It is shown that to place the accelerating trend of complexity in the context of Big History, we need to distinguish the two forms (arms) of megaevolution so far in the universe. The first arm of evolution is the decelerating development of physical matter and energy into galaxies, stars, and planets from the initial Big Bang. The second arm of evolution is the accelerating rate of complexity evolution in the form of life, humans, and civilizations, which is the main concern of this book. The book is organized to present these historical megatrends, models, interpretations, future scenarios, and more philosophical questions along with the realization and debate about their limitations and uncertainty.

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 up to the early 1970s 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 billions 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.

The current article investigates the relation between values and modernization applying some elements of the method proposed by Inglehart and Welzel (the authors of the Human Development Sequence Theory) to the data of Shalom Schwartz. The values survey by Schwartz specifies two main value axes, namely, conservation versus openness to change and self-transcendence versus self-enhancement. Our research has revealed that the correlation between these two value axes differs in its direction when estimated for “macro-Europe” (that includes Europe and former settlement colonies of North and South America and Oceania) and “Afroasia” (that includes Asia and Africa). In “macro-Europe,” we deal with a significant positive correlation between openness to change and self-transcendence, whereas in “Afroasia,” this correlation is strong, significant, and negative. We investigate the possible impact of modernization on this difference. To do this, we approximate modernization through such indicators as gross domestic product (GDP) per capita and the proportions of the labor force employed in various sectors of economy. We find that, in both megazones, modernization is accompanied by increasing openness to change values. As for the self-transcendence/self-enhancement axis, we propose two possible explanations of the different dynamics observed in Europe and in “the East” (Asia and North Africa), namely, (a) that Eastern and Western societies find themselves at different modernization stages and (b) that this difference is accounted for by different civilizational patterns. Further analysis suggests that the latter explanation might be more plausible.