A quantitative analysis of worldwide long-term technology growth: From 40,000 BCE to the early 22nd century

Andrey Korotayev

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.

Technological Forecasting & Social Change 155 (2020) 119955 Contents lists available at ScienceDirect Technological Forecasting & Social Change journal homepage: www.elsevier.com/locate/techfore A quantitative analysis of worldwide long-term technology growth: From 40,000 BCE to the early 22nd century Leonid Grinina,b, Anton Grininc, Andrey Korotayeva,b, T ⁎ a National Research University Higher School of Economics, Moscow, Russian Federation Institute of Oriental Studies, Russian Academy of Sciences, Moscow, Russian Federation c International Center for Education and Social and Humanitarian Studies, Moscow, Russian Federation b A B S T R A C T 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. 1. INTRODUCTION 1.3. Relevant research gaps and how to ﬁll them 1.1. General context So, technological growth is one of the most important factors affecting society's transformations and development. Thus, it is extremely important to identify some patterns in the history of technological development and use these to attempt to anticipate forthcoming transformations in technologies and society. Unfortunately, there are few well-grounded studies which could describe technological development in a systematic and consistent way and provide scientiﬁc explanations of why and how the technological revolutions occur. In general, the entirety of human history, especially during the last few centuries, may be regarded (albeit, with signiﬁcant qualiﬁcations) as a history of achievements of science and technology, especially information technologies (Kurzweil 2001; Galor and Tsiddon 1997; Kremer 1993; Carree 2003; Phillips 2011; Kayal 1999; Grinin and Grinin, 2015c, 2016; Grinin et al., 2017b). This makes the issue of longterm trends and patterns in technological growth rates especially important. 1.2. What has been done within the general context The issue of the technological growth rate has been discussed in Technological Forecasting and Social Change for many years. Researchers have published interesting (but often contradictory) scenarios and many debates, amongst which it appears necessary to single out the Huebner–Modis debate on the possible declining trend in worldwide innovation (Huebner 2005; Modis 2005), as well as discussions dealing with Kurzweil's singularity (Ayres 2006; Modis 2006; Magee and Devezas 2011; Linstone, 2014 ). There are also some (albeit too few) works that provide consistent forecasts of technological development based on identiﬁed developmental trends (Modis 1999; Martino 2003; Farmer and Lafond 2015). ⁎ 1.4. Research questions This article aims to answer the following questions: What is the long-term pattern of the acceleration of the technological growth? Is it exponential or hyperbolic? How can this pattern be described mathematically? Is an acceleration of technological growth likely to be observed in the forthcoming decades? What could be the driver of such an acceleration? Is a slowdown of technological growth likely to be observed afterwards? What could cause such a slowdown? How could such a slowdown aﬀect socioeconomic and sociopolitical relations? What is the relationship between global ageing and technological progress? Why is global ageing likely to be one of the most important factors aﬀecting technological growth in the near future? Corresponding author. E-mail address: akorotaev@hse.ru (A. Korotayev). https://doi.org/10.1016/j.techfore.2020.119955 Received 24 July 2019; Received in revised form 30 December 2019; Accepted 4 February 2020 Available online 05 March 2020 0040-1625/ © 2020 Elsevier Inc. All rights reserved. Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. principle can be represented by six phases. Our mathematical analysis is based on this six-phase pattern: (1) The ﬁrst phase—starting—is the beginning of a production revolution. A new production principle emerges in one or a few places, although in rather undeveloped, incomplete forms. (2) The second phase is that of primary modernization. It is associated with a wider diﬀusion of new production forms, as well as with strengthening and the vigorous expansion of a new production principle. (3) The third phase is completion of the production revolution. The production principle acquires advanced characteristics. (4) The fourth phase is the stage of maturity and expansion. It relates to the diﬀusion of new technologies into most regions and spheres of production. The production principle acquires its mature form, and this leads to important changes in the socioeconomic sphere. (5) The ﬁfth phase is that of absolute dominance of a production principle. It leads to an intensiﬁcation of production and the full realization of the potential of the principle. (6) The ﬁfth phase is that of non-system phenomena, a preparatory phase for transition to a new production principle. New inventions and improvements in technologies lead to the emergence of non-system elements which pave the way for the formation of a new production principle. Under favourable conditions, these elements form a new system. So, the current cycle closes, but in some societies the transition to a new production principle starts, and the cycle will repeat at a new level. Based on this six-phase cycle of the production principle, we perform our calculations of the speed of technological progress, where the transition from one stage to the next is considered as a phase transition. For a description of the history of technological changes within the hunter-gatherer, craft-agrarian, and trade-industrial production principles see Section 1 of the Supporting Online Materials. A more detailed description of the scientiﬁc-cybernetic production principle and the Cybernetic revolution can be found below in the following subsection. The scientiﬁc-cybernetic production principle and the Cybernetic revolution. The scientiﬁc-cybernetic production principle is only in its ﬁrst stages (see Figs. 1, 2); only its ﬁrst phase has ended, and the second phase is in progress. Hence, all the calculations of the forthcoming phases' lengths are highly hypothetical. These calculations are presented in Tables 1 and 2, below. The ﬁrst phase of the scientiﬁc-cybernetic production principle took place between the 1950s and mid-1990s, when a vigorous development of information technologies and the start of real economic globalization were observed. It is also connected with the transition to scientiﬁc methods in production and circulation management. Especially important changes took place in information technologies. In addition, this production revolution had a few other directions: in energy technologies, in synthetic materials production, automation, space exploration, and agriculture. However, its main results are still forthcoming. As the reader should remember, the ﬁrst phase of a new production principle corresponds to the initial phase of a new production revolution (see Fig. 1). The production revolution that began in the 1950s and continues to the present was sometimes called the ‘scientiﬁc-technical’ revolution in its early period (e.g., Benson and Lloyd 1983). However, it would be more appropriate to call it the Cybernetic revolution, since its main changes will imply increasing opportunities to control various processes by means of self-regulated systems. The second phase of the scientiﬁc-cybernetic production principle (the intermediate phase of the Cybernetic revolution, see Fig. 1) began in the mid-1990s in conjunction with the development and wide diffusion of user-friendly computers, communication technologies such as 1.5. To whom is this paper relevant? Due to a rather wide range of research questions raised in this article, it could be relevant to a wide readership—including not only experts in technological forecasting and its social consequences, but also to general futurologists, economists, demographers, business and public planners, economic historians, political scientists and politicians, sociologists, anthropologists, and even philosophers. 2. THEORETICAL background To address the goals outlined above, we use, ﬁrstly, the theory of production principles, which has been in development for almost 30 years. It allows an understanding of the logic of technological development within the historical process and the suggested periodization. The theory has previously been described in detail (Grinin, 2006a, Grinin, 2006b; Grinin, 2007a, Grinin, 2007b, Grinin, 2012a, Grinin, 2012b; 2013; Grinin and Grinin, 2013a, Grinin and Grinin, 2013b, 2014, Grinin and Grinin, 2015; Grinin and Grinin, 2015; Grinin and Grinin, 2015c, ; 2016; Grinin and Korotayev, 2015a; Grinin et al., 2017b). Production Principles and Production Revolutions. A large number of technological breakthroughs have been observed in human history. As we have already argued (Grinin et al., 2017b), amongst the large technological breakthroughs in history, the most important are the three technological or production revolutions: 1) the Agrarian revolution (the Neolithic revolution); 2) the Industrial revolution; and 3) the Cybernetic revolution. From our point of view, each revolution initiates a new stage of development of the world's productive forces, as well as a transition to a new stage of technological evolution. The point is that each production revolution entails a transition to a fundamentally new production system; the beginning of each marks the borders between corresponding production principles. 1 Agrarian revolution (from 12,000–10,000 BP to 5500–3000 BP). Resulted in the transition to systematic food production using a new type of energy (the power of domestic animals), and, on this basis, the transition to a complex social division of labour. This revolution was also connected with the use of new power sources (animal power) and new materials. 2 Industrial revolution (the last third of the 15th through the ﬁrst third of the 19th centuries). Resulted in production being concentrated in industry and being carried out using machines. Not only was manual labour replaced by machines, but biological energy was replaced by water and steam energy. 3 Cybernetic revolution (from 1950 to the 2060/2070s). Has already led to the emergence of powerful information technologies, and in the future will stimulate transition to the wide use of self-regulating systems in diﬀerent spheres of activity. These systems will be able to function without human intervention. The Cybernetic revolution is not over yet. We believe that it will provide huge steps in improving human health, quality of life, and our ability to inﬂuence and control the human body (for more details see below; see also Grinin et al., 2017b; Grinin and Grinin, 2015, Grinin and Grinin, 2015c, 2016, 2020). Phases of production principles. Every production revolution can be regarded as an integral part of the production principle. The production revolution is the ﬁrst ‘half’ of the production principle, whereas the development of mature technologies based on the production principle occurs during the second half.1 The cycle of a production (footnote continued) innovative phase (when new technologies acquire their mature characteristics). For more information about the cycle of production revolutions and their structural interconnection with production principles see Grinin et al., 2017a (as well as our works mentioned above). 1 The cycle of each production revolution looks as follows: the initial innovative phase (emergence of a new revolutionizing production sector)—the modernization phase (diﬀusion, synthesis and improvement of new technologies)—the ﬁnal 2 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. Fig. 1. Phases of the Cybernetic revolution. Fig. 2. Development of the scientiﬁc-cybernetic production principle. Table 1 Chronology of production principle phases. Figures before brackets correspond to absolute dates (BP); ﬁgures in brackets correspond to years BCE. Bold values indicate phase lengths (in thousands of years). Production principle 1st phase 2nd phase 3rd phase 4th phase 5th phase 6th phase Overall for production principle 1. Hunter-gatherer 40,000–30,000 BP (38 000–28 000 BCE) 10 10,000–7300 (8000–5300 BCE) 2.7 1430–1600 0.17 1955–1995* 0.04 30,000–22,000 (28 000–20 000 BCE) 8 7300–5000 (5300–3000 BCE) 2.3 1600–1730 0.13 1995–2030 0.035 22,000–17,000 (20 000–15 000 BCE) 5 5000–3500 (3000–1500 BCE) 1.5 1730–1830 0.1 2030–2055 0.025 17,000–14,000 (15 000–12 000 BCE) 3 35,000–2200 (1500–200 BCE) 1.3 1830–1890 0.06 2055–2070 0.015 14,000–11,500 (12 000–9500 BCE) 11,500–10,000 (9500–8000 BCE) 40,000–10,000 (38 000–8000 BCE) 2.5 2200–1200 (200 BCE– 800 CE) 1.0 1890–1929 0.04 2070–2080 0.01 1.5 800 СЕ–1430 CE 30 10,000–570 (8000 BCE –1430 CE) 9.4 1430–1955 0.525 1955–2090 0.135–0.160 2. Craft-agrarian 3. Trade-industrial 4. Scientiﬁccybernetic ⁎ 0.6 1929–1955 0.025 2080–2090 0.01 Note: Starting from the second column of the row we give our estimates of the expected lengths of the phases of the scientiﬁc-cybernetic production principle. continues to the present. Before we begin to discuss future transformations, it is appropriate to clarify our understanding of the rates of modern and future technological progress. There are a number of scholars who believe that the cell phones, and so on. Medicine and biotechnologies have also made signiﬁcant progress, as well as some other innovative ﬁelds (see Grinin and Grinin, 2015, Grinin and Grinin, 2015, Grinin and Grinin, 2015c: part 3; Grinin et al., 2016: Chs. 3–4; Grinin et al., 2017b). This phase 3 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. Table 2 Production principles and their phase lengths (in thousands of years). Production principle 1st phase 2nd phase 3rd phase 4th phase 5th phase 6th phase Overall 1. 2. 3. 4. Hunter-gatherer Craft-agrarian Trade-industrial Scientiﬁc-cybernetic 10 2.7 0.17 0.04 8 2.3 0.13 0.035* 5 1.5 0.1 0.025 3 1.3 0.06 0.015 2.5 1.0 0.04 0.01 1.5 0.6 0.025 0.01 30 9.4 0.525 0.135 ⁎ Note: This row indicates our estimates of the expected lengths of the phases of the scientiﬁc-cybernetic production principle. On mathematical equations, global ageing, etc. We use wellknown mathematical equations that allow us to compare our results with the results of researchers who measure the rate of general evolution on Earth. We also pay some attention to the question of a singularity in acceleration patterns, since there are grounds to expect that its detection could help to identify important inﬂection points in the processes under study. The issue of a global history singularity has been discussed quite actively for more than a decade (see, e.g., Panov 2005, 2017, 2020; Kurzweil 2005; Ayres 2006; Modis 2006, 2020; Magee and Devezas 2011; Shanahan 2015; Callaghan et al., 2017; Korotayev 2018, 2020; Nazaretyan 2015, Nazaretyan, 2016, Nazaretyan 2017, 2018, 2020; LePoire 2020). This subject became especially popular after the 2005 publication of Raymond Kurzweil's (Google's director of engineering) book The Singularity Is Near. We seek to identify actual mechanisms and relationships to explain the reasons for possible slowdown in the future speed of technological process. We associate very big changes in technological development with global ageing in the future (as one of the most important results of technological progress), but, as we will see, the eﬀect of ageing on the speed of technological progress is non-linear and creates diﬀerent effects at diﬀerent phases. There has been a great deal of discussion in Technological Forecasting and Social Change about the form future changes in profession will take. For example, most analysts predict extensive automation and robotization, including the complete replacement of human labour in a number of professions (e.g., Frey and Osborne 2017). It is worth noting that the impact of global ageing on the speed and direction of scientiﬁc-technological progress is understudied (Galor and Weil 2000; Prettner 2013; Tsirel 2008; De Grey and Rae, 2008), and global ageing aﬀects technological, economic, political, social and other spheres in various ways (Fukuyama 2002; Goldstone et al., 2015d; Grinin and Grinin, 2015c, Grinin and Grinin, 2015, Grinin 2017; Grinin et al., 2016; Grinin and Korotayev 2010, Grinin and Korotayev, 2015, Grinin and Grinin, 2015c, Grinin and Korotayev, 2016a, Grinin and Korotayev, 2016b; Grinin et al., 2017b; Harper 2006; Powell and Khan 2013; Goldstone 2015; Coleman and Rowthorn 2015; Park and Shin 2015; Haas 2015; Zimmer 2016). speed of technological and scientiﬁc progress is already slowing down (Maddison 2007; Teulings and Baldwin 2014; Phillips 2011; Korotayev and Bozhevolnov 2010); it is also possible to observe this if we compare the number of inventions per decade in 1950–1960 with that in 1970–1990 according to Bunch and Hellemans’ database (2004). However, we do not think that the speed of future technological progress will gradually slow, nor that it will be constant. For the time period our theory allows us to make predictions that the speed change will be nonlinear. At the ﬁrst stage of the Cybernetic revolution, the speed of technical progress accelerated, and in the second stage (which we have been in since the 1990s), it slowed. We believe that this deceleration will not change until the mid-2030s or beginning of the 2040s, after which technological growth will experience a new acceleration. There will then be a gradual slow-down up to the point of singularity, with a subsequent change of the pattern (see below). The third phase of the scientiﬁc-cybernetic production principle is likely to begin in approximately the 2030s. It will mean the beginning of the ﬁnal phase of the Cybernetic revolution, which in our view may become the epoch of ‘self-regulating systems’. The ﬁnal phase of this revolution may start in the sphere of medicine and will be connected with its innovative branches; this will lead to serious modiﬁcation of human organism and, perhaps, change its biological nature (for more details see Grinin and Grinin, 2015c, Grinin et al., 2016; Grinin et al., 2016b; LE Grinin L., Grinin A., and Korotayev 2017a). The drivers of the ﬁnal phase of the Cybernetic revolution will be medical technologies, additive manufacturing (3D printers), nano- and bio-technologies, robotics, IT, and cognitive technologies,2 which will combine to form a sophisticated system of self-regulating production. We can denote this complex as MANBRIC convergence.3 amongst these, medical technologies will become the main integrating centre (see Grinin and Grinin, 2015c, 2016, 2020; Grinin and Korotayev, 2016a, Grinin and Korotayev, 2016b; Grinin et al., 2016b; Grinin L., Grinin A., and Korotayev 2017a). The fourth phase implies that, in the next two decades, the sector of self-regulating systems will rapidly improve and diﬀuse to various regions at enormous speed. MANBRIC technologies will reach their developed forms and will occupy a central place in the new production principal. At the same time, this will be a period of signiﬁcant growth in life expectancy and, accordingly (against the background of low fertility), a period of rapid global ageing that will also involve regions that are still ‘young’, including sub-Saharan Africa and South Asia (Grinin and Grinin, 2015c, 2016; Grinin et al., 2016b; Grinin L., Grinin A., and Korotayev 2017a, Grinin et al., 2017). The expected lengths of the fourth, ﬁfth, and sixth phases of the scientiﬁc-cybernetic production principle are 2055–2070, 2070–2080, and 2080–2090, respectively (see Tables 1 and 2 below, and Grinin, 2006b for more detail). 3. METHODS We combine various methods: historical, comparative, evolutionary, logical, theoretical and mathematical modelling. We use rather simple mathematical methods that allow us to ﬁnd the general pattern of the acceleration of technological growth rate (operationalized as the frequency of technological phase transitions per unit of time). For this purpose, we apply the methodology proposed by Alexander Panov (2005, 2017, 2020) and one based on work published in this journal (in particular, by Theodore Modis, 2002, 2005). The novelty of our research lies in our attempt to present a brief frame of qualitative model in which the rate of change in the population age structure correlates with the development of future technologies. We obtain a nontrivial result, according to which the process of global ageing can accelerate and change the direction of technological progress in the coming decades, and then the ageing of society can slow 2 Note that one of the most important directions of the evolution of IT and cognitive technologies within the MANBRIC convergence is the development of artiﬁcial intelligence (AI). 3 The order of the letters in the acronym does not reﬂect our understanding of the relative importance of areas of the complex. For example, biotechnologies will be more important than nanotechnologies and additive manufacturing. The order is determined simply by convenience of pronunciation. 4 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. stable (see Tables 3 and 4). All of this is conﬁrmed by the calculations in Tables 3 and 4, according to which the stable proportions of phase lengths and their combinations remain intact with the change of production principles (see Section 2 of the Supporting Online Materials). So, our quantitative analysis presented in the tables above indicates the following points: a) the evolution of each production principle in time has recurrent features; there are stable mathematical proportions between the lengths of phases and phase combinations within each production principle (Tables 3 and 4); b) the cycle analysis clearly indicates that the technological development rate increases sharply as a result of production revolutions; c) the analysis of stable proportions of production principle cycles makes it possible to propose some tentative forecasts—in particular, with respect to the lengths of the future phases of the fourth production principle. Mathematical interpretation of the technological progress: methodology and calculations. Each production principle is a sixphase cycle. The beginning of each phase can be considered as an important technological shift or phase transition. As a result of our periodization, 24 phases and corresponding 23 phase transitions have been identiﬁed (Table 5). The chronology of the identiﬁed phases is presented in the same table. As a rule, complex and long-term processes cannot proceed evenly, an observation that also applies to technological evolution. As we noted above, technological progress is a series of accelerations and decelerations in the speed of technological development. There is an idea that the mechanism of such rhythms is associated with the slowdown of progress due to constant obstacles, such as lack of knowledge (Kayal 1999). Of course, this is true in general. However, according to our theory, the acceleration and deceleration of technological progress depends on the functional features of each time phase within a superlong cycle of technological changes (or a production principle). At some stages there is a kind of ‘explosion’ of innovations, where one can see acceleration of technological progress (e.g., the ﬁrst and third stages of production principle), while at others, these innovations are improving and spreading, thus slowing down (e.g., at the second stage of the production principle). At some stages (e.g., the ﬁfth) a powerful expansion of the production principle occurs, while at others, a slowdown is observed under the inﬂuence of crises (e.g., the last stage). To calculate the technological growth rate, we apply the methodology proposed by Alexander Panov (2005,2020), according to which the temporal distance between phase transitions (temporal length of the phases) is recalculated as the frequency of phase transitions = number of phase transitions per year = macroevolutionary growth rate. In Panov's case, this was the speed of planetary macroevolutionary development; in our case, this variable can be interpreted as the technological growth rate within historical process (equally appropriately called the macrotechnological growth rate). It is noticeable that, as in Panov's time series—like in the similar time series of Theodore Modis (2002, 2003), Raymond Kurzweil (2001, 2005) and David LePoire (2009, 2013) (see Korotayev 2018, 2020 for an analysis of these time series)—the temporal length of phases in the time series systematically decreases, whereas the macrotechnological growth rate increases in a similarly systematic way, following a rather remarkable pattern (see Table 5). Calculation of the singularity given the ongoing nature of the scientiﬁc-cybernetic production principle. It is important to note down scientiﬁc-technological progress in the late 21st and early 22nd centuries. One can assume that the current consumption pattern may also change under the inﬂuence of the global ageing process. And this change, in turn, will have a serious impact on the entire production structure and on scientiﬁc-technological progress (as we will discuss further later). 4. RESULTS Mathematical interpretation of technological progress (in the framework of historical processes). The main objective of this subsection is to present the following results: (1) To show the duration of each of the four production principles and the duration of each of the six stages within one production principle. These data are presented in Tables 1 and 2, which show a) the general time parameters of the production principles; b) the acceleration of technological evolution both within a production principle from one stage to another, as well as comparison with the previous and subsequent production principles; c) data that allow us to summarize the technological narrative and chronological description of historical process. (2) To show that a production principle is not just a certain stage of development of the world-systemic productive forces, but a rather complex cycle of technical innovations and organizational-technological system rearrangements of manufacturing. It inevitably requires changes in various spheres of society and also brings new changes. Tables S3 and S4 show calculations of the relationships between the stages (and combinations of stages) within each production principle and demonstrate that each cycle of the production principle retains surprising consistency, which cannot be accidental. For example, the duration of the ﬁrst stage of each production principle in ranges from 28 to 33% of the duration of the entire production principle. Recall that these are amongst the most important stages of production revolutions. The ratio of the duration of stages to each other is also quite close, for example, in all four principles of production—the ratio varies within a rather narrow framework. There is a small scatter of proportions, oscillating around a certain value in all 19 ratios (given in Tables S3 and S4). These stable ratios demonstrate certain deep and fundamental patterns of technological development and technological evolution in the framework of the historical process. All of this allows us to make some predictions about the duration of the future stages of the scientiﬁc-cybernetic production principle. (3) To calculate the acceleration of technological progress, the results of which we will present below. This subsection serves as the basis for the conclusions of the following subsections. We present dates for all phases of all production principles in Table 1. However, it should be considered that for convenience in chronology all dates are averaged. The absolute lengths of the phases in thousands of years are presented in Table 2. Thus, the proposed periodization demonstrates stable patterns of recurrent developmental cycles with a shortening of the period (each of which includes six phases); however, each subsequent cycle was shorter than the previous one due to the acceleration of technological growth. Note that these are recurrent cycles, because within each cycle the development follows the same pattern in some respect: every phase within every cycle plays a functionally similar role; what is more, the proportions of the lengths of the phases and their combinations remain Table 3 Ratio of each phase (and phase combination) length to the total length of respective production principle (%). Production principle 1 2 3 4 5 6 1–2 3–4 5–6 1–3 4–6 1. Hunter-Gatherer 2. Craft-Agrarian 3. Trade-Industrial 4. Scientiﬁc-Cybernetic Average 33.3 28.7 32.4 29.6 31 26.7 24.5 24.8 25.9 25.5 16.7 16.0 19 18.5 17.6 10 13.8 11.4 11.1 11.6 8.3 10.6 7.6 7.4 8.5 5 6.4 4.8 7.4 5.9 60 53.2 57.1 55.6 56.5 26.7 29.8 30.5 29.6 29.2 13.3 17 12.4 14.8 14.4 76.7 69.1 76.2 74.1 74.0 23.3 30.9 23.8 25.9 26.5 5 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. Table 4 Comparison of phase length ratios for each production principle (%). Production principle 1:2 2:3 3:4 4:5 5:6 (1 + 2): (3 + 4) (3 + 4): (5 + 6) (1 + 2 + 3): (4 + 5 + 6) 1. Hunter-Gatherer 2. Craft-Agrarian 3. Trade-Industrial 4. Scientiﬁc-Cybernetic Average 125 117.4 130.8 114.3 121.4 160 153.3 130 140 144.2 166.7 115.4 166.7 166.7 149.7 120 130 150 150 133.3 166.7 166.7 160 100 160.9 225 178.6 187.5 187.5 190.3 200 175 246.2 200 205.3 328.6 224.1 320 285.7 282.1 singularity date by obtaining a hyperbolic curve that describes our time series in the most accurate way. The results of this analysis are presented in Fig. 4 (note that our mathematical analysis has identiﬁed the singularity date for this time series as 2018 CE). The same ﬁgure is presented on a double logarithmic scale in Fig. 5. Let us now analyse the results. As we see, our power-law regression on the technological growth phase transitions provides a best ﬁt equation (Eq. (1)) describing this time series in a rather accurate (R2 = 0.98) way: Table 5 Production principle phases, their dates, lengths and dynamics of technological growth rate (for empirically observed data points). Production principle phases Date of the phase start Phase length (years) Macrotechnological growth rate (frequency of phase transitions per year) Hunter-gatherer 1 Hunter-gatherer 2 Hunter-gatherer 3 Hunter-gatherer 4 Hunter-gatherer 5 Hunter-gatherer 6 Craft-agrarian 1 Craft-agrarian 2 Craft-agrarian 3 Craft-agrarian 4 Craft-agrarian 5 Craft-agrarian 6 Trade-industrial 1 Trade-industrial 2 Trade-industrial 3 Trade-industrial 4 Trade-industrial 5 Trade-industrial 6 Scientiﬁccybernetic 1 Scientiﬁccybernetic 2 40,000 BP 30,000 BP 22,000 BP 17,000 BP 14,000 BP 11,500 BP 10,000 BP 5300 BCE 3000 BCE 1500 BCE 200 BCE 800 CE 1430 1600 1730 1830 1890 1929 1955 10,000 8000 5000 3000 2500 1500 2700 2300 1500 1300 1000 630 170 130 100 60 39 26 40 1.0 1.3 2.0 3.3 4.0 6.7 3.7 4.3 6.7 7.7 1.0 1.6 5.9 7.7 1.0 1.7 2.6 3.8 2.5 × × × × × × × × × × × × × × × × × × × 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 Vt = 1.55 , x 0.9 (1) where Vt is the global macrotechnological development rate, x is the time remaining until the singularity, and 1.55 and 0.9 are constants. Note that the denominator's exponent (0.9) turns out to be rather close to 1; hence, there are some grounds to use this equation in the following simpliﬁed form: Vt = 1.55 , x (2) where Vt is the global macrotechnological development rate, x is the time remaining until the singularity, and 1.55 is a constant. Of course, x (the time remaining until the singularity) at moment t equals t* – t, where t* is the time of singularity. Thus, 1995 x = t* − t Hence, Eq. (2) can be re-written as Eq. 3: that the singularity does not indicate the point where the value of a given variable actually becomes inﬁnite; rather, it indicates the point before which the hyperbolic shape of the curve should change to a diﬀerent trajectory implying a certain slowdown of the processes that have been observed in recent decades (Huebner 2005; LePoire 2005; Phillips 2011; Korotayev 2018, 2020). Below, we will discuss the possibility of a new acceleration of technological growth. We believe that the calculation of the singularity can be done both with the empirically observed data only, and using some theoretically predicted data points, as far as we can anticipate the technological development. That is why we use a dual approach to determining the singularity. In the ﬁrst case, we show that if we use our days as the last point for calculations, the result will be close to what Kurzweil, Modis, and Panov have, which shows that our mathematical apparatus is quite adequate. However, only a mathematical apparatus without an essential theoretical part is obviously not enough. And since we – hopefully – have convincingly proved that the slowdown and acceleration of the technological process occur cyclically, we give below the calculation of the singularity in accordance with the forecast of the expected acceleration of the technological process after the 2030s and the 2040s. And this calculation of the singularity constitutes an important part of our paper, The graphic presentation of the macrotechnological growth rate detected in our time series is as shown in Fig. 3. It is not diﬃcult to see that the general shape of the resultant curve is unmistakably hyperbolic, and it is well known the hyperbolic function has an explicit mathematical singularity. Let the X-axis represent the time before the singularity (whereas the Y-axis will represent the technological growth rate)—and calculate the Vt = 1.55 , t* − t (3) where Vt is the global macrotechnological development rate at time t, t* is the time of singularity, and 1.55 is a constant, Finally, let us recollect that our least squares analysis of the phase transition points described in Table 5 has identiﬁed the singularity date as 2018 CE. Thus, Eq. (3) can be further re-written as: Vt = 1.55 . 2018 − t (4) Of course, in a more general form it should be written as Vt = C , t* − t (5) where C and t* are constants. Note that an algebraic equation of the type yt = C t* − t (5) can be regarded as the solution of the following diﬀerential equation: dy y2 = dt C (6) (see, e.g., Korotayev et al., 2006a: 118–120). Thus, the acceleration pattern implied by Eq. (4) can be spelled out as follows: dV V2 = ≈ 0.65V 2. 1.55 dt (7) Thus, the overall pattern of acceleration of global technological 6 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. Fig. 3. Dynamics of the global macrotechnological growth rate (frequency of phase transitions per year), 40,000 BP to the late 20th century. Fig. 4. Scatterplot of the phase transition points described in Table 5 with the power-law regression line (ﬁtted with the least-squares method) that identiﬁes the date of singularity as 2018 CE (natural scales). in macrotechnological development rate tended to be accompanied by a fourfold increase in the acceleration speed of this development rate; a 10-fold increase in macrotechnological development rate tended to be accompanied by a 100-fold increase in the acceleration speed of this development rate; and so on… The past tense is used in the statement above because the global growth rate that described rather accurately the technological growth phase transitions data points presented above in Table 5 with model (4) / (5) can be spelled out as follows: throughout most of human history (at least since the Upper palaeolithic Revolution) the increase in macrotechnological growth rate a times tended to be accompanied by an a2 increase in its acceleration speed; thus, a twofold increase 7 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. Fig. 5. Scatterplot of the phase transition points described in Table 5 with the power-law regression line (ﬁtted with the least-squares method) identifying the date of singularity as 2018 CE (double logarithmic scale). dy y2 = ≈ 0.5y 2 . 2.054 dt technological growth does not appear to have followed this pattern in recent decades due to the slowdown mentioned above (otherwise, incidentally, it would have become inﬁnite in 2018). Below, we will discuss the possibility and implications of a new acceleration of global technological growth. Notes about acceleration patterns. Note that a rather similar acceleration pattern has been earlier detected for the Modis–Kurzweil series of ‘canonical milestones / complexity jumps’ (Modis 2002, 2003; Kurzweil 2005) as well as Panov series of ‘global phase transitions / biospheric revolutions’ (Panov 2005, 2017, 2020; Korotayev 2018, 2020). Incidentally, the Modis–Kurzweil series starts with the origin of Milky Way 10 billion years ago and ends with the emergence of the Internet and human genome sequencing around 1995, whereas the Panov series begins with the origin of life on the Earth 4 billion years ago and ends with information globalization, which Panov dates to 1991 CE. Indeed, the acceleration pattern detected in the Modis–Kurzweil series is described with 99.89% accuracy by Eq. 8: y= 2.054 , (2029 − t )1.003 On the other hand, the acceleration pattern detected in the Panov series is described with 99.91% accuracy by Eq. (11) (Korotayev 2018, 2020): y= 2.054 , 2029 − t 1.886 . (2027 − t )1.01 (11) The simpliﬁed version of this model is given by Eq. (11), y= 1.9 . 2027 − t (11) An algebraic equation of this type can be regarded as a solution of the following diﬀerential equation, very similar to the one we obtained above for the Modis–Kurzweil series, as well as for our series of technological phase transitions: dy y2 = ≈ 0.5y 2 . dt 1.9 (12) As we can see, all three series are described accurately by similar mathematical models with similar parameters, including t* (the singularity time point); the explanation of this phenomenon is provided in Section 3 of the Supporting Online Materials. Calculation of the singularity, considering the predicted phases of the scientiﬁc-cybernetic production principle. As we have said above, there are diﬀerent ways to estimate the singularity point in respect to the theoretical approaches to forecast the future of development of technological progress. Note that Eq. (1) has been calculated solely on the basis of empirically observed data points. However, the theory of production principles allows us to forecast a few more data points. (8) where y is the global macrodevelopment rate (number of phase transitions per a unit of time), and 2029 CE is the best-ﬁt singularity point estimate, The simpliﬁed version of this model is yt = (10) (9) this algebraic expression can be regarded as a solution for the following diﬀerential equation: 8 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. than in Eq. 1; hence, there are even stronger grounds to use this equation in a simpliﬁed form, Table 6 Production principle phases, their dates, lengths and dynamics of technological growth rate (for the empirically observed and forecast data points). Vt = 3.32 , x Production principle phases Date of the phase's start Phase length (years) Macrotechnological growth rate (frequency of phase transitions per year) Hunter-gatherer 1 Hunter-gatherer 2 Hunter-gatherer 3 Hunter-gatherer 4 Hunter-gatherer 5 Hunter-gatherer 6 Craft-agrarian 1 Craft-agrarian 2 Craft-agrarian 3 Craft-agrarian 4 Craft-agrarian 5 Craft-agrarian 6 Trade-industrial 1 Trade-industrial 2 Trade-industrial 3 Trade-industrial 4 Trade-industrial 5 Trade-industrial 6 Scientiﬁccybernetic 1 Scientiﬁccybernetic 2 Scientiﬁccybernetic 3 Scientiﬁccybernetic 4 Scientiﬁccybernetic 5 Scientiﬁccybernetic 6 40,000 BP 30,000 BP 22,000 BP 17,000 BP 14,000 BP 11,500 BP 10,000 BP 5300 BCE 3000 BCE 1500 BCE 200 BCE 800 CE 1430 1600 1730 1830 1890 1929 1955 10,000 8000 5000 3000 2500 1500 2700 2300 1500 1300 1000 630 170 130 100 60 39 26 40 1.0 1.3 2.0 3.3 4.0 6.7 3.7 4.3 6.7 7.7 1.0 1.6 5.9 7.7 1.0 1.7 2.6 3.8 2.5 1995 35 2.9 × 10−2 2030 25 4.0 × 10−2 2055 15 6.7 × 10−2 5.1. Global ageing as a factor inﬂuencing the technological growth rate 2070 10 1.0 × 10−1 Ageing and technological progress: a positive feedback loop. We believe that global ageing will be one of the most important factors in the coming decades. We have shown in previous articles how the process of global ageing may develop up to the 2070s and how it may inﬂuence technological progress (Grinin L., Grinin A., and Korotayev 2017a; see also Grinin and Grinin, 2015a; Grinin and Korotayev, 2015b, Grinin and Korotayev, 2015c, Grinin and Korotayev, 2015d, Grinin and Korotayev, 2015e, Grinin and Korotayev, 2016a, Grinin and Korotayev, 2016; Grinin and Grinin, 2015c, Grinin and Grinin, 2015d, 2017). The present article is a continuation of our research regarding the correlation between global ageing and technological development, one which allows us to signiﬁcantly expand the forecast horizon and obtain new results. The important result is that global ageing can cause a new technological acceleration, with a change in direction, and by the late present century and the early next century it is likely to slow down technological growth and cause a change in its direction. In this subsection, we will look at how and why global ageing in the coming decades could become one of the most important drivers of technological breakthroughs through the 2070–2080s. In the next section, we will discuss why global ageing will later become an obstacle to technological progress. As we expect, a new technological breakthrough will begin around the 2030s, starting in new branches of medicine and related areas: bioand nano-technologies, additive and cognitive technologies, and some others. It will also mark the beginning of the ﬁnal phase of the Cybernetic revolution. As we have pointed out before (Grinin et al., 2017b), for the start of such breakthroughs to take place in the 2030s in the sphere of new medicine, the world will have the following prerequisites: the explosive growth of the elderly portion of the population; a growing economy's need for labour resources and the state's interest in increasing the working capacity of older people, as well as a growing number of well-to-do and educated people concerned about their health. Huge ﬁnancial resources will also be accumulated for technological breakthroughs: pension funds, which will increase at a rapid pace; government funding directed to health and social needs; increased spending on health from an ageing population and a growing world middle class. All of these resources can provide high investment attractiveness to various venture capital projects, and, in the long term, × × × × × × × × × × × × × × × × × × × where Vt is the global macrotechnological development rate, x is the time remaining until the singularity, and 3.32 is a constant. Finally, as our least-squares analysis of the phase transition points described in Table 6 has identiﬁed the singularity date as 2106 CE, Eq. (15) can be further re-written: 10 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 −4 Vt = 3.32 x 0.98 3.32 . 2106 − t (16) Thus, if our forecast produced on the basis of the production principle theory is justiﬁed, there are grounds to expect that the global macrotechnological growth rate will return for some time in the forthcoming decades to a hyperbolic trajectory—this time with the singularity parameter equal to 2106. This implies that in the late 21st and the early 22nd century the rate of global macrotechnological growth will experience one more decline, and there are some grounds (which will be spelled out in the next section of this paper) to expect that this decline will be much more pronounced than that of recent decades. 5. DISCUSSION 2080 Indeed, we have demonstrated above that there are grounds to expect that the second phase of the scientiﬁc-cybernetic production principle (the intermediate phase of the Cybernetic revolution) that began in the mid-1990s will continue until around 2030, when there are grounds to expect the third phase—the beginning of its ﬁnal phase, which we expect may become the epoch of ‘self-regulating systems’, the vast expansion of opportunities to purposefully inﬂuence and direct various natural and production processes. This phase expected to continue until around 2055, when there are grounds to forecast the start of the fourth phase, which implies that the sector of self-regulating systems will rapidly improve over the next two decades, and will diﬀuse to various regions at enormous speed. At the same time, this should be a period of signiﬁcant growth in life expectancy. The duration of the last two phases have been estimated above to be around 20 years. This allows us to forecast a few data points to add to the list of empirically estimated data points, resulting in Table 6. A mathematical analysis of the resultant time series yields the results in Fig. 6. The same ﬁgure is presented on a double logarithmic scale below (Fig. 7). Let us analyse these new results. As we see, our power-law regression on the technological growth phase transitions including data points presented in Table 6 (which includes four data points projected on the basis of the assumed new wave of acceleration of global macrotechnological growth rate forecast by the production principle theory) has identiﬁed the following best-ﬁt equation describing this time series in a rather accurate (R2 = 0.98) way: Vt = (15) (14) where Vt is the global macrotechnological development rate, x is the time remaining until the singularity, and 3.32 and 0.98 are constants. Note that the denominator's exponent (0.98) is much closer to 1 9 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. Fig. 6. Scatterplot of the phase transition points (both empirically estimated and forecast) described in Table 6 with the power-law regression line (ﬁtted with the least squares method) identifying the singularity date as 2106 CE (natural scales). Fig. 7. Scatterplot of the phase transition points (both empirically estimated and forecast) described in Table 6 with the power-law regression line (ﬁtted with the least squares method) identifying the singularity date as 2106 CE (double logarithmic scale). 10 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. cohorts in later stages of life (aged 60 and older) is going to be greater than that for cohorts in earlier stages (Danigelis et al., 2007). However, this may be true only for some narrow areas. Our study focuses on wider aspects: the desire for technological innovation and consumption of new goods, and adaptability to them. From the point of view of adaptation to technological progress, in the pursuit of changes and the rate of acquisition of new skills, older people are much less adept than their younger counterparts. In any case, the psychology of older people is diﬀerent from the psychology of young people.6 In general, acquiring new skills is more diﬃcult for older people than for young people (e.g., Zemlyakova and Pomuran, 2014; for an example about the diﬃculties elderly people experience in adapting to the Internet, see Neskromnyh and Mamadaliev, 2017). In addition, older people are generally less productive than young people—e.g., people aged 40–65 compared to workers aged 20–40 (Goldstone 2015), whose productivity tends to increase rapidly with increasing experience and education (Lee and Mason 2011),7 not to mention people older than 65. As for consumerism, older people who have already acquired, experienced and seen a lot, have largely lost their desire to pursue new things and become less active than the young. The current situation in the Japanese economy, where the proportion of the elderly is growing, and the proportion of the young is decreasing, conﬁrms this fact. This demographic structure of the population cannot contribute to noticeable economic growth. The Japanese economy has suﬀered from a weak period of GDP growth, with two and a half decades of deﬂation due to an ageing population that does not want to spend much money and prefers to save instead. No wonder Japan's mood is rather depressed (Coleman and Rowthorn 2015: 31; Ogawa et al., 2005; Coulmas 2007; Grinin and Korotayev 2014, 2017, 2018). In addition to slowing consumption in an older society, the most important engine of development—the need for career growth, wellbeing and success—will fade away. With a decrease in the number of children, investments in the younger generation and the need for their provision, another important factor for development, will begin to weaken. UN Population Division forecasts rather conﬁdently predict that by the end of this century no signiﬁcant population growth will be observed in the overwhelming majority of the countries of the world, and that many will experience population decline (UN Population Division 2019). Throughout human history, population growth has been the most important development driver of development (Kuznets 1960; Boserup 1965; Grossman and Helpman 1991; Aghion and Howitt 1998; Simon 2000; Jones 2005; Korotayev et al., 2006a, 2006b; Khaltourina et al., 2006; Kapitza 1996; Grinin and Grinin, 2015c, 2016, 2017; Grinin et al. 2014; Korotayev and Markov 2015; Korotayev 2005, 2007a, 2012, 2013, 2018, 2020; Dolgonosov 2016; Fomin 2020). Therefore, it is likely that in 50–70 years, that is, by the end of the 21st century, the situation will change signiﬁcantly around the world, even in those societies where large ‘youth bulges’ and high birth rates are observed, i.e., in most or in all tropical African countries (Korotayev and Zinkina 2014, Korotayev and Zinkina, 2015 ; Zinkina and Korotayev, 2014a, Zinkina and Korotayev, 2014b; Grinin and Grinin, 2015c, 2017). In the long term, the number of elderly people will increase worldwide. Thus, in the next few decades, the behaviour of societies will be diﬀerent (see Grinin et al., 2017b). This will probably coincide with the period of transition to a certain societal stability after the end of the Cybernetic revolution. Of course, other scenarios are also possible—for example, in the case of a climate deterioration, some societal a very wide demand for innovative medical technologies. We also noted above that the MANBRIC complex will be formed in the process of the Cybernetic revolution, and new medical technologies will play an integrating role. This will have a double eﬀect: on the one hand it will aﬀect the growth of life expectancy, its physiological quality, and increase the age limit on physical activity. On the other hand, the problem of the explosive growth of the number of older people will become more acute, especially because of pension costs and labour shortages. As a result, medical technologies will rapidly develop under the inﬂuence of an ageing population (Phillips 2011), and this will expand the search for opportunities to create “smart”, self-regulating systems, including robots, which can largely replace human labour, especially in the service sector (Frey and Osborne 2017), including complex services (e.g., in the ﬁelds of elder care, education, medicine, etc.) (DeCanio 2016).4 Thus, until the last third of our century, the ageing of the population will not impede technological and other development. On the contrary, the process of global ageing itself will be the driving force of change, reform and acceleration of technological innovation. Global ageing and technological progress in the last third of the 21st and the beginning of the 22nd century: the potential for negative feedback. This period corresponds to the ﬁfth and sixth phases, when there will be numerous changes. In particular, a growing number of social self-regulating systems will mostly operate autonomously, regulating the behaviour of large numbers of people in certain situations. They can be used to create positive or negative behavioural stimuli (carrot and stick method) to regulate human behaviour.5 We believe that this will be the beginning of the transition to a new economic system (see below) due to the increasing level of complexity of selfregulating systems and serious advances in medicine (see above). But especially great impulses will be introduced by the process of global ageing, which by this time will cover all countries. This phenomenon will have fundamental and contradictory consequences and will be accompanied by profound painful changes and confrontations in societies within the World System. The link between global ageing and technological progress is nonlinear. At some point, the positive feedback we have mentioned above is likely to be replaced by negative feedback. Why? It is important to note that older people are more conservative—this is not just a popular belief, but a fact conﬁrmed by rigorous scientiﬁc research (see, e.g., Grinin L. and Grinin A. 2017; Korotayev et al., 2017; Korotayev, Shulgin 2018; Shulgin et al., 2019; see also Tsirel 2008). Of course, we do not claim that older people are absolutely conservative, but only that in general they have less needs and a desire for innovations than young people. In areas such as medicine and pharmaceuticals, older people may tend to innovate more often than young people. There are studies whose authors claim that the change for 4 It is not possible to consider within this article the eﬀects of global aging and increasing labor shortages (see Grinin and Korotayev, 2016; Grinin et al., 2017a, Grinin et al., 2017b). Of course, in the process of development of the scientiﬁc-cybernetic production principle, there will be signiﬁcant changes in the number of people employed in various professions, as well as major changes in the professional nomenclature; some of these professions will begin to disappear under the inﬂuence of new technologies (including robotization). In our opinion, unqualiﬁed services will be particularly at risk. At the same time, the sphere of qualiﬁed and highly qualiﬁed services will undergo considerable transformations (see Grinin and Grinin, 2015c for more detail). But, as a result of the rapid ageing of the population, we expect that the total amount of labor resources will decrease faster (at least initially) than the technological progress of MANBRIC technologies will cut jobs (see Grinin and Grinin, 2015c; Grinin and Korotayev, 2016a; Grinin et al., 2017a, Grinin et al., 2017b). 5 Even today one can observe such regulatory systems, for example, car insurance, when a more skilled driver pays less. A system of total regulation of social behavior is already announced in China (Chin, Wong 2016). 6 A good example is the study of foreign languages. It is well known that children and teenagers learn foreign languages more easily than elderly people. 7 According to other research, labor productivity peaks between the ages of 35 and 54 (Park and Shin 2015: 109). 11 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. corresponding to the beginning of the ﬁnal phase of the Cybernetic revolution. Thirdly, this acceleration will continue up to the late 21st century. Fourthly, technological growth at the end of the 21st century will gradually slow down to the singularity point, in the year 2106. As we have described, the factor of global ageing will play a leading role here. After the singularity point, the rate of technological progress will slow down compared to that of the previous epoch. Fifthly, the rate of technological growth will experience a slowdown, and it is diﬃcult to predict any subsequent acceleration in the 22nd century (at least, in its ﬁrst half). Probably the most important point is that the pattern of scientiﬁc and technological development itself will change dramatically. Thus, such a slowdown will mean that the old type of technological progress is beginning to transform into a new one, and, most likely, a transition to new forms of social relations will begin. This article has raised many problems, most of which require further research. Firstly, the measurement of the speed of technological progress and, accordingly, conclusions and forecasts from the obtained data can be made by other methods. Measuring the speed of technological progress by other methods would make it possible to check and reﬁne our forecasts and dates, and also allow us to see new aspects of the problem. We are currently working on the creation of a database of inventions, from the ancient past of humankind to the present, using which it will be possible to make new calculations of the speed of technological progress. Secondly, we discuss the problem of the relationship between global ageing and technological progress. We consider global ageing one of the most important (and fundamentally new in history) factors, one that can accelerate and then cause scientiﬁc and technological progress to slow. However, it is necessary to investigate more aspects of the relationship between global ageing and technological progress, as well the relationship between global ageing and numerous future social and economic transformations. Thirdly, we have pointed out that at the third, and especially in subsequent phases of the scientiﬁc-cybernetic production principle, there will be signiﬁcant changes in the number of people employed in various professions, as well as major changes in the nomenclature of professions. Some professions will begin to disappear under the inﬂuence of new technologies (including robotization). In our opinion, unqualiﬁed services will be particularly at risk. At the same time the sphere of qualiﬁed and highly qualiﬁed services will undergo considerable transformations. However, we have indicated that as a result of the rapid ageing of the population, we expect that the available labour resources will decrease faster (at least, at ﬁrst) than the technological progress of MANBRIC technologies will cut jobs. This direction—in particular, the relationship between global ageing and increasing labour shortages, between technological progress (in particular, created by artiﬁcial intelligence), robotics, and other components of MANBRIC technologies, and job cuts/labour saving—requires additional research, which we hope to conduct in the near future. Fourthly, we suggest that the late 21st century and early 22nd century will be decisive for human civilization. Fundamentally new socio-economical relationships will begin to emerge, the outlines of which are not yet clear. As a result, the modern consumption model will start to change dramatically. We have oﬀered some ideas about possible reasons and trends for such transformations. However, this subject demands much more scrupulous research. degradation may also occur. Thus, it is possible that the ageing of society, with the end of global population growth and improved social planning capabilities, will contribute to the transition of global society to a more comfortable and slow development (the so-called sustainable development, which is much discussed) by the end of this century or at the beginning of the 22nd century. All of these factors will aﬀect scientiﬁc and technical progress and its slowdown (see also LePoire and Korotayev 2020 for the discussion of some other possible causes of this slowdown). 5.2Transition to a new economic model The abovementioned conservatism may lead not only to a slowdown in development, but also to a transition to another economic system. The current model is associated with an increasing consumption. Consume more today than yesterday, and tomorrow more than today, is largely an absurd model. Also, sometimes the desire for sustainable GDP growth seems absurd. However it works and will work for decades, especially for poor countries whose populations are not satisﬁed with their level of consumption. Thus, ageing can change people's needs, especially in conditions of the stabilization of the population or its reduction. As a result, under the inﬂuence of all above mentioned future changes, the model measuring economic growth in GDP should be replaced (Coleman and Rowthorn 2015: 37). The modern consumption model will also change. Transformation of the modern consumption economic model will be a complex process that may change many important aspects of our life. Above, we mentioned Japan as an example of an ageing society. It also provides an example of development without GDP growth alongside scientiﬁc and technological development. The ‘Japanese disease’ has recently spread to European countries, partly due to the ageing of their populations (there are other reasons as well, although we do not address them in this article; for more details see Grinin and Korotayev 2014, 2017, 2018). Overall, the Cybernetic revolution and ageing should ultimately transition society into a new economic model without an endless increase in consumption. In such a case, the growth model in the economy should diﬀer from that of today; it is likely to include some parameters of quality and longevity. Accordingly, business models may change, although it is not very clear how this will happen. 6. CONCLUSION In this article we consider the long-term dynamics of technological progress, presenting one option for measuring its speed throughout the entire historical process based on the theory of technological (or production) revolutions and the theory of production principles. This approach allows us to measure the speed of technological progress as well as to make some predictions. Thus, our research covers a very wide span between the upper palaeolithic or human revolution and the forthcoming ‘post-human’ revolution, the consequences of which are still unclear, but which will obviously start a new era. 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) by a simple 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, while t0 and C are constants; t0 can be interpreted as a ‘technological singularity’ point. In concluding, we would like to mention again that so far there has been a tendency to an increase in technological growth on the macroscale, albeit with ﬂuctuations. However, as we have seen, future technological growth will not be inﬁnite. In this article, we describe a scenario of how, when, and why this rate will change. First, the slowdown in technological growth in recent decades, beginning in the 1970s, can be explained as a general ﬂuctuation of technological growth. We view this slowdown as a necessary precondition for further rapid growth. Secondly, our analysis shows that there are a number of reasons to expect that the global technological growth rate will return in the forthcoming decades to a hyperbolic trajectory for some time, AUTHOR STATEMENT All the authors have contributed equally to this article. Acknowledgement This article is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE) in 2020 with support by Russian Science 12 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. Foundation (Project No. 18–18–00254). Korotayev, A. 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Leonid GRININ, PhD in Philosophy, is a Senior Research Professor at the Laboratory for Monitoring of the Sociopolitical Destabilization Risks at the National Research University Higher School of Economics, Moscow, Russia, as well as the Deputy Director of the Eurasian centre for Big History & System Forecasting and Senior Research Professor at the Institute for Oriental Studies of the Russian Academy of Sciences in Moscow. He is the Editor-in-Chief of the journal Age of Globalization (in Russian), as well as a co-editor of the international journals Social Evolution & History and Journal of Globalization Studies. Hiscurrent research interests include sociopolitical destabilization, macrohistory and long- 14 Technological Forecasting & Social Change 155 (2020) 119955 L. Grinin, et al. House; in Russian) and a number of articles including ‘Macroevolution of Technology’ and ‘Global Technological Transformations’. term trends, sociocultural evolution, theory of history, world-systems studies, long-term development of political systems, globalization studies, economic cycles, and Big History studies. Dr Grinin is the author of more than 380 scholarly publications in Russian and English, including 26 monographs. These monographs include Philosophy, Sociology, and the Theory of History (2007, in Russian); Productive Forces and Historical Process (2006, in Russian); State and Historical Process (3 vols, 2009–2010, in Russian); Social Macroevolution: World System Transformations (2009, in Russian); Macroevolution in Biological and Social Systems (2008, in Russian); Global Crisis in Retrospective: A Brief History of Upswings and Crises (2010, in Russian); Macrohistory and Globalization (2012); Cycles, Crises, and Traps of the Modern World-System: Kondratiev's, Juglar's and Secular Cycles, Global Crises, and the Malthusian and Post-Malthusian Traps (2012, in Russian); Great Divergence and Great Convergence. A Global Perspective (Springer, 2015), Economic Cycles, Crises, and the Global Periphery (Springer, 2016). Andrey V. KOROTAYEV has a PhD in Middle Eastern Studies from the University of Manchester and a DrSc in History from the Russian Academy of Sciences. He heads the Laboratory for Monitoring of the Sociopolitical Destabilization Risks at the National Research University Higher School of Economics, Moscow, Russia. He is also Senior Research Professor at the Eurasian centre for Big History and System Forecasting of the Institute of Oriental Studies and Institute for African Studies, Russian Academy of Sciences. He is the author of over 300 scholarly publications, including such monographs as Ancient Yemen (Oxford University Press, 1995), World Religions and Social Evolution of the Old World Oikumene Civilizations: A Cross-Cultural Perspective (The Edwin Mellen Press, 2004), Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth (URSS, 2006), Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends (URSS, 2006), Great Divergence and Great Convergence. A Global Perspective (Springer, 2015), Economic Cycles, Crises, and the Global Periphery (Springer, 2016). He is a laureate of a Russian Science Support Foundation in ‘The Best Economists of the Russian Academy of Sciences’ Nomination (2006); in 2012 he was awarded with the Gold Kondratieﬀ Medal by the International N. D. Kondratieﬀ Foundation. Anton GRININ, PhD in Biological Sciences, is a Senior Research Fellow of the International centre for Education and Social and Humanitarian Studies, Moscow as well as Leading Researcher of the Volgograd Centre for Social Research. His-main research interests include Big History, evolution, biotechnologies, global technological transformations and forecasts. He is the co-author of the monograph From Biface to Nanorobots: The World on the Way to the Epoch of Self-Regulating Systems (2015; Uchitel Publishing 15

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