The 21st Century Singularity and Global Futures: A Big History Perspective (World-Systems Evolution and Global Futures) 9783030337292, 3030337294

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World-Systems Evolution and Global Futures

Andrey V. Korotayev David J. LePoire Editors

The 21st Century Singularity and Global Futures A Big History Perspective

World-Systems Evolution and Global Futures Series Editors Christopher Chase-Dunn, University of California, Riverside, CA, USA Barry K. Gills, Political and Economic Studies, University of Helsinki, Helsinki, Finland Leonid E. Grinin, National Research University Higher School of Economics, Moscow, Russia Andrey V. Korotayev, National Research University Higher School of Economics, Moscow, Russia

This series seeks to promote understanding of large-scale and long-term processes of social change, in particular the many facets and implications of globalization. It critically explores the factors that affect the historical formation and current evolution of social systems, on both the regional and global level. Processes and factors that are examined include economies, technologies, geopolitics, institutions, conflicts, demographic trends, climate change, global culture, social movements, global inequalities, etc. Building on world-systems analysis, the series addresses topics such as globalization from historical and comparative perspectives, trends in global inequalities, core-periphery relations and the rise and fall of hegemonic core states, transnational institutions, and the long-term energy transition. This ambitious interdisciplinary and international series presents cutting-edge research by social scientists who study whole human systems and is relevant for all readers interested in systems approaches to the emerging world society, especially historians, political scientists, economists, sociologists, geographers and anthropologists.

More information about this series at http://www.springer.com/series/15714

Andrey V. Korotayev
David J. LePoire Editors

The 21st Century Singularity and Global Futures A Big History Perspective

123

Editors Andrey V. Korotayev National Research University Higher School of Economics Moscow, Russia

David J. LePoire Argonne National Laboratory Argonne, IL, USA

Institute of Oriental Studies Russian Academy of Sciences Moscow, Russia

ISSN 2522-0985 ISSN 2522-0993 (electronic) World-Systems Evolution and Global Futures ISBN 978-3-030-33729-2 ISBN 978-3-030-33730-8 (eBook) https://doi.org/10.1007/978-3-030-33730-8 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Foreword

One of humanity’s great achievements has been to write an evidence-based account that began with the Big Bang almost 14 billion years ago and then continues in coherently developed chapters until our own time. From quarks to atoms, stars, galaxies, chemicals, terrestrial planets, increasingly complex forms of life, and then increasingly complex societies, the narrative is one that begins with relative simplicity and then becomes increasingly complex. Especially the earlier periods could last for a long time before there was a transition to the next. Robert Hazen, in his book, The Story of the Earth, tongue in cheek named one of his chapters, “The Boring Billion.” Many things stayed pretty much the same on Earth for a huge number of years. However, the chapters in the history of our universe often cover decreasing amounts of time. The pace of emergent complexity quickens over time. There have admittedly been previous times of rapid change. There may have been a grand unification epoch between 10−43 and 10−36 s after the Big Bang, not exactly a long era by traditional historians’ standards. This may have been followed by an electroweak epoch between 10−36 and 10−32 s. The inflationary epoch and the rapid expansion of space may have been wrapped up before 10−32 s. The hadron epoch may have gone all the way between 10−6 and 1 s. The lepton epoch may have lasted a relative eternity of 9 s between 1 s and 10 s. What did they do with all that time? Rapid change was not restricted to the beginning of time; it is occurring throughout our universe right now. Galaxies at the edge of our observable universe are speeding away from us almost at the speed of light, many of them slipping forever beyond our view. Still, in many ways, the pace of change and the rate of emergent complexity have indeed greatly increased over time. Carl Sagan made this more comprehensible by imagining that universal history has taken place within one year rather than over 13.82 billion years. If we imagine that the Big Bang took place on January 1, then our own solar system did not appear until months later, in September. Single cells originated on Earth in October. Multicellular life in early December. Dinosaurs were predominant on December 25. Human ancestors walked upright on two legs for the first time at 10:30 pm on December 31. Humans emerged first at 11:52. Plato was writing about 5 s ago. Columbus arrived in America 1.2 s ago. Within the last few seconds, we have gone from agricultural, to industrial, and now to digital economies. And the pace of change in the past second has sped up.

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John von Neumann (1903–1957) is credited as the first to discuss the idea of technological singularity, or the mind-boggling pace of changes in the mode of human life brought about by technological developments. Alvin Toffler drew on this idea in his 1970 book, Future Shock, which sold over 6 million copies. In it, Toffler warned of a “super-industrial society” whose rate of change would overwhelm people. The pace of change and increasing complexity has continued to quicken even more since the beginning of the computer age. Gordon Moore, a co-founder of Intel, predicted in 1965 that the number of integrated circuits, or computing power, would double about every two years. While the number of transistors on integrated circuits in 1970 was about 1000, by 2018 the number had increased to 50,000,000,000. Ray Kurzweil is fond of reminding us that the smart phones we have in our pockets are many times more powerful than the computers that got NASA’s Apollo missions to the moon. Computers’ ability to process information is approaching infinite speeds. People across the world have been increasingly connected through the use of their computers, which themselves are connected in the Internet. Computers increasingly communicate directly with each other; they increasingly control technology in an “Internet of things.” For over a half century, we have worried about the menacing computer, Hal, in the 1968 film “2001: A Space Odyssey.” When will computers depend less on human programmers and begin to learn and act on their own? Connected to 3D printers, when do they start building a better world on their own? Will they start fighting on their own? In an Army of None: Autonomous Weapons and the Future of War, Paul Scharre considers future battles between drones controlled by computers. Will they decide when to initiate conflict? Perhaps computers will start considering humans to be somewhat superfluous, a rather outdated backdrop to the main event that has left biology behind. Predictions about when this may actually happen vary. It is at least a few decades in the future, and maybe always will be. The emergence of digital singularity, or computing power beyond human ability and control only begins the issue. Another area is demographics. Two hundred thousand years ago, there were just a few thousand humans. Twelve thousand years ago, there were about 4 million people. Two thousand years ago, the number of people had risen, but only to about 190 million. The number had increased to a billion just after 1800 CE. It was 1.65 billion in 1900. In 2000, it was 6 billion. In 2019, there were 7.7 billion people, with some projections of almost 11 billion by the end of our century, and over 36 billion within 200 years. If this was not an infinite rate of growth, it was still stunningly high and seemingly beyond our ability to control. If it is not a demographic singularity, it is still a historically high level of growth that is presenting us with issues that we have never before faced. At some point, the trend cannot continue. New and stunning levels of digital and demographic growth are combined in a zone of technological singularity. Technological advances have long compensated for our biological deficiencies. Lacking good claws and fangs, our ancestors fashioned stone tools. We did not lament that evolution did not grant us fins or

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wings; we invented boats and airplanes. We routinely use glasses and contacts to improve our sight, aids to improve our hearing, exoskeletons when we are quadriplegic, pacemakers for our hearts, artificial knees and hips, brain implants to control seizures, and much more. When will we have artificial red blood cells that carry oxygen after a heart attack, chips added to improve our memory or analysis, or be able to download our thought waves to computers? Technological breakthroughs seem to herald medical singularity. Exponential rates of change in these areas, as well as in energy use, the environment, economic convergence, global interdependence, and so many others have put us well on track toward a point of singularity. Instead of feeling frenzied, overwhelmed, or shocked by our current situation, Andrey V. Korotayev and David J. LePoire, along with other authors in their co-edited volume, The 21st Century Singularity in the Big History Perspective, offer us analysis and evidence-based scenarios for our future. Together, the authors carefully and methodically examine historical mega-trends, models, and future implications of the singularity. They deal with fundamental questions about how we can know during a period of such rapid changes and what it means to be in this time of rapid change. What are epistemology and ontology during the zone of singularity? The authors demand of themselves conceptual clarity to give us a clear picture of the whirl of our almost infinite pace of change and dizzying complexities. The authors present a big history account that helps us understand ourselves as that part of the universe which is able to self-consciously imagine, plan for, produce, and manage future increases in complexity. If we are able to do this well enough to make that future sustainable, it will be because of the type of contribution that this volume makes. If we fail, the universe will go on without us. Lowell S. Gustafson President International Big History Association Philadelphia, USA

Contents

The Twenty-First-Century Singularity in the Big History Perspective: An Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexander Panov, David J. LePoire and Andrey V. Korotayev

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The Twenty-First-Century Singularity in the Big History Perspective—A Re-analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrey V. Korotayev

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Exploring the Singularity Concept Within Big History . . . . . . . . . . . . . David J. LePoire

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Historical Mega-Trends Forecasting the Growth of Complexity and Change—An Update . . . . . 101 Theodore Modis Hyperbolic Evolution from Biosphere to Technosphere . . . . . . . . . . . . . 105 Alexey Fomin Big History and Singularity as Metaphors, Hypotheses, and Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Sergey Tsirel Big History Trends in Information Processes . . . . . . . . . . . . . . . . . . . . . 145 Ken Solis and David J. LePoire Plurality: The End of Singularity? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Alessio Plebe and Pietro Perconti Energy Flow Trends in Big History . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 David J. LePoire and Mathew Chandrankunnel The Deductive Approach to Big History’s Singularity . . . . . . . . . . . . . . 201 Sergey Grinchenko and Yulia L. Shchapova

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Models Near-Term Indications and Models of a Singularity . . . . . . . . . . . . . . . 213 David J. LePoire and Tessaleno Devezas Is Singularity a Scientific Concept or the Construct of Metaphysical Historicism? Implications for Big History . . . . . . . . . . . . . . . . . . . . . . . 225 Graeme Donald Snooks Future Implications Threshold 9: Big History as a Roadmap for the Future . . . . . . . . . . . . . 267 Elise Bohan Dynamics of Technological Growth Rate and the Forthcoming Singularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Leonid Grinin, Anton Grinin and Andrey V. Korotayev The Twenty-First Century’s “Mysterious Singularity” in the Light of the Big History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Akop Nazaretyan Global Brain: Foundations of a Distributed Singularity . . . . . . . . . . . . . 363 Cadell Last The Cybernetic Revolution and the Future of Technologies . . . . . . . . . . 377 Leonid Grinin and Anton Grinin Complexity in the Future: Far-from-Equilibrium Systems and Strategic Foresight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 David Baker Future Technological Achievements as a Challenge for Post-singularity Human Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 Sergey Tsirel Singularity of Evolution and Post-singular Development in the Big History Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 Alexander Panov Epistemology and Ontology Big History by Mathematics: Information, Energy, and the Singularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Claudio Maccone The Twenty-First-Century Singularity: The Role of Perspective and Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Marc Widdowson

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About the Singularity in Biological and Social Evolution . . . . . . . . . . . . 517 Sergey Malkov The Transition to Global Society as a Singularity of Social Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 Sergey Dobrolyubov Evolution, the ‘Mechanism’ of Big History, Predicts the Near Singularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 John S. Torday How Singular Is the Twenty-First-Century Singularity? . . . . . . . . . . . . 571 Andrey V. Korotayev Conclusion Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 David J. LePoire and Andrey V. Korotayev

Editors and Contributors

About the Editors Andrey V. Korotayev has a Ph.D. in Middle Eastern Studies from the University of Manchester and a Dr.Sc. 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 Center 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). At present, together with Askar Akaev and Georgy Malinetsky, he coordinates the Russian Academy of Sciences Presidium Project “Complex System Analysis and Mathematical Modeling of Global Dynamics.” 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. David J. Lepoire has a Ph.D. in Computer Science from DePaul University and a BS in Physics from CalTech. He has worked in environmental and energy areas for many governmental agencies over the past 25 years. Topics include uncertainty techniques, pathway analysis, particle detection tools, and physics-based modeling. He has also explored historical trends in energy, science, and environmental transitions. His research interests include complex adaptive systems, logistical transitions, the role of energy and environment in history, and the application of new technologies to solve current energy and environmental issues.

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Contributors David Baker Department of Modern History, Big History Institute, Macquarie University, Sydney, Australia Elise Bohan Big History Institute, Macquarie University, Sydney, Australia Mathew Chandrankunnel Dharmaram Vidya Kshetram University, Bangalore, India Tessaleno Devezas Atlântica School of Management Sciences, Health, IT & Engineering, Lisbon, Portugal Sergey Dobrolyubov International Center for Education and Social and Humanitarian Studies, Moscow, Russia Alexey Fomin International Center for Education and Social and Humanitarian Studies, Moscow, Russia Sergey Grinchenko Institute of Informatics Problems of the Federal Research Centre “Informatics and Control”, Russian Academy of Sciences, Moscow, Russia Anton Grinin International Center for Education and Social and Humanitarian Studies, Moscow, Russia Leonid Grinin National Research University Higher School of Economics, Moscow, Russia; Eurasian Center for Big History and System Forecasting, Institute of Oriental Studies, Russian Academy of Sciences, Moscow, Russia; Faculty of Global Studies, Lomonosov Moscow State University, Moscow, Russia Andrey V. Korotayev National Research University Higher School of Economics, Moscow, Russia; Eurasian Center for Big History and System Forecasting, Institute of Oriental Studies, Russian Academy of Sciences, Moscow, Russia; Faculty of Global Studies, Lomonosov Moscow State University, Moscow, Russia Cadell Last Systems Research, Bertalanffy Center for the Study of Systems Science, Vienna, Austria David J. LePoire Argonne National Laboratory, Lemont, IL, USA Claudio Maccone International Academy of Astronautics (IAA), Istituto Nazionale Di Astrofisica (INAF), Turin (Torino), Italy Sergey Malkov Institute of Economics of the Russian Academy of Sciences, Moscow, Russia; National Research University Higher School of Economics, Moscow, Russia Theodore Modis Growth Dynamics, Lugano, Switzerland

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Akop Nazaretyan Eurasian Center for Big History and System Forecasting, Institute of Oriental Studies, Russian Academy of Sciences, Moscow, Russia Alexander Panov Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia Pietro Perconti Department of Cognitive Science, University of Messina, Messina, Italy Alessio Plebe Department of Cognitive Science, University of Messina, Messina, Italy Yulia L. Shchapova Archaeology Department, Faculty of History, M. V. Lomonosov Moscow State University, Moscow, Russia Graeme Donald Snooks Research School of Economics, Australian National University, Canberra, Australia Ken Solis Milwaukee, WI, USA John S. Torday Department of Pediatrics, Harbor-UCLA Medical Center, Torrance, CA, USA Sergey Tsirel St. Petersburg Mining University, Saint Petersburg, Russian Federation Marc Widdowson Amarna Ltd., Bourne, Lincs, UK

The Twenty-First-Century Singularity in the Big History Perspective: An Overview Alexander Panov, David J. LePoire and Andrey V. Korotayev

Introductory Notes Many major transitions are currently underway in demography, energy use, environment, economic convergence, and global interdependence. With so much rapid change, often timescales for decisions are limited to about 5 years in the future. It is somewhat paradoxical then that this current rapid change is guiding us to look at very long timescales. This motivation arises because one explanation of the current rapid change is that it is a continuation of a very long-term trend throughout Big

A. Panov (&) Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia e-mail: [email protected] D. J. LePoire Argonne National Laboratory, Lemont, IL, USA e-mail: [email protected] A. V. Korotayev National Research University Higher School of Economics, Moscow, Russia e-mail: [email protected] Eurasian Center for Big History and System Forecasting, Institute of Oriental Studies, Russian Academy of Sciences, Moscow, Russia Faculty of Global Studies, Lomonosov Moscow State University, Moscow, Russia © Springer Nature Switzerland AG 2020 A. V. Korotayev and D. J. LePoire (eds.), The 21st Century Singularity and Global Futures, World-Systems Evolution and Global Futures, https://doi.org/10.1007/978-3-030-33730-8_1

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History1 (for standard accounts of the Big History, see, e.g., Christian 2004, 2018; Brown 2007; Christian et al. 2014; Spier 2010). Only now when we observe the change trend within our lives do we fully appreciate the consequences and implications. This book was developed to help understand the basis for this view along with the various deeper explanations as to why it is happening as well as why we can understand it. But beyond just understanding, we attempt to articulate some of the potential issues and implications to help facilitate future scenario development and their considerations. The rapid change leading to “some essential singularity” was articulated early by John von Neumann in the 1950s. According to Ulam (1958: 5), von Neumann maintained: “the ever-accelerating progress of technology and changes in the mode of human life… gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.” Later, Sagan (1977) popularized the cosmic calendar to demonstrate the relatively slow rates of change leading to humans and to civilization. These realizations were only possible because of the scientific inquiries and tools necessary to measure the time of events. Often these included some aspects of radioactive decay which forms natural clocks on many timescales. The cosmological context was formed by combining the twentieth-century discoveries in physics with the astronomical measurements of the cosmic background microwave radiations and the expansion of the universe seen in the cosmic redshift of galaxies (see, e.g., Bryson 2003). While the timescale is somewhat known, some of the major questions in this history are not fully understood such as the nature of the Big Bang, the (dark) substance of the universe, the origin of life, the meaning of consciousness, and the sustainability of technological civilization. It is important to explore these topics and trends, not just to further understand our origin, but also to put into context our possible future scenarios, to interpret trends and help guide decisions by identifying options and possible consequences. Often civilizations at a smaller scale have failed to be sustainable because of their belief in the continuing expanding trends without regard to their marginal benefits (Tainter 1996). For example, the Easter Islanders, in their very limited island, continued the competition to construct the stone statues along the coast by using a seemingly unlimited supply of trees which were needed to move the stones. This worked well until the trees were depleted leading to diminished ecological conditions with consequent lower sustainable population (Diamond 2005). So, we approach this topic, understanding the limitations of data, interpretation, and trend extrapolation. It is important to remember that the megatrend toward a singularity does not mean that the singularity will happen, but instead there might be some limitations and changes in the trend. In this book, we have various perspectives from those interpreting the continuing pattern as toward a technological singularity, a bounded logistic pattern, or no pattern at all. According to the definition of the International Big History Association, “Big History seeks to understand the integrated history of the Cosmos, Earth, Life, and Humanity, using the best available empirical evidence and scholarly methods” (IBHA 2020).

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Placing the Current Singularity Trend into Big History Context 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 megaevolution is the decelerating development of physical matter and energy into galaxies, stars, and planets from the initial Big Bang. The second arm of megaevolution is the accelerating rate of complexity evolution in the form of life, humans, and civilizations, which is the main concern of this book (Fig. 1). This increasing complexity requires additional information to overcome the second law of thermodynamics tendency toward thermal equilibrium (death). Instead, it marches further from this natural equilibrium toward a stable disequilibrium (e.g., Nazaretyan 2001, 2005) maintained by a constant flow of energy under information control. This concept of complexity correlates with various definitions of complexity in mathematics, such as the minimum length of the text describing its structure. Both arms proceed from combining two existing structures to form a new emergent structure. This process is known as aromorphosis (Galimov 2001; Grinin et al. 2009, 2011). Between these jumps of structure, there is a rather smooth evolutionary process. A complex system cannot arise “from scratch”; such a system is always the result of combinations of systems of the previous level of evolution. Evolution is not engaged in strategic planning and preliminary calculation of its aromorphoses; it works only with the material that it already has at hand and can immediately use.2 It is useful to explore some of the events in the first arm which starts with the Big Bang with many events happening (although at a decelerating rate) in the first three minutes (Weinberg 1977), followed by a much slower condensation into galaxies. This process mostly occurs through cooling of the universe by expansion. It is important to note that while some processes reach their thermal equilibrium, others (such as the fusion of protons and nuclides) do not. This is important since it leaves much energy later to support the second arm of life through the energy production in stars. After an imperceptible fraction of a second after the Big Bang, matter existed in the form of a plasma consisting of free quarks, leptons, photons, and other particles, which are considered elementary, structureless in quantum field theory (called a quark-gluon plasma). The universe had a very simple description: It was, in fact, only a list of types of particles and fields plus temperature, which uniquely determined the density and all other properties of the medium. After a certain decrease in 2

So not all the most important evolutionary solutions look optimal. As a fun example, we can note the structure of the eye of vertebrates, when the optic nerve attaches to the retina from the outside, creating a blind spot. This makes absolutely no sense, as evidenced by the structure of the eye of cephalopod mollusks. It is arranged in the same way as in vertebrates, but the nerve is attached on the back of the retina, so there is no blind spot. Why is the eye of vertebrates so ridiculous? Apparently, the first direct ancestor of vertebrates purely by chance had an eye of such a structure, and evolution had no choice but to begin the development of the type of vertebrates, starting with what it is. Such evolutionary omissions (there are many other examples) constitute the most important confirmation of the conservatism of evolution in biology.

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Fig. 1 Megaevolutionary processes in the Big History perspective (LePoire 2004). The arm starting at the bottom left shows increasing complexity. The other arm is the enabling system (natural or technological environment) in which it evolved. As the size of the increasingly complex objects grows, the smaller the system or tool involved. The first arm is the decelerating rate of events after the Big Bang up to the formation of planets. The second arm is the evolution of life, humans, and civilization. The line showing the construction of larger atoms (nuclei) by supernovae is a critical step leading to planets which enable the second arm to develop and accelerate

the temperature due to the expansion of the universe, quarks were bound by gluons (carriers of strong interaction) into composite particles—hadrons (neutrons, protons, and others)—the first stable structural formations. The structure of matter was spontaneously complicated, and the basis for a new level of organization of matter was elements of the previous level. Objects of a new level of organization of matter consisted of objects of the previous level. Some other particles, such as electrons, were still free. After some additional cooling of the universe, the primary protons— the composite objects of the previous level of evolution—were connected with electrons (the process of recombination of electrons). A higher-level structure was formed—a hydrogen atom, which included, as a substructure, the products of self-organization of previous levels: protons and electrons. The previous pattern of evolution was repeated. At some phase of the evolution of inorganic matter in the universe, the first stars were formed—also composite objects, which were formed mainly from hydrogen and helium atoms (Chaisson 2014). During the evolution of stars, heavy chemical elements are produced in quantities sufficient to form earth-like planets. Heavy elements are thrown into space in the process of supernova explosions. Here, we

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have another type of conservatism: Heavy elements could not appear without stars, and the existence of stars is a necessary prerequisite for the appearance of heavy elements, but the stars themselves are not included, obviously, in the composition of heavy chemical elements. In its future existence, heavy elements can do without stars, forming, for example, structures of a new type: gas–dust clouds (from which stars of the next generations are formed), planets, etc. The following examples belong to biological evolution (Ward and Kirschvink 2015). It is not known exactly how this happened, but somehow the first living creatures emerged from complex organic compounds (perhaps the so-called RNA world was also an intermediate step). Anyway, the first living creatures conservatively included elements of the previous phase of evolution—complex organic molecules. Most likely, the first living objects were prokaryotes—the simplest cells that do not contain the cell nucleus and other intracellular organelles. The next evolutionary level was eukaryotes. Each eukaryotic cell is a symbiont of several highly specialized prokaryotic cells. Again, we have a “made from” conservatism. Further, multicellular beings are, in fact, colonies of highly specialized unicellular eukaryotes. Again, we have a “made from” conservatism. Finally, we turn to social evolution. Any society consists of separate individuals —social evolution is conservatively based on the previous purely biological evolution (Stewart-Williams 2018). At a certain stage of social evolution, consciousness arises, and then the mind in the human sense. Humanity, being the carrier of the mind, includes many individual biological specimens, conservatively based on all previous biological evolution. Every single person, being a carrier of the spirit, no matter how you understand it, remains at the same time an animal. It may seem that the first arm is in some sense more trivial compared to the second. But it is not so! It is easy to imagine a universe where the evolution of matter ends very early. For example, atoms cannot arise (for this it is enough to disturb the delicate mass balance of proton, neutron, and electron), galaxies cannot arise (insufficient amount of dark matter), etc. Even for the realization of the first arm of evolution, an extremely delicate balance of fundamental constants is required (Rozental 1980). For example, the transition connecting the first and second arms of evolution has a curious feature: Heavy elements are formed during stellar evolution due to the existence of an excited state of carbon nuclei with an energy almost matching that of the colliding 4He and 8Be nuclei.3 3

That is why the nucleus of very short-lived beryllium-8 in stars can merge with the helium nucleus, resulting in a carbon nucleus. This merger is a critical link from which the synthesis of heavy elements begins. At the same time, the existence of this energy level looks like a completely coincidental circumstance. If it were not there, the heavy chemical elements in our universe would never have been synthesized, and the emergence of life would have become impossible. It can be noted here that the presence of this state is, in a certain sense, more random than a random, successful selection of the values of the fundamental constants described by Rozental (1980). If such quantities as the mass of a proton, neutron, and electron and the fine structure constant are indeed fundamental, then the energy level in the carbon nucleus is not distinguished by anything among a multitude of such objects and is something really completely random. The fact that so much depends on some random energy level of the nucleus seems completely incredible.

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It is difficult to get rid of the impression that the two in some way completely “natural,” although essentially different strongly conservative arms of evolution are “stuck together” with each other in some completely “unnatural” way with the help of a very whimsically arranged weak conservative link. This causes an association with something like a key and a keyhole. There is a reason to assume that we are here and now at the end point of the second arm of the evolution. Evolution enters a blow-up regime and cannot continue with the same rate of growth of speed—the end of the second evolutionary arm is the final singular point at which the speed of evolution should formally turn into infinity. That is why the point of singularity is unattainable; therefore, near it the mode of the evolution must inevitably change. We are no more than a few decades away from the point of singularity, or, in slightly different terms, we have already entered a more or less prolonged “zone of singularity.” The question is what is behind this point of singularity? Are we at the beginning of the third arm of evolution, and what can it be, if so? Maybe it will again be a new evolution arm with a slowdown? And should we not expect the same “artificial” character of a link of the second arm with the third, as well as of the first one with the second? Will this link be strong conservative, or weak conservative? Is it possible to see signs of an answer to these questions in the present time? Does not the “duty” of organizing such a link lie on our conscience? It is rather curious that the question of the nature of the link of the second arm with the third one is easily connected with the problem of artificial intelligence (AI). More precisely, the question can be associated with the ability to create a strong AI (Kurzweil 2012). By a strong (or general) AI is meant an AI that surpasses the intellect of all the humankind in all respects. Obviously, such an AI should be capable of self-development (this follows simply from the fact that people, after all, were able to create a strong AI; therefore, a strong AI should have similar abilities by definition). Being capable of self-development, a strong AI will not need further contact with its parent and humanity and, in principle, can proceed to an independent evolution in full isolation from the human mind that created it. This may mean weak conservative link of a new, cybernetic, evolutionary line with the previous, biological one. On the contrary, if the creation of a strong AI is impossible, then the AI will have to exist in symbiosis with the human mind that gave rise to it; mind and AI can form a single supersystem of a new evolutionary level (which actually already seems to be happening), and the transition to the third arm of evolution will then be strong conservative—the supersystem is based on both biological intelligence and AI, as on subsystems. The same will happen if a strong AI is possible, and is created once, but for some reason it does not want to separate itself from humanity. What awaits us? It is not yet completely clear whether the above questions are even correctly formulated, but, essentially, the idea of the two arms of megaevolution,4 the nature of the links between the arms, at least inevitably leads to the need for their formulation. For some more detail on the two arms of megaevolution, see also Chapter “Exploring the Singularity Concept within Big History” (LePoire 2020) and Chapter “Big History and Singularity as Metaphors, Hypotheses and Predictions” (Tsirel 2020a) of the present collective monograph.

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Book Organization 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 first two chapters present an overview of the major trends and topics. Andrey V. Korotayev takes us through the construction of the data, which seems to fit a relatively simple model, along with a high-level explanation [Chapter “The Twenty-First Century Singularity in the Big History Perspective. A Re-Analysis” (Korotayev 2020b)]. 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, 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 with a singularity in the region of 2029. This is similar to the earlier independent analysis by the Russian physicist Alexander Panov. This function is also similar to the equation discovered in 1960 by Heinz von Foerster concerning dynamics of the world population. All this indicates the existence of global macroevolutionary patterns over a few billion years, which can be surprisingly accurately described by extremely simple mathematical functions. However, there seems to be no reason to expect a continuation of this trend to an unprecedented acceleration of technological development near the time of the trends’ singularity. Instead, it is reasonable to interpret this point as an indication of an inflection point, after which the pace of global evolution will begin to systematically slowdown in the long term. David LePoire then outlines some of the topics associated with these trends including associated megatrends in other areas such as energy flow, organization, information control, and entropy in the environment [Chapter “Exploring the Singularity Concept within Big History” (LePoire 2020)]. The trend of life’s accelerating increase in complexity throughout its history on earth suggests that a unique time (a unique or singular event, i.e., the Singularity) might be realized soon. At this unique time, the growth trend might display unusual behavior. Debate continues whether the rate of change at the Singularity will further accelerate, slow down, or demonstrate other behavior (e.g., flattening, collapse). Very basic questions about this historical trend concern the causes such as mathematical conditions of growth and factors like energy, environment, and information. Further details include determination of indications of the Singularity’s behavior (e.g., time, number, type) and the pattern of substructure (e.g., timing, transition characteristics) leading up to the Singularity. Finally, possible extensions to the pattern are considered in cosmological history, near-term transition to sustainability, and construction of potential far-future scenarios and implications.

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PART I: Historical Megatrends consists of six chapters discussing other potential historical trends that include integrating long-range topics such as geology and biology as well as the potential for the trends’ end with the complexity of developing artificial intelligence. If viewed as a complex adaptive system, these are expected to be patterns in related aspects such as energy flow and information. However, this part starts with an update of one of the groundbreaking papers. The impact of human perception is raised to question the reality of these trends. However, the trend seems to facilitate understanding of these long timescales. Theodore Modis presents an update of his groundbreaking 2002 paper in the journal Technological Forecasting and Social Change [Chapter “Forecasting the Growth of Complexity and Change—An Update” (Modis 2020)]. In that paper, he analyzed the compilation of major events over the life of the universe development and evolution on earth to construct a pattern that seemed logistic or exponential when the time was plotted on a log scale. The last event in that analysis was the Internet. In this update, Modis contrasts the predictions of the next major technological steps with both a continuing hyperbolic trend and a logistic trend. He suggests that since the new steps do not seem to be realized yet, that the bound on innovation rate of the logistic trend might be more probable. Also, based on his experience, logistic curves exhibit a certain limited growth beyond their initial chaotic beginning, which is consistent with the interpretation of the milestone curve as being logistic instead of exponential. Alexey Fomin supplements the human population growth trend with trends throughout biological evolution (number of species and rate of sedimentation) and later technological activity [Chapter “Hyperbolic Evolution from Biosphere to Technosphere” (Fomin 2020)]. This set of data forms a continuous display of hyperbolic growth through biologic evolution, human evolution, and technology evolution. It is expected that further changes might occur through the application of artificial intelligence, human–computer connections, and robotics. Sergey Tsirel presents comparisons and potential integration of geological, biological, and social evolution tending to the point of a singularity [Chapter “Big History and Singularity as Metaphors, Hypotheses and Predictions” (Tsirel 2020a)]. Differences are highlighted in geological processes without agency, biological evolution with continual testing of new forms including those with higher complexity, and social history that seems to have a built-in mechanism of its self-destruction. According to Tsirel, the factor of acceleration by a factor of about 2.5–3 could be due to psychological reasons, for us to recognize confidently separate time periods. It is noted that geometric progressions with this factor often found in descriptions of the geological environment and geological time. It is concluded that segmentation of history with the help of phase transition points is necessary, if not for explanation, then for the perception and understanding of both human history and the history of the whole earth. Ken Solis and David LePoire then explore an associated aspect of complex adaptive system evolution, the aspect of information gathering and control, and how it can be applied to counter the natural trend toward higher entropy [Chapter “Big History Trends in Information Processes” (Solis and LePoire 2020)]. This chapter

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reviews the changes in information processes through the evolution of life, humans, and civilization. An analysis of the events in this sequence was previously done by the late Richard Coren to identify a hyperbolic trend. Various aspects are considered along the information development including generation, diffusion, storage, error correction, levels of abstraction, and unanticipated complexities. Each of these aspects might hinder or slow down further progress as the technologies enable the ability to construct artificial intelligence. Alessio Plebe and Pietro Perconti extend this analysis with current rapid trends in the development of artificial intelligence including aspects that might lead to a slowdown [Chapter “Plurality: The End of singularity?” (Plebe and Perconti 2020)]. The Singularity is a very intriguing future scenario to ponder, but it is even a quite controversial theoretical issue. Turning back to their previous (Plebe and Perconti 2013) skepticism about the Singularity hypothesis, based on an alternative slowdown hypothesis for artificial intelligence (AI), the authors consider the new possibilities of the so-called AI renaissance and the opportunities provided by the techniques collected under the name of deep learning in order to suggest a “pluralistic” view on Singularity. Plurality refers to the two following AI features: the compositionality of its subdomains and the spreading of intelligence in the social environment. A new kind of singularity might emerge from the nature of compositionality of subdomains and the “bearer problem,” i.e., the detachment between intentional content and its producer in a future scenario characterized by a massive spreading of intelligence in smart devices and the Internet. This kind of singularity for intelligence, however, could lead toward a “broken intelligence,” that is, an intelligence without anyone owns or uses it, more than toward the usually supposed “superintelligence.” Then, David LePoire and Mathew Chandrankunnel combine to explore another associated trend in energy flows first suggested by Eric Chaisson (2001); there are many patterns in energy flow and use, but larger environmental impacts seem to be leading to a major transition toward sustainability which might also impact development rate [Chapter “Energy Flow Trends in Big History” (LePoire and Chandrankunnel 2020)]. They review the roles of energy flow in Big History including the evolution of mechanisms to extract increasing amounts of energy in a controlled way to overcome the trend toward chaos (entropy). The events in this evolution seem to follow a hyperbolic trend toward a singularity time. The energy flow density work of Chaisson is reviewed with new possible avenues of exploration including the total amount of energy flow in an evolving system. Currently, a major transition is from fossil fuels to renewable energy. Some details of this transition include the role of nuclear energy especially in quickly developing countries where it provides a reliable base power with known technology as an insurance against the variable and developing technology of solar and wind energy technology. PART II: Models. This part of the book looks at potential models at various levels of abstraction. While the simplest, most mathematical, and abstract model is the modified exponential growth with collective learning leading to a hyperbolic form as presented in Chapter “The Twenty-First Century Singularity in the Big

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History Perspective. A Re-Analysis” (Korotayev 2020b), there are many other aspects to consider. Such aspects include the analogies to physical and social systems, more detail in the dynamics, questions about stochastic effects, and patterns that may continue beyond the unique (singularity or inflection) time. Sergey Grinchenko and Yulia Shchapova contend that a singularity does not need to lead to unhindered growth but instead could be the limiting time of a series of ever-accelerating processes [Chapter “The Deductive Approach to Big History’s Singularity” (Grinchenko and Shchapova 2020)]. The proposed concept of an “informational-systemic singularity” (ISS) is such a series based on basic information technologies which represents a technological–social component of Big History. The Zhirmunsky–Kuzmin series is applied to this data—i.e., a temporal geometric progression with the denominator “e to the degree minus e.” The identified times in this series include the approximate times of 30 million, 2 million, 120 thousand, and 8 thousand years ago, along with the more recent times of 1446, 1946, 1979, 1981 CE. Another example of a chronology is the archeological “Fibonacci’s” model, where the time around 1981 CE corresponds to a transition between the current historical stage of humanity and its following stage. This event is defined as the time of the maximum hierarchy levels in the human system. Further development processes would be co-adaptive. David J. LePoire and Tessaleno Devezas note that the concept of a trend toward a singularity has been discussed now for over 50 years [Chapter “Near-term Indications and Models of a Singularity” (LePoire and Devezas 2020)]. While many focus on the accelerated rate of technology change, other indicators also seem to be showing similar trends to near-term rapid peaks such as population, fossil-fuel use, world views, financial indices, environmental impact, and inequality. While simple models such as a hyperbolic trend fit some of these (e.g., population growth until recently), there are also other patterns such as discrete steps in the hyperbolic growth, more linear periodic K-waves, and a need to model what may happen near the inflection time, both before and after. Various models have been considered which exhibit hyperbolic growth such as fractal dynamics of critical systems, complex adaptive systems bifurcation patterns, and combination of logistic and hyperbolic patterns. Lessons learned from recent rapidly changing systems might complement the models in providing possible near-term scenarios as the inflection time is reached and passed. Some lessons might come from one community (fundamental physics researchers) that was impacted from a change in the rate of progress in the early twentieth century. Other lessons might be gleaned from the seemingly qualitative peak in technology change at about the same time. Graeme Donald Snooks provides an alternative view, from the author of a very early description of the acceleration [Chapter “Is Singularity a Scientific Concept, or the Metaphysical Construct of Historicism? Implications for Big History” (Snooks 2020)]. In particular, he challenges the methodology, the measurement, and the interpretation employed by various writers in this field. (This is further discussed and rebutted in the conclusion.) Interpretation of the data, methodology, and extrapolation are identified as important issues. He disparages analysis that only fits and extrapolates mathematical curves and instead advocates derivation of

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deeper models that help understand the mechanisms underlying the phenomena with the hope of gaining a greater perspective. While the editors agree with many of these generic issues, this specific analysis seems to be inconsistent as further discussed in the conclusion. PART III: Future Implications. The book continues with eight chapters on potential future implications, scenarios, and actions. Future implications include effects of more integrated cyber and human (i.e., cyborg) systems, initiatives like the Global Brain project and applications of new fundamental technologies, especially to medicine. Scenarios often include the potential for the rate of change to slow down due to increasing complexities or aging due to demographic trends. Identified actions include educational awareness, greater international collaborative efforts, and application of strategic foresight. Insightful implications of a slowdown after a singularity might be the relative speed at which other similar civilizations progress. This leads to another possible hint at the resolution of the Fermi Paradox. Elise Bohan presents how the trends of Big History might be used to construct future scenarios (i.e., the Threshold 9 of Big History) [Chapter “Threshold 9: Big History as a Roadmap for the Future” (Bohan 2020)]. The trends of the Great Acceleration of Steffen et al. (2015) and Law of Accelerating Returns by Ray Kurzweil (2005) combine with the current discussion of Transhumanism by such researchers as Nick Bostrom (2005, 2009, 2014). The periodization of Big History thresholds and technological trends by Ray Kurzweil are compared. Both are compatible with the trend toward a singularity. The issues of transhumanism, which include jobs, education, and legal rights, are explored as they begin to surface today in, for example, privacy rights and legal responsibility with self-driving cars. Finally, the impacts of these future scenarios could be determined by the choices of the current generation in school. Various approaches are developed to facilitate educational exploration of both future scenarios and historical lessons. Leonid Grinin, Anton Grinin, and Andrey V. Korotayev explore possible connections between technological progress and social processes that might lead to a slowdown [Chapter “Dynamics of Technological Growth Rate and the Forthcoming Singularity” (Grinin et al. 2020)]. Many important social processes already indicate slowing trends, such as demographic development and urbanization. Indeed, there are some indications that a slowdown began as early as the 1970s. However, according to the theory of production principles, there are strong fluctuations in the acceleration of technological progress. The authors assume that at the moment technological progress is in the fourth, i.e., the scientific and cybernetic, production principle. According to this theory, they expect a powerful acceleration of technological progress in the area of the 2030s–2070s, partially fueled by advances in medicine. The resulting aging of the population might be a factor in the process of slowing down. In this case, if the expected time points are taken into account, the point of singularity, according to the authors’ calculations, is estimated to be around 2106. That is, with this method of calculation, a new wave of acceleration is expected to continue into the twenty-first century but then slows down near the end of the century.

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Akop P. Nazaretyan reviews the current understanding of the trend in Big History toward a singularity and the possible actions that might control the direction as it approaches [Chapter “The Twenty-First Century’s “Mysterious Singularity” In the Light of the Big History” (Nazaretyan 2020)]. Part of this is based on resolving the technological–humanism balance which has been tilting toward the application of technology to military concerns as a consequence of an “us versus them” mentality. To escape this trend, an international educational program is proposed to develop cooperative worldviews which incorporate the lessons of Big History and an understanding of how current decisions might impact the consequences of the trend toward the Singularity. Cadell Last reviews the ongoing work and possible directions and implications of the Global Brain initiative started at the Free University of Brussels under Francis Heylighen [Chapter “Global Brain: Foundations of a Distributed Singularity” (Last 2020)]. The distributed nature of the Global Brain would form from increasing capacity of the Internet to develop semantic and problem-solving techniques integrated with human processes. A metaphor is created of an organically developing system with a global database that leads to emergent phenomena such as emergent global consciousness and awareness. Leonid Grinin and Anton Grinin analyze the evolution of technology from the beginning of human history [Chapter “The Cybernetic Revolution and the Future of Technologies” (Grinin and Grinin 2020)]. They describe the direction of technological transformations, discuss, and explain the present and forthcoming technological changes. The analysis of technological evolution mainly focuses on the second half of the twentieth century. A detailed analysis of the latest technological revolution is presented, which is denoted as “Cybernetic,” along with some forecasts about its development up to the end of the twenty-first century. It is shown that the development of various self-regulating systems will be the main trend of this revolution. It is argued that the technological transition of the final phase of the cybernetics revolution will start in medicine, which is to be the keystone of technological convergence forming the system of MANBRIC technologies (based on medicine, additive, nano, bio, robotic, IT and cognitive technologies). Today, we are at the threshold of post-human revolution, the era of an intensive impact on the human body. The authors consider the directions of this revolution such as considerable life extension, organ replacement, brain–computer interfaces, robotics, genome editing, etc. It is very important to understand the mechanisms of technological development and to measure the possible risks arising from them. David Baker explores the concept of complexity to better understand the coming next threshold in Big History [Chapter “Complexity in the Future: Far-FromEquilibrium Systems and Strategic Foresight” (Baker 2020)]. A crucial question for practitioners of Big History is whether we should expect a continuation of increasing complexity or a deceleration or collapse of complexity in the near future. The “future sections” of the majority of high-profile Big History narratives predominantly paint a binary between catastrophe and a green sustainable future. A minority of big historians have explored what technology and society could look like if complexity does continue to rise. Yet for greater specificity about what that near future may look like,

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we must go beyond disorganized speculation based on technological trends, fads, and rhetoric. Not to mention our own wishful inclinations. Complexity is understood in very broad and general terms, but a more detailed understanding of what complexity is, what its variables are, how it can be measured, and how it changes, will give us a more detailed view of complexity in the future. In essence, with more data on the pattern comes a greater ability to make stronger projections. This is where a more structured approach involving strategic foresight and complexity studies will allow us to profile the near and deep future with a great deal more clarity. Sergey Tsirel considers challenges to liberal democracies and welfare states while building a society with different social structure [Chapter “Future Technological Achievements as a Challenge for Post-Singularity Human Society” (Tsirel 2020b)]. It examines problems, such as inequality and insufficient employment, of transitioning to a post-singular society. A scenario is constructed where a new society with growing automation, artificial intelligence, but reduced employment will not have time to fully form by the time the second stage of the transition begins. This second stage includes genetic engineering and the possible division of humanity into various non-intersecting and unequal beings. The later cyborgization of people might be necessary for the survival of humanity. Alexander Panov considers post-singularity development and its implications for future scenarios and the SETI effort [Chapter “Singularity of Evolution and Post-Singular Development in the Big History Perspective” (Panov 2020)]. The ability of a civilization to overcome a singularity border (a system crisis) determines important features of a civilization in an intensive post-singular phase of development. A number of features of post-singular civilization can stimulate its “strong communicativeness,” which is a prerequisite for the formation of the “galactic cultural field.” Post-singular civilizations—carriers of the cultural field—are considered as potential partners in interstellar communication and as our own potential future. Indeed, an expanded SETI effort could help overcome the Singularity crisis. PART IV: Epistemology and Ontology. The chapters of this part of the book seek to answer such questions as follows: Why can we know? How is this related to our evolution of worldviews? How much is the matter of perception relevant? Can we separate the hyperbolic acceleration into major phases and logistic nested progress? Claudio Maccone suggests a mathematical hypothesis connecting the number of current species on earth with the age of the earth through the application of techniques designed to describe lifecycles of general forms, e.g., species and civilizations, with a segmented function which includes a translated log-normal distribution [Chapter “Big History by Mathematics: Information, Energy, and the Singularity” (Maccone 2020)]. The sequence of the peaks of these distributions forms an overall evolutionary (Cladistics) curve which can be interpreted with stochastic methods used in the financial industry (geometric Brownian motion or Black–Scholes equation). The path of this function is interpreted to form a knee, which is consistent with the Kurzweil predicted singularity time. Marc Widdowson aims to strengthen confidence in the Singularity concept by distinguishing fundamental properties of cosmic evolution from chance or artifacts of human perception [Chapter “The Twenty-First Century Singularity: The Role of

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Perspective and Perception” (Widdowson 2020)]. The appearance of a crescendo of increasing complexity in cosmic evolution occurs partly because our ability to distinguish events of evolutionary significance is governed by a Weber–Fechner law (i.e., relative rather than absolute change is important). This results in a tendency to overemphasize more recent events. The chapter explores the connection between the choices made by authors of evolutionary datasets and the resulting parameters of the fitted models. This makes it possible to compare and reconcile different datasets and leads to the suggestion that the evolution of cosmic complexity is a combinatorial process involving a series of juxtaposed logistics, in which, as one trend burns out, another one takes over. Sergey Malkov uses mathematical modeling, to consider the phenomenon of singularity in the biological and social history [Chapter “About the Singularity in Biological and Social Evolution” (Malkov 2020)]. 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 acceleration pattern indicates the transitivity of its current state, while the time of singularity in this hyperbolic trend indicates the end of the transition process. Sergey V. Dobrolyubov considers three phases of social evolution: adaptive, structural, and cognitive (in the past, present, and future, respectively) [Chapter “The Transition to Global Society as a Singularity of Social Evolution” (Dobrolyubov 2020)]. These phases are separated by two phase transitions (which can also be considered as two singularities)—the Neolithic transition and the global transition. Social evolution is based on the phases’ differing means of individual and societal competition. In the present structural phase, individual competition leads to inequality, whereas societal competition leads to greater uniformity of societal structure. The combination of societal expansion and evolutionary growth limits leads to lifecycles of these societies. The size of interacting societies tends to increase throughout evolution toward inclusion of all the humankind. This global society can be considered a final point (singularity) of the structural evolution phase. Then, society’s metamorphosis further continues in the cognitive phase, which might rely directly on individuals’ need for cognition and self-realization, and not on social institutions. A mathematical trend is developed for the timing of these transformations toward this global singularity. It estimates a transformation to a distinct, larger societal organization type every 2000 years starting with the early Neolithic settlements in 10,000 BCE and culminating in the global singularity in about 4000 CE. John S. Torday explores the connection of the slowing down after the Big Bang singularity and the current accelerating trend of life to the near singularity in unicellular life [Chapter “Evolution, the ‘Mechanism’ of Big History, Predicts the

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Near Singularity” (Torday 2020)]. The single cell represents the ability to live with the first principles of physiology (to gain energy, respond to environment, maintain order, and reproduce) by organizing the fundamentals of matter and their laws (quantum mechanics) and to continue to develop to more complex forms (biological evolution). This has seen new meaning with the recent determination of hereditary environmental effects of epigenomics which allow the environmental experiences of the parents to be passed to offspring which starts as a single cell. Nature is reflective in accelerating toward a new singularity, recapitulating the original singularity of the Big Bang. Andrey V. Korotayev discusses in some detail the possibility of the Singularity being a product of biased human perception described by the Weber–Fechner law [Chapter “How singular is the Twenty-First Century Singularity?” (Korotayev 2020a)]. 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 concluding chapter [Chapter “Conclusion” (Korotayev and LePoire 2020)] analyzes and summarizes the authors’ views and editors’ comments. It presents a brief summary of the findings in each part of the book and integrates them into a current perspective of approaches, issues, research gaps, implications, and controversies. The approaches include the way each of the trends were constructed and analyzed along with the critique and attempts at resolution as presented in other chapters. Research gaps were identified in many chapters including collection and validation of data, e.g., energy flow throughout history. Implications are identified throughout the book including the way history is viewed, the way potential future scenarios are constructed and analyzed, and the potential for SETI efforts. In general, it is shown that the study of the twenty-first-century Singularity allows to detect a number 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.

References Baker D (2020) Complexity in the future: the special relationship between far-from-equilibrium systems and strategic foresight. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 397–417. https:// doi.org/10.1007/978-3-030-33730-8_18 Bohan E (2020) Threshold 9: Big History as a roadmap for the future. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 267–286. https://doi.org/10.1007/978-3-030-33730-8_13 Bostrom N (2005) A History of transhumanist thought. J Evol Technol 14:1–25 Bostrom N (2009) The future of humanity. Geopolit, Hist Int RelatS 1(2):41–78 Bostrom N (2014) Superintelligence: paths, dangers, strategies. Oxford University Press, Oxford Bryson B (2003) A short history of nearly everything. Broadway Books, New York Brown CS (2007) Big History: from the Big Bang to the present. The New Press, New York

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Chaisson E (2001) Cosmic evolution: the rise of complexity in nature. Harvard University Press, Cambridge, Massachusetts Chaisson E (2014) The natural science underlying Big History. Sci World J 2014:1–41. https://doi. org/10.1155/2014/384912 Christian D (2004) Maps of time: an introduction to Big History. University of California Press, Berkeley Christian D (2018) Origin story: a big history of everything. Allen Lane, London Christian D, Brown CS, Benjamin C (2014) Big history: between nothing and everything. McGraw Hill, New York Diamond J (2005) Collapse: how societies choose to fail or succeed. Penguin, New York Dobrolyubov S (2020) The Transition to Global Society as a Singularity of Social Evolution. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 535–558. https://doi.org/10.1007/978-3-030-33730-8_24 Fomin A (2020) Hyperbolic evolution from biosphere to technosphere. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 105–118. https://doi.org/10.1007/978-3-030-33730-8_5 Galimov E (2001) Fenomen zhizni. URSS, Moscow Grinchenko S, Shchapova Y (2020) The deductive approach to Big History’s Singularity. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 201–210. https://doi.org/10.1007/978-3-030-33730-8_10 Grinin L, Grinin A (2020) The cybernetic revolution and the future of technologies. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 377–396. https://doi.org/10.1007/978-3-030-33730-8_17 Grinin L, Grinin A, Korotayev AV (2020) Dynamics of technological growth rate and the 21st century singularity. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 287–344. https://doi.org/10.1007/9783-030-33730-8_14 Grinin L, Markov A, Korotayev AV (2009) Aromorphoses in biological and social evolution: some general rules for biological and social forms of macroevolution. Soc Evol Hist 8(2):6–50 Grinin L, Markov A, Korotayev AV (2011) Biological and social aromorphoses: a comparison between two forms of macroevolution. Evolution 1:162–211 IBHA (2020) International big history association website. https://bighistory.org/ Korotayev AV (2020a) How singular is the 21st century Singularity?. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 571–595. https://doi.org/10.1007/978-3-030-33730-8_26 Korotayev AV (2020b) The 21st century Singularity in the Big History perspective. A re-analysis. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 19–75. https://doi.org/10.1007/978-3-030-33730-8_2 Korotayev AV, LePoire D (2020) Conclusion. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 599– 620. https://doi.org/10.1007/978-3-030-33730-8_27 Kurzweil R (2012) How to create a mind: the secret of human thought revealed. Viking Penguin, New York Last C (2020) Global brain: foundations of a distributed singularity. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 363–375. https://doi.org/10.1007/978-3-030-33730-8_16 LePoire DJ (2004) A ‘perfect storm’ of social and technological transitions. Futur Res Q 20(3):25–39 LePoire DJ (2020) Exploring the singularity concept within Big History. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 77–97. https://doi.org/10.1007/978-3-030-33730-8_3 LePoire DJ, Chandrankunnel M (2020) Energy flow trends in Big History. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 185–200. https://doi.org/10.1007/978-3-030-33730-8_9

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LePoire DJ, Devezas T (2020) Near-term Indications and models of a singularity trend. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 213–224. https://doi.org/10.1007/978-3-030-33730-8_11 Maccone C (2020) Big History by mathematics: information, energy, and the Singularity. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 469–487. https://doi.org/10.1007/978-3-030-33730-8_21 Malkov S (2020) About the singularity in biological and social evolution. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 517–534. https://doi.org/10.1007/978-3-030-33730-8_23 Modis T (2020) Forecasting the growth of complexity and change—an update. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 101–104. https://doi.org/10.1007/978-3-030-33730-8_4 Nazaretyan A (2001) Tsivilizatsionnyye krizisy v kontekste Universal’noy istorii. PER SE, Moscow Nazaretyan A (2005) Big (Universal) History paradigm: versions and approaches. Soc Evol Hist 4 (1):61–86 Nazaretyan A (2020) The 21st century’s “mysterious singularity” in the light of the Big History. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 345–362. https://doi.org/10.1007/978-3-030-33730-8_15 Panov A (2020) Singularity of evolution and post-singular development in the Big History perspective. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 439–465. https://doi.org/10.1007/9783-030-33730-8_20 Plebe A, Perconti P (2013) The slowdown hypothesis. In: Eden AH, Moor JH, Søraker JH, Steinhart E (eds) Singularity hypotheses. Springer, Berlin, pp 349–365. https://doi.org/10. 1007/978-3-642-32560-1_17 Plebe A, Perconti P (2020) Plurality: the end of singularity? In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 163–184. https://doi.org/10.1007/978-3-030-33730-8_8 Rozental I (1980) Physical laws and the numerical values of fundamental constants. Phys Usp 23:296–305. https://doi.org/10.1070/PU1980v023n06ABEH004932 Sagan S (1977) The dragons of Eden: speculations on the evolution of human intelligence. Random House, New York Snooks GD (2020) Is singularity a scientific concept, or the metaphysical construct of historicism? Implications for Big History. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 225–263. https://doi.org/10. 1007/978-3-030-33730-8_12 Solis K, LePoire DJ (2020) Big History trends in information processes. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 145–161. https://doi.org/10.1007/978-3-030-33730-8_7 Spier F (2010) Big history and the future of humanity. Wiley, Chichester Steffen W, Broadgate W, Deutsch L, Gaffney O, Ludwig C (2015) The trajectory of the anthropocene: the great acceleration. Anthropocene Rev 2(1):81–98. https://doi.org/10.1177/ 2053019614564785 Stewart-Williams S (2018) The ape that understood the universe: how the mind and culture evolve. Cambridge University, Cambridge Tainter JA (1996) Complexity, problem solving, and sustainable societies. In: Constanza R, Segura O, Martinez-Alier J (eds) Getting down to earth. Island Press, Washington DC, pp 61–76 Torday J (2020) Evolution, the ‘mechanism’ of Big History, predicts the near Singularity. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 559–570. https://doi.org/10.1007/978-3-030-33730-8_25 Tsirel S (2020a) Big History and Singularity as metaphors, hypotheses and prediction. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 119–144. https://doi.org/10.1007/978-3-030-33730-8_6

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Tsirel S (2020b) Future Technological Achievements as a Challenge for Post-Singularity Human Society. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 419–437. https://doi.org/10.1007/978-3-03033730-8_19 Ulam S (1958) Tribute to John von Neumann. Bull Am Math Soc 64(3):1–49 Ward P, Kirschvink J (2015) A new history of life: the radical new discoveries about the origins and evolution of life on earth. Bloomsbury, London Weinberg S (1977) The first three minutes: a modern view of the origin of the universe. Basic Books, New York Widdowson M (2020) The 21st century Singularity: the role of perspective and perception. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 489–516. https://doi.org/10.1007/978-3-030-33730-8_22

Alexander Panov graduated from Moscow State University, Department of Physics. At present, he is a lead researcher at the Moscow State University Skobeltsyn Institute of Nuclear Physics (MSU SINP), and is DSc (Physics and Mathematics). His major works are devoted to nuclear physics, surface physics, quantum theory of measurement, cosmic rays physics, and problems of universal evolution / Big History. He is the author of about 130 articles in the Russian and international academic press, as well as the author of the monograph Universal Evolution and Problems of the Search for Extraterrestrial Intelligence (SETI). David J. Lepoire has a Ph.D. in Computer Science from DePaul University and a BS in Physics from CalTech. He has worked in environmental and energy areas for many governmental agencies over the past 25 years. Topics include uncertainty techniques, pathway analysis, particle detection tools , and physics-based modeling. He has also explored historical trends in energy, science, and environmental transitions. His research interests include complex adaptive systems, logistical transitions, the role of energy and environment in history, and the application of new technologies to solve current energy and environmental issues. Andrey V. Korotayev has a Ph.D. in Middle Eastern Studies from the University of Manchester and a Dr.Sc. 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 Center 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.

The Twenty-First-Century Singularity in the Big History Perspective—A Re-analysis Andrey V. Korotayev

This chapter 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 the Russian Science Foundation (Project No. 18-18-00254).

Introduction The issue of the Global History Singularity (or even the Big History Singularity) is being discussed rather actively nowadays (see, e.g., Eden et al. 2012; Shanahan 2015; Callaghan et al. 2017; Nazaretyan 2015a, 2016, 2017, 2018). This subject has been made especially popular by Raymond Kurzweil, Google technical director in the field of machine training, first of all with his book The Singularity Is Near (2005), but also with such activities as the establishment of the Singularity University (2009) and so on. To the field of the Big History, the issue of the singularity has been brought by big historians such as Akop Nazaretyan [(2005a, b, 2009, 2013, 2014, 2015a, b, 2016, 2017, 2018; see also his Chapter “The TwentyFirst Century’s “Mysterious Singularity” in the Light of the Big History” in the present monograph (Nazaretyan 2020)], Alexander Panov [(2004, 2005a, b, 2006, 2008, 2011, 2017; see also his Chapter “Singularity of Evolution and Post-singular Development in the Big History Perspective” in the present monograph

A. V. Korotayev (&) National Research University Higher School of Economics, Moscow, Russia e-mail: [email protected] A. V. Korotayev Eurasian Center for Big History and System Forecasting, Institute of Oriental Studies, Russian Academy of Sciences, Moscow, Russia Faculty of Global Studies, Lomonosov Moscow State University, Moscow, Russia © Springer Nature Switzerland AG 2020 A. V. Korotayev and D. J. LePoire (eds.), The 21st Century Singularity and Global Futures, World-Systems Evolution and Global Futures, https://doi.org/10.1007/978-3-030-33730-8_2

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(Panov 2020)], and Graeme Donald Snooks [(2005); see also his Chapter “Is Singularity a Scientific Concept or the Metaphysical Construct of Historicism? Implications for Big History” in the present monograph (Snooks 2020)]. In the Big History perspective, the “Singularity hypothesis” might be of some interest, as it virtually suggests a rather exact dating of the onset of Big History Threshold 9 (around 2045 CE). However, let us find out if those calculations of the singularity timing can indeed be used to identify the possible date of the nearest Big History threshold.

Kurzweil–Modis Time Series and Mathematical Singularity Raymond Kurzweil was one of the first to arrange the major evolutionary shifts of a very significant part of the Big History along the hyperbolic curve that can be described by an equation with a mathematical singularity. For example, at page 18 of his bestseller The Singularity is Near (2006) he reproduces the following figure (see Fig. 1)1: However, rather surprisingly, Kurzweil does not appear to have recognized that the curve represented at this figure is hyperbolic, and that it is described by an equation possessing a true mathematical singularity (what is more, the value of this singularity, 2029, is not so far from the one professed by Kurzweil himself). This appears to be explained first of all by some mathematical inaccuracies of the Google technical director (suffice to mention that he consistently calls the global evolution acceleration pattern “exponential” without paying attention to the point that the exponential function does not have any singularity). Against this background, it appears a bit surprising that Kurzweil himself does know about the notion of mathematical singularity and describes it more or less accurately. Indeed, at pages 22–23 of his bestseller he provides a fairly accurate description of the concept of “mathematical singularity”: “To put the concept of Singularity into further perspective, let’s explore the history of the word itself. ‘Singularity’ is an English word meaning a unique event with, well, singular implications. The word was adopted by mathematicians to denote a value that transcends any finite limitation, such as the explosion of magnitude that results when dividing a constant by a number that gets closer and closer to zero. Such a mathematical function never actually achieves an infinite value, since dividing by zero is mathematically ‘undefined’ (impossible to calculate). But the value of y exceeds any possible finite limit (approaches infinity) as the divisor x approaches zero” (pp. 22–23).

What is more, he supplies his description of the concept of “mathematical singularity” at page 23 with a rather appropriate illustrating diagram (see Fig. 2):

Actually, a prototype of this figure (but in a double logarithmic scale) was reproduced by Kurzweil already in 2001 in his essay “The Law of Accelerating Returns” at page 5.

1

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Fig. 1 “Countdown to Singularity” according to Raymond Kurzweil. Source Kurzweil 2005: 18 (reproduced with permission of Raymond Kurzweil)

Fig. 2 A mathematical singularity. Source Kurzweil 2005: 23 (reproduced with permission of Raymond Kurzweil)

However, having provided his fairly adequate description of the “mathematical singularity” concept, Kurzweil appears to be losing any interest in this concept— suddenly switching to the use of the term “singularity” by astrophysicists (p. 23).

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One of the most enigmatic things in Kurzweil’s book is that he manages not to notice that the shape of the hyperbolic curve at his figure “A mathematical singularity” (page 23 of Kurzweil’s book, see Fig. 2) is fundamentally identical (though, of course, rotated 180°) with one of the curves of his figure “Countdown to Singularity” (page 18 of the same book, see Fig. 1). What is more, as we will see below, the mathematical model providing the best-fit approximation of the curve of the type seen in Fig. 1 is basically identical with the hyperbolic function displayed in Fig. 2, that is y = k/x. Thus, if Kurzweil had done a basic mathematical analysis of the time series in his Fig. 1, he would have found that it is best described by a mathematical equation of the type he features in his Fig. 2 (with such a really slight difference that we would have “2” rather than “1” in the equation’s numerator2). What is more, he would have discovered that the mathematical singularity of the best-fit equation describing Kurzweil’s “Countdown to Singularity” curve is 2029, which is not so much different from 2045, suggested by him in his book, and that is simply identical with the date proposed by Kurzweil most recently (Ranj 2016)3.

Panov’s Transformation Another amazing thing is that what was not done by Kurzweil in 2005 was done in 2003 by Alexander Panov.4 Panov analyzed an essentially similar time series taken from entirely different sources but arrived at very similar conclusions, but in a much more advanced form. It is very important that he made a step (to which Kurzweil was very close but which he did not make actually) that allowed him to make the analysis of the time series in question much more transparent and to identify the singularity date in a rigorous way. In his 2005 book, Kurweil plotted at the Y-axis of his diagrams “time to next event,” which hindered for him their interpretation in a rather significant way. In his 2001 essay at page 5 while analyzing a diagram with a similar time series (whose source, incidentally, was not indicated), Kurzweil began speaking about the acceleration of “paradigm shift rate” (Kurzweil 2001: 5), but (as is rather typical for the Google chief engineer) almost immediately switched to another theme. However, what was necessary to make his diagrams much more intelligible was to plot at Y-axis not “time to next event,” but just “paradigm shift rate”—just as was done 2

And with a slightly different calculation mode than the one that we will apply below, the denominator of this equation will be a number that is only slightly different from “1”. 3 To be more exact, this is the date, when according to the most recent Kurzweil forecast, the humans will become immortal, which still can well be considered as a sort of singularity (as well as a rather valid candidate for the possible dating for Threshold 9 of the Big History)—even if we actually deal with the radical increase in the human (or posthuman?) life expectancy rather than with the immortality per se, as this would still imply the change of the biological nature of the humans, which cannot but affect the course of the human history in a rather dramatic way. 4 His calculations described below were first presented in November 2003 at the Academic Seminar of the State Astronomical Institute in Moscow (Nazaretyan 2005a, b: 69) and subsequently published in his articles (Panov 2004, 2005a, b, 2006, 2011, 2017) and monograph (Panov 2008).

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Fig. 3 Dynamics of the global macrodevelopment rate according to Panov. source Nazaretyan 2018: 31, Fig. 3

by Panov. Indeed, to transform the time to next paradigm shift into paradigm shift rate one needed to do a rather simple thing—to take one year and to divide it by time to next paradigm shift; this will yield a number of paradigm shifts per year, that is just a “paradigm shift rate.” As we have already said, this was not done by Kurzweil but was done by Panov who obtained the following graphs as a result (see Fig. 3): In Fig. 3, the left-hand diagram depicts the acceleration of the global macroevolution rate starting from 4 billion BP, whereas the right-hand diagram describes this for the human part of the Big History.5 Note immediately that Panov’s left-hand curve in Fig. 3 is a mirror image of Kurzweil’s “Countdown to Singularity” graph (see Fig. 4): However, the mathematical interpretation of Panov’s graph is much easier and more straightforward. Note that Panov himself denoted the variable plotted at Yaxis as “frequency of the phase transitions per year.” However, it is quite clear that Panov’s “phase transition” is a synonym of Kurzweil’s “paradigm shift,” whereas “frequency of the phase transitions per year” describes just “paradigm shift rate” or global evolutionary macrodevelopment rate. This transformation makes it much easier to detect rigorously the pattern of acceleration of the global macrodevelopment rate.

5

Note that the left-hand diagram was only presented by Panov at the Academic Seminar of the State Astronomical Institute in November 2003, whereas in his printed works he only reproduces the right-hand diagram, using another visualization of the global macrodevelopment acceleration for the whole of the global history since 4 billion BP. On the other hand, the left-hand diagram was reproduced in print by Akop Nazaretyan (2015a: 357; 2018: 31) with reference to Panov.

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Fig. 4 Comparison between Kurzweil’s “Countdown to Singularity” and Panov’s graphic depiction of the dynamics of the “frequency of global phase transitions” (= global macroevolution rate)

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Modis–Kurzweil Time Series: A Mathematical Analysis Below, we will perform a mathematical analysis of Kurzweil’s time series along the lines suggested by Panov (though with some modifications of ours). In addition to Kurzweil’s “Countdown to Singularity” graph in single logarithmic scale presented in Fig. 1, Kurzweil publishes two other versions of this graph in double logarithmic scale (see Figs. 5 and 6): Though the time series presented in Fig. 5 looks for me a bit more convincing than the one presented in Fig. 6, I have decided to analyze the time series in Fig. 6 due to the following reason. The point is that the source of data for Fig. 5 remains entirely obscure; hence, I do not see any way to reconstruct the respective time series in such a detail that is necessary for its formal mathematical analysis. There are no such problems with the source of data for Fig. 6, as Kurzweil indicates it very clearly. This is a paper by Theodore Modis “The Limits of Complexity and Change” (2003) prepared in its turn on the basis of his earlier article published in the Technological Forecasting and Social Change (2002). Fortunately, Modis provides all the necessary dates in his articles, which makes it perfectly possible to analyze this time series mathematically. We will start our analysis with the abovementioned transformation, i.e., replace “time to next event” with “paradigm shift rate” * “phase transition rate” * “macrodevelopment rate.” The result looks as follows (see Fig. 7):

Fig. 5 First log–log version of Kurzweil’s “Countdown to Singularity” graph. Source Kurzweil 2005: 17 (reproduced with permission of Raymond Kurzweil)

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Fig. 6 Second log–log version of Kurzweil’s “Countdown to Singularity” graph (= “canonical milestones”). Source Kurzweil 2005: 20 (reproduced with permission of Raymond Kurzweil)

Applying the same technique (“Countdown to Singularity”) as the one used by Kurweil for Fig. 1, we would obtain for this time series the following graph (see Fig. 8): In Fig. 9, we can see that one figure is an exact mirror image of the other (see Fig. 9a, b). It can be clearly seen that the curve in Fig. 7 (Fig. 9a) is virtually the same as the hyperbolic one in Fig. 2 representing the mathematical singularity. At the next step, let the X-axis represent the time before the singularity (whereas the Y-axis will represent the macrodevelopment rate)—and calculate the singularity date by getting such a power-law curve that would describe our time series in the most accurate way. The results of this analysis are presented in Fig. 10 (as has been mentioned above, our mathematical analysis has identified the singularity date for this time series as 2029 CE). Below, the same figure is presented in the double logarithmic scale (see Fig. 11): Let us now analyze the results. As we see, Kurzweil time series is described precisely with a mathematical function of a type y = k/x having an explicit mathematical singularity that was described by Kurzweil at pages 22–23 of his book— surprisingly without understanding of its relevance for the mathematical description of the “Countdown to Singularity” time series presented by him just a few pages before (pp. 17–20). Indeed, our power-law regression of the last “Countdown to Singularity” time series has identified the following best-fit equation describing this time series in an almost ideally accurate (R2 = 0.999) way: y¼

2:054 ; x1:003

ð1Þ

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Fig. 7 Kurzweil’s “canonical milestones” graph (see Fig. 6) transformed with Panov’s technique (single logarithmic scale)

where y is the global macrodevelopment rate, x is the time remaining till the singularity, and 2.054 and 1.003 are constants. Note that the denominator’s exponent (1.003) turns out to be only negligibly different from 1 (well within the error margins); hence, there are all grounds to use this equation in the following simplified form: y¼

2:054 ; x

ð2Þ

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Fig. 8 Kurzweil’s “canonical milestones” graph (see Fig. 6) with single logarithmic scale

where y is the global macrodevelopment rate, x is the time remaining before the singularity, and 2.054 is a constant. Thus, we find out that the Kurzweil–Modis data series is the best described mathematically just by a simple hyperbolic function of that very type that he presents at pages 22–23, with the only difference that it has 2 (rather than 1) in the numerator.6

6

Or, to be exact, 2.054.

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Fig. 9 “Panov’s” diagram a is a mirror image of “Kurzweil’s” b one

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Fig. 10 Scatterplot of the phase transition points from the Modis–Kurzweil list with the fitted power-law regression line (with a logarithmic scale for the Y-axis)—for the Singularity date identified as 2029 CE with the least squares method

Exponential and Hyperbolic Patterns of Global Acceleration: A Comparison Let us stress again that the mathematical analysis demonstrates rather rigorously that the development acceleration pattern within Kurzweil’s series is not exponential (as is claimed by Kurzweil), but hyperexponential, or, to be more exact, hyperbolic (see Fig. 12). Let us recollect that, with a logarithmic scale for the Y-axis, an exponential curve looks like a straight line (whereas a hyperbolic line looks like an exponential curve). On the other hand, in double logarithmic scale the hyperbolic curve looks like a straight line, whereas the exponential curve looks like an inversed exponential line. Thus, Fig. 12 demonstrates how wrong Kurzweil is when he claims that the megaevolution has followed the exponential acceleration pattern, indicating that this pattern was not exponential but hyperbolic.

Formula of Acceleration of the Global Macroevolutionary Development in the Modis–Kurzweil Time Series To make the model more transparent, it makes sense to make a small transformation of Eq. (2). Let us recollect that this is a slightly simplified version of Eq. (1) that was used to generate the hyperbolic curves in Fig. 12, and it looks as follows:

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Fig. 11 Scatterplot of the phase transition points from the Modis–Kurzweil list with the fitted power-law regression line (double logarithmic scale)—for the Singularity date identified as 2029 CE with the least squares method

y¼

2:054 ; x

ð2Þ

where y is the global macrodevelopment rate, x is the time remaining before the singularity, and 2.054 is a constant. Of course, x (the time remaining till the singularity) at the moment of time t equals t* − t, where t* is the time of singularity. Thus, x ¼ t  t: Hence, Eq. (2) can be rewritten in the following way: yt ¼

2:054 ; t  t

ð3Þ

where yt is the global macrodevelopment rate at time t, t* is the time of singularity, and 2.054 is a constant.

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(a)

(b)

Fig. 12 Scatterplot of the phase transition points from the Modis–Kurzweil list with fitted power-law/hyperbolic and exponential regression lines: a with a logarithmic scale for the Y-axis; b double logarithmic scale. Solid curves have been generated by the best-fit exponential model, whereas dashed curves have been generated by the hyperbolic equation

Finally, let us recollect that our least square analysis of the transformed Modis– Kurzweil series has identified the singularity date as 2029 CE. Thus, Eq. (3) can be further rewritten in the following way: yt ¼

2:054 : 2029  t

ð4Þ

Of course, in a more general form it should be written as follows: yt ¼

C ; t  t

ð5Þ

where C and t* are constants. Equation (4) generates curves that demonstrate an extremely accurate fit with empirical estimates and that are presented in Figs. 13, 14, and 15. The curve generated by this extremely simple equation describes in an unusually accurate way the planetary macroevolution acceleration pattern at the scale of billions of years (see Fig. 13):

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Fig. 13 Fit between the empirical estimates of the macrodevelopment rate and the theoretical curve generated by the hyperbolic equation yt = 2.054/(2029 − t), 10 billion BCE–2000 CE, with a logarithmic scale for the Y-axis

Fig. 14 Fit between the empirical estimates of the macrodevelopment rate and the theoretical curve generated by the hyperbolic equation yt = 2.054/(2029 − t), 2 billion–2,200,000 BCE, with a logarithmic scale for the Y-axis

However, if we “zoom in” Fig. 13 to see in more detail the recent two billions of years, we will see that Eq. (4), notwithstanding its extreme simplicity, turns out to be as capable to describe rather accurately the planetary macroevolution acceleration pattern (see Fig. 14).

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A. V. Korotayev

Fig. 15 Fit between the empirical estimates of the macrodevelopment rate and the theoretical curve generated by the hyperbolic equation yt = 2.054/(2029 − t), 400 000 BCE–2000 CE, with a logarithmic scale for the Y-axis

If we zoom in further—to see in some detail the global macroevelutionary development acceleration during the last hundreds of thousands of years of Big History (corresponding to the prehistory and history of the humankind)—we will see a similarly astonishingly close fit between the curve generated by model (4) and the empirical estimates of the global macroevolution rate (see Fig. 15): Finally, if we concentrate on the last millennia of the “human history” phase of the Big History, we will see that the same equation describes them as accurately (see Fig. 16): I would stress again that the curve accurately describing the acceleration of human history after 10 BCE (Fig. 16) and the curve as accurately describing the acceleration of planetary macroevolution before the appearance of humans have been generated by the same equation—the simplest Eq. (4). As we see, a very simple hyperbolic equation yt = 2.054/(2029 − t) describes the general pattern of the macrodevelopment rate acceleration observed up until recently in an extremely accurate way for all the main eras. In fact, model (4) has a rather straightforward “physical sense.” Indeed, let us calculate the macroevolution rate around 200 years before the “singularity” (that is, around 1829) using this equation in a further simplified form (yt = 2/(2029 − t)): y1829 = 2/(2029 − 1829) = 2/200 = 1/100. Thus, we arrive at the following result: “Around 1800 CE, a typical rate of global macroevolution was about one macroevolutionary shift (e.g., Industrial Revolution) per century”—that is macroevolution around that time proceeded at the scale of centuries. The same calculations for the time point about 2000 years before the singularity (before present)—around 1 CE in 29 CE would yield the following result: y29 = 2/ (2029 − 29) = 2/2000 = 1/1000—that is macroevolutionary shifts (e.g., Axial Age

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35

Fig. 16 Fit between the empirical estimates of the macrodevelopment rate and the theoretical curve generated by the hyperbolic equation yt = 2.054/(2029 − t), 10,000 BCE–2000 CE, with a natural scale for the both axes

revolution) tended to happen at the scale of one per millennium and the evolution proceeded at that time at the scale of millennia. On the other hand, around 18,000 BCE we would find that planetary macroevolution occurred at the scale of tens of thousands of years, around 200,000 years before present (BP)—at the scale of hundreds of thousands of years (around one global phase transition per 100 thousand years), around 2 million BP—at the scale of millions of years, around 20 million BP —at the scale of tens of millions of years, around 200 million BP—at the scale of hundreds of millions of years, and around 2 billion BP—at the scale of billions of years (that is, approximately one planetary macroevolutionary phase transition per one billion of years). In other words, with every decrease of the time to present (to the “singularity”) by an order of magnitude (from 2 billion BP to 200 million BP, from 200 million BP to 20 million BP, from 20 million BP to 2 million BP, etc.) the rate of global macroevolutionary development every time also increased just by an order of magnitude. And for me, such an acceleration pattern makes a perfect sense. Note that algebraic equation of the type yt ¼

C ; t  t

ð5Þ

can be regarded as solution of the following differential equation: dy y2 ¼ dt C (see, e.g., Korotayev et al. 2006a: 118–120).

ð6Þ

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A. V. Korotayev

Thus, the acceleration pattern implied by Eq. (4) can be spelled out as follows: dy y2 ¼  0:5y2 : dt 2:054

ð7Þ

Verbally, the overall pattern of acceleration of planetary macroevolution that describes so accurately the Modis–Kurzweil series of “complexity jumps” with model (4)/(5) can be spelled out as follows: “The increase in macroevolutionary development rate a times is accompanied by a2 increase in the acceleration speed of this development rate; thus, a twofold increase in macroevolutionary development rate tends to be accompanied by a fourfold increase in the acceleration speed of this development rate; an increase in macroevolutionary development rate 10 times tended to be accompanied by 100 times increase in the acceleration speed of this development rate; and so on.” Now, let us apply a similar methodology to analyze mathematically the series of global macroevolutionary “phase transition”/“biospheric revolutions” compiled by Alexander Panov (2005a, b; see also Panov 2008, 2011, 2017). However, before we do this I would like to analyze a few points.

Time Series of Panov and Modis–Kurzweil—An External Comparative Analysis Alexander Panov and Theodore Modis compiled their time series entirely independently of each other. As suggest my personal communications with both Panov and Modis, none of them knew that at almost the same time7 in another part of Europe another person compiled a similar time series (Alexander Panov worked in Moscow, whereas Theodore Modis worked in Geneva). As we will see below, they relied on entirely different sources and the resultant time series turned out to be very far from being identical. Indeed, the Modis time series (2003) standing behind Kurzweil’s “Canonical Milestones” graph (Kurzweil 2005: 20) looks as follows—we reproduce below this time series as it was published in Modis’ essay in the Futurist (2003), as it is this version of Modis’ series that is reproduced by Kurzweil and that has been analyzed mathematically above; however, we sometimes use fuller versions of the description of some Modis “milestones” from his 2002 article in the Technological Forecasting and Social Change:

Modis first presented his results in an article in Technological Forecasting and Social Change (that Panov only read in March 2018 after it was sent to him by me) in 2002, whereas Panov first presented his results next year at the Academic Seminar of the State Astronomical Institute in Moscow.

7

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(1) Origin of Milky Way, first stars—10 billion years ago.8 (2) Origin of life on Earth, formation of the solar system and the Earth, oldest rocks—4 billion years ago. (3) First eukaryotes, invention of sex (by microorganisms), atmospheric oxygen, oldest photosynthetic plants, plate tectonics established—2 billion years ago. (4) First multicellular life (sponges, seaweeds, protozoans)—1 billion years ago. (5) Cambrian explosion/invertebrates/vertebrates, plants colonize land, first trees, reptiles, insects, amphibians—430 million years ago. (6) First mammals, first birds, first dinosaurs—210 million years ago. (7) First flowering plants, oldest angiosperm fossil—139 million years ago. (8) First primates/asteroid collision/mass extinction (including dinosaurs)—54.6 million years ago. (9) First hominids, first humanoids—28.5 million years ago. (10) First orangutan, origin of proconsul—16.5 million years ago. (11) Chimpanzees and humans diverge, earliest hominid bipedalism—5.1 million years ago. (12) First stone tools, first humans, Homo erectus—2.2 million years ago. (13) Emergence of Homo sapiens—555,000 years ago. (14) Domestication of fire/Homo heidelbergensis—325,000 years ago. (15) Differentiation of human DNA types—200,000 years ago. (16) Emergence of “modern humans”/earliest burial of the dead—105,700 years ago. (17) Rock art/ptotowriting—35,800 years ago. (18) Techniques for starting fire—19,200 years ago. (19) Invention of agriculture—11,000 years ago.9 (20) Discovery of the wheel/writing/archaic empires/large civilizations/Egypt/ Mesopotamia—4907 years ago (21) Democracy/city states/Greeks/Buddha [Axial Age]—2437 years ago. (22) Zero and decimals invented, Rome falls, Moslem conquest—1440 years ago. (23) Renaissance (printing press)/discovery of New World/the scientific method— 539 years ago (24) Industrial Revolution (steam engine)/political revolutions (French and USA) —225 years ago. (25) Modern physics/radio/electricity/automobile/airplane—100 years ago. (26) DNA structure described/transistor invented/nuclear energy/WWII/Cold War/Sputnik—50 years ago. (27) Internet/human genome sequenced—5 years ago.

Actually, Modis starts with the “Big Bang”; however, Kurzweil, quite reasonably, prefers to start the series with the origins of the Milky Way. 9 A more popular version of Modis presentation (2003) appears to contain a misprint indicating 19,200 years ago as the date of the invention of agriculture. This misprint is absent from the more academic version of Modis presentation (2002), on which we rely at this point. 8

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A. V. Korotayev

* Note that Modis himself maintains rather explicitly that “present time is taken as year 2000” (Modis 2003: 31). Indeed, this makes good sense for “milestones” (24)–(27) above. However, there are some indications that Modis compiled first versions of his milestone list a few years before 2000 and appears not to have adjusted a few datings to the 2000 present point in his 2003 publication. Otherwise, it is difficult to understand his datings of milestones (20), (21), and (23). Thus, Modis (2002: 393–401) indicates the following list of sources he consulted to compile the time series above: Barrow and Silk 1980; Burenhult 1993; Heidmann 1989; Johanson and Edgar 1996; Sagan 1989; Schopf 1991; to this, Modis also adds “Timeline of the Universe” (American Museum of Natural History, Central Park West at 79th Street, New York), Encyclopedia Britannica,10 “the web site of the Educational Resources in Astronomy and Planetary Science (ERAPS), University of Arizona”,11 “Private communication, Paul D. Boyer, Biochemist. Nobel Prize 1997. Dec 27, 2000,” “a timeline for major events in the history of life on earth as given by David R. Nelson, Department of Biochemistry at the University of Memphis, Tennessee” (http://drnelson.utmem.edu/evolution2. html) (see Table 1). On the other hand, Panov relied on entirely different sources12 (see Table 1). As we see, there was not a single source consulted by both Modis (2002, 2003) and Panov (2005a) when they compiled their series of “canonical milestones/biospheric revolutions.” Their reference lists are 100% different. What is more, they mostly relied on sources belonging to different scientific traditions. Indeed, Modis relied exclusively on the works of Western scientists published in English.13 In a striking contrast to this, out of 30 references consulted by Panov (2005a), 18 are works of Russian scientists published in Russia; 9 are works of Western scientists translated into Russian; and just 3 references are original works of Western scientists in English.

10

Without providing any exact references. Without providing its URL. 12 At least when preparing his first list of “phase transitions/biospheric revolutions” in Russian (Panov 2004, 2005a). Note that when preparing the publication of his results in English Panov (2005b) added to his originally overwhelmingly Russian bibliography eight references in English (Begun 2003; Carrol 1988; Jones 1994; Nazaretian 2003; AH 1975; AP 1975; JBW 1975; TK 1975) and one reference in German (Jaspers 1955). One cannot exclude that this might have affected some of Panov’s datings of some of his “biospheric revolutions” (there are indeed some slight difference in datings between Panov 2005a and b). Note that these new references included four articles in Encyclopedia Britannica, which made the list of sources in Panov 2005b not as perfectly different for Modis’ list as the list of sources in Panov 2005a (because Modis also lists Encyclopedia Britannica among his list of sources). So, for the sake of “the purity of experiment” we decided to rely for our calculations on Panov’s list of “phase transitions” provided in his original publication of his results in Russian (2005a) rather than in English (2005b). 13 Though one of his sources (Heidmann 1989) is a translation into English of a book originally written in French. 11

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Table 1 Comparison of sources used by Modis (2002, 2003) and Panov (2005a) for the compilation of their lists of phase transitions/“biospheric revolutions”/“canonical milestones”/ “evolutionary turning points”/“complexity jumps” Sources consulted by Theodore Modis for the compilation of his phase transition list published in Modis 2002, 2003

Sources consulted by Alexander Panov for the compilation of his phase transition list published in Panov 2005a

Works by Russian scientists published in Russian: (1) Boriskovsky (1970), (2) Boriskovsky (1974a), (3) Boriskovsky (1974b), (4) Boriskovsky (1978); (5) Diakonov (1994)a; (6) Fedonkin (2003); (7) Galimov (2001); (8) Kapitza (1996b); (9) Keller (1975); (10) Lopatin (1983); (11) Muratov, Vahrameev (1974); (12) Nazaretian (2004); (13) Rozanov (1986); (14) Rozanov (2003); (15) Rozanov, Zavarzin (1997); (16) Shantser (1973); (17) Zavarzin (2003); (18) Zaytsev (2001) Works by Western scientists translated into Russian: (1) Antiseri and Reale (2001); (2) Begun (2004); (3) Carrol (1992), (4) Carrol (1993a), (5) Carrol (1993b); (6) Foley (1990); (7) Jaspers (1991); (8) Kring and Durda (2004); (9) Wong (2003) Original publications of the works of Western scientists in English: (1) Alvarez et al. (1980); (2) Orgel (1998); (3) Wood (1992) a This book is also available in English Diakonov (1999) (1) Barrow and Silk (1980); (2) Burenhult (1993); (3) Heidmann (1989); (4) Johanson and Edgar (1996); (5) Sagan (1989); (6) Schopf (1991); to this Modis also adds (7) “Timeline of the Universe” (American Museum of Natural History, Central Park West at 79th Street, New York) (8) Encyclopedia Britannica, (9) “the web site of the Educational Resources in Astronomy and Planetary Science (ERAPS), University of Arizona” (10) “Private communication, Paul D. Boyer, Biochemist. Nobel Prize 1997. Dec 27, 2000” (11) “a timeline for major events in the history of life on earth as given by David R. Nelson, Department of Biochemistry at the University of Memphis, Tennessee” (http:// drnelson.utmem.edu/evolution2.html)

Against this background, it is hardly surprising that Panov’s list of phase transitions (2005a: 124–127; b: 221) has turned out to be very far from identical with the one of Modis14: 1. The origin of life—4  109 years ago. The biosphere after its appearance was represented by nucleusless procaryotes and existed the first 2–2.5 billion years without any great shocks.

14

The description of Panov’s phase transitions/“biospheric revolutions” has been taken from 2005 Panov’s presentation of his findings in English (Panov 2005b: 221); however, the datings of those phase transitions are from the earlier Russian version (Panov 2005a); I indicate explicitly the difference between those datings when it is observed. Note that for our calculation below we have used the datings from Panov 2005a (not Panov 2005b). In cases when Panov 2005a indicated time ranges rather than exact time points, we have used middle values for our calculations—for example, Panov (2005a) indicates as the date of his “biospheric revolution 5” (“hominoid revolution/the beginning of the Neogene period”) 25–20  106 years ago, whereas for our calculations we use the intermediate value for this time range (22.5  106 years ago).

40

A. V. Korotayev

2. Neoproterozoic revolution (oxygen crisis)—1.5  109 years ago. Cyanobacteria had enriched the atmosphere by oxygen that was a strong poison for anaerobic procaryotes. Anaerobic procaryotes started to die out, and anaerobic procaryote fauna was changed by an aerobic eucaryote and multicellular one. 3. Cambrian explosion (the beginning of Paleozoic era)—590–510  106 years ago.15 All the modern phyla of metazoa (including vertebrates) appeared during a few of tens of million years. During the Paleozoic era, the terra firma was populated by life. 4. Reptiles revolution (the beginning of Mesozoic era)—235  106 years ago. Almost all Paleozoic amphibia died out. Reptiles became the leader of the evolution on the terra firma. 5. Mammalia revolution (the beginning of the Cenozoic era)—66  106 years ago. Dinosaurs died out. Mammalia animals became the leader of the evolution on the terra firma. 6. Hominoid revolution (the beginning of the Neogene period)—25–20  106 years ago.16 A big evolution explosion of Hominoidae (apes). There were 14 genera of Hominoidae between 22 and 17 millions years ago—much more than now. The flora and fauna became contemporary. 7. The beginning of Quaternary period (Anthropogene)—4.4  106 years ago.17 The first primitive Homo genus (Hominidae) separated from Hominoidae. 8. Palaeolithic revolution—2.0–1.6  106 years ago.18 Homo habilis, the first stone implements. 9. The beginning of Chelles period—0.7–0.6  106 years ago.19 Fire, Homo erectus. 10. The beginning of Acheulean period—0.4  106 years ago. Standardized symmetric stone implements. 11. The culture revolution of neanderthaler (mustier culture)—150–100  103 years ago. Homo sapiens neanderthalensis. Fine stone implements, burial of deadmen (a sign of primitive religions). 12. The Upper Palaeolithic revolution—40  103 years ago. Homo sapiens sapiens became the leader of culture revolution. Development of advanced hunter instruments—spears and snares. Imitative art is widespread. 13. Neolithic revolution—12–9  103 years ago. Appropriative economy [foraging] had been replaced by productive economy [food production]. 14. Urban revolution (the beginning of the ancient world)—4000–3000 B.C. Appearance of state formations, written language, and the first legal documents. 15. Imperial antiquity, Iron Age, the revolution of the axial time—800–500 B.C.20 The appearance of a new type of state formations—empires, and a culture

570  106 years ago according to Panov (2005b). 24  106 years ago according to Panov (2005b). 17 4–5  106 years ago according to Panov (2005b). 18 2–1.5  106 years ago according to Panov (2005b). 19 0.7  106 years ago according to Panov (2005b). 20 750 B.C. according to Panov (2005b). 15 16

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16.

17.

18.

19.

41

revolution. New kinds of thinkers such as Zaratushtra, Socrates, Budda, and others. The beginning of the Middle Ages—400–630 CE.21 Disintegration of Western Roman Empire, widespread Christianity and Islam, domination of feudal economy. The beginning of the New Time [Modern Period], the first Industrial Revolution—1450–1550 CE22 Appearing of manufacture, printing of books, the new time culture revolution, etc. The Second Industrial Revolution (steam and electricity)—1830–1840.23 Appearance of mechanized industry, the beginning of globalization in the information field (telegraph was invented in 1831), etc. Information revolution, the beginning of the postindustrial epoch—1950. The main part of population of industrial countries works in the field of information production and utilization or in the service field, not in the material production.

In his Russian 2005 publication (Panov 2005a: 127), Panov adds to these “Phase Transition 19. Crisis and Collapse of the Communist Block, Information Globalization—1991 CE.” The respective data point is not found in diagrams below, but it has been used to estimate the macroevolutionary development rate for the previous data point (#18). Against the background of the above-discussed radical difference in the source base of Modis and Panov and the total independence of their research activities, it is hardly surprising to see that Panov’s list of “biospheric revolutions” differs from the Modis–Kurzweil series of “canonical milestones” in many rather significant ways: (1) Modis–Kurzweil list contains 27 “canonical milestones,” whereas Panov’s series only includes 20 “biospheric revolutions.” Thus, at least seven Modis– Kurzweil milestones have no parallels in the Panov series. (2) There is just one “milestone” for which both Modis and Panov have more or less exactly the same name and date (Modis–Kurzweil 2 = Panov 0). There is also one milestone (Modis–Kurzweil 26 = Panov 18), to which Modis and Panov give the same date, while giving to it totally different names. (3) There are a few milestones to which Modis and Panov give distantly similar names and roughly (but not exactly) similar dates (e.g., Modis–Kurzweil 23  Panov 16; Modis–Kurzweil 19  Panov 12; Modis–Kurzweil 17  Panov 11; Modis–Kurzweil 9  Panov 5). In one case, Modis and Panov give to the same milestone (Modis–Kurzweil 5 * Panov 2) the same name, but rather different dates. (4) However, for very substantial parts of those series the correlation between them looks very distant indeed. For example, for the period between 400 million years ago and 150,000 years ago this correlation looks as follows (see Table 2): 21

A.D. 500 according to Panov (2005b). A.D. 1500 according to Panov (2005b). 23 1830 according to Panov (2005b). 22

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A. V. Korotayev

Table 2 Correlation between the phase transition lists of Modis and Panov for the period between 400 million years ago and 150,000 years ago Modis–Kurzweil series

Panov (2005a) series

(6) First mammals, first birds, first dinosaurs —210 million years ago (7) First flowering plants, oldest angiosperm fossil—139 million years ago (8) First primates/asteroid collision/mass extinction (including dinosaurs)—54.6 million years ago (9) First hominids, first humanoids—28.5 million years ago (10) First orangutan, origin of proconsul— 16.5 million years ago (11) Chimpanzees and humans diverge, earliest hominid bipedalism—5.1 million years ago (12) First stone tools, first humans, Homo erectus—2.2 million years ago (13) Emergence of Homo sapiens— 555,000 years ago (14) Domestication of fire/Homo heidelbergensis—325,000 years ago (15) Differentiation of human DNA types— 200,000 years ago

(3) Reptiles revolution (the beginning of Mesozoic era)—235 million years ago (4) Mammalia revolution (the beginning of the Cenozoic era). Dinosaurs died out. Mammalia animals became the leader of the evolution on the terra firma—66 million years ago (5) Hominoid revolution (the beginning of the Neogene period). A big evolution explosion of Hominoidae (apes)—22.5 million years ago (6) The beginning of Quaternary period (Anthropogene)/the first primitive Homo genus (Hominidae) separated from Hominoidae—4.4 million years ago (7) Palaeolithic revolution/Homo habilis, the first stone implements—1.8 million years ago (8) The beginning of Chelles period— 650,000 years ago. Fire, Homo erectus (9) The beginning of Acheulean period. Standardized symmetric stone implements— 400,000 years ago

As one can see for a major part of the planetary history (between the Cambrian explosion and the formation of Homo sapiens sapiens), the correlation between the two series is really weak; they look as really independent (and rather different) series.

Panov Time Series: A Mathematical Analysis Now, knowing all this, let us analyze Panov’s time series the same way we have analyzed above the Modis–Kurzweil list of “canonical milestones.” The results of such an analysis look as follows (see Fig. 17): In the double logarithmic scale, the fit between the power-lower model y = 1.886/x1.01 (where x denotes the number of years before the singularity point defined as 2027 CE) and the empirical estimates of Panov looks as follows (see Fig. 18): Actually, I expected that the equation best describing the Panov series should look fairly similar to the one best describing the Modis–Kurzweil one; but, to tell the truth, I did not expect that they would look so similar (especially, keeping in

Global macrodevelopment rate (frequency of phase transitions per year)

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43

1.E+00 1.E-01

y = 1.886x-1.01 R² = 0.9991

1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Billions of years before the Singularity Fig. 17 Scatterplot of the phase transition points from Panov’s list with the fitted power-law regression line (with a logarithmic scale for the Y-axis)—for the Singularity date identified as 2027 CE with the least squares method

Fig. 18 Scatterplot of the phase transition points from Panov’s list with the fitted power-law regression line (double logarithmic scale)—for the singularity date identified as 2027 CE with the least square method

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A. V. Korotayev

mind that Modis and Panov relied on totally different sources, and that the resultant lists of “canonical milestones” were very far from being identical). However, the resultant equations turned out to be extremely similar (this is especially striking taking into consideration the point that neither Modis nor Panov tried to approximate their time series with Eq. (10)). Indeed, in the unsimplified form the power-law equation best describing the acceleration pattern in the Modis– Kurzweil series looks as follows (see Fig. 10): y¼

2:054 ð2029  tÞ1:003

;

ð8Þ

where, let us recollect, y is the global macrodevelopment rate (number of phase transitions per unit of time) and 2029 CE is the best-fit singularity point estimate. In the meantime, the power-law equation best describing the acceleration pattern in the Panov (2005a) series looks as follows (see Fig. 18): y¼

1:886 ð2027  tÞ1:01

:

ð9Þ

In general form, the respective equation looks as follows: y¼

C ðt 

 t Þb

:

ð10Þ

This equation has three parameters—C, t*, and b. Note that all the three parameters turn out to be extremely close for both Modis–Kurzweil and Panov.

Formulas of the Acceleration of Global Macroevolutionary Development in Panov and Modis–Kurzweil Series: A Comparison Indeed, the comparison of the best-fit power-law equations for both series yields the following results (see Table 3): Actually, for me the most impressive result was not even that the singularity (t*) parameters for both regressions have turned out to be so close (just 2 years difference!). For me, an even more impressive point is that exponent b in both cases has turned out to be so close to 1, which, incidentally, allows to reduce an already very simple power-law Eq. (10) yt ¼

C ðt

 t Þb

ð10Þ

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Table 3 Comparison between two acceleration formulas The power-law equation of type (10) demonstrating the best fit with the Modis– Kurzweil series

The power-law equation of type (10) demonstrating the best fit with the Panov series

2:054 y ¼ ð2029t (8), R2 = 0.9989 Þ1:003

1:886 y ¼ ð2027t (9), R2 = 0.9991 Þ1:01

to an even simpler hyperbolic Eq. (5): yt ¼

t

C : t

ð5Þ

Even the third parameter in Eq. (10) also turns out to be very similar for both Modis–Kurzweil (C = 2.1) and Panov (C = 1.9). A special remark should be said about the extremely close fit that theoretical curves generated by the extremely simple equations of (5) type demonstrate with both Modis–Kurzweil and Panov series. With respect to Modis–Kurzweil, Eq. (5) describes 99.89% of all the variation of planetary macroevolution development rate in the period of a few billion of years, whereas for Panov this fit reaches whopping 99.91%—on the other hand, the extreme closeness of R2 values for both regressions (just a 0.02% difference!) is rather impressive in itself [I would stress again that this it looks especially impressive taking into consideration the fact that neither Modis nor Panov tried to approximate their time series with Eqs. (5) or (10)]. Needless to say, that the differential acceleration pattern for Panov also turns out to be very close to Modis–Kurzweil. Indeed, as we have already mentioned, there are sufficient grounds to simplify Eq. (9) y¼

1:886 ð2027  tÞ1:01

ð9Þ

to the simple hyperbolic version (11): y¼

1:9 : 2027  t

ð11Þ

As we remember, such an algebraic equation can be regarded as a solution of the following differential equation that is very similar to the one that we obtained above for the Modis–Kurzweil series: dy y2 ¼  0:5y2 : dt 1:9

ð12Þ

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Thus, the overall pattern of acceleration of planetary macroevolution that describes so accurately the Panov series of “biospheric revolutions” turns out to be virtually identical with the one that we have detected above for the Modis–Kurzweil series: “The increase in macroevolutionary development rate a times is accompanied by a2 increase in the acceleration speed of this development rate; thus, a twofold increase in macroevolutionary development rate n times tends to be accompanied by a fourfold increase in the acceleration speed of this development rate; an increase in macroevolutionary development rate 10 times tended to be accompanied by 100 times increase in the acceleration speed of this development rate; and so on.” To my mind, all these indicate 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.

A Striking Discovery of Heinz Von Foerster It appears appropriate to recollect at this point that in their famous article published in the journal Science in 1960 von Foerster, Mora, and Amiot presented their results of the analysis of the world population growth pattern. They showed that between 1 and 1958 CE the world’s population (N) dynamics can be described in an extremely accurate way with the following astonishingly simple equation: Nt ¼

C ðt  tÞ0:99

;

ð13Þ

where Nt is the world population at time t, and C and t* are constants, with t* corresponding to the so called demographic singularity. Parameter t* was estimated by von Foerster and his colleagues as 2026.87, which corresponds to November 13, 2026; this made it possible for them to supply their article with a public relation masterpiece title—”Doomsday: Friday, 13 November, A.D. 2026” (von Foerster, Mora, Amiot 1960). Note that von Foerster and his colleagues detected the hyperbolic pattern of world population growth for 1 CE–1958 CE; later, it was shown that this pattern continued for a few years after 1958, and also that it can be traced for many millennia BCE (Kapitza 1996a, b, 1999; Kremer 1993; Tsirel 2004; Podlazov 2000, 2001, 2002; Korotayev et al. 2006a, b). In fact Kremer (1993) claims that this pattern is traced since 1,000,000 BP, whereas Kapitza (1996a, b, 2003, 2006, 2010) even insists that it can be found since 4,000,000 BP. It is difficult not to see that the world population growth acceleration pattern detected by von Foerster in the empirical data on the world population dynamics between 1 and 1958 turns out to be virtually identical with the one that has been detected above with respect to both Modis–Kurzweil and Panov series describing

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the planetary macroevolutionary development acceleration. Note that the power-law regression has yielded for all the three series the value of exponent b being extremely close to 1 (1.003 for the Modis–Kurzweil series, 1.01 for Panov, and 0.99 for von Foerster). However, the resultant proximity of parameter t* (that is, just the singularity time point) estimates is also really impressive (the power-law regression suggests 2029 for the Modis–Kurzweil series, 2027 for Panov series, and just the same 2027 for von Foerster series24). We have already mentioned that, as was the case with Eqs. (8) and (9), in von Foerster’s Eq. (13) the denominator’s exponent (0.99) turns out to be only negligibly different from 1, and as was already suggested by von Hoerner (1975) and Kapitza (1992, 1999), it can be written more succinctly as Nt ¼

t

C : t

ð14Þ

As we see the resultant equation turns out to be entirely identical with Eq. (5) that described so accurately the overall planetary macrodevelopment acceleration pattern since at least 4 billion years ago. Note that Eq. (14) has turned out to be as capable to describe in an extremely accurate way the world population dynamics (up to the early 1970s), as Eq. (5) is capable to describe the overall pattern of macrodevelopment acceleration (at least between 4 billion BCE and the present). We will show just an example of such a fit. Let us take Eq. (14). Now replace t* with 2027 (that is, the result of just rounding of von Foerster’s number, 2026.87), and replace C with 215,000.25 This gives us a version of von Foerster–von Hoerner–Kapitza Eq. (14) with certain parameters: Nt ¼

215000 : 2027  t

ð15Þ

The overall correlation between the curves generated by von Foerster’s equation and the most detailed series of empirical estimates looks as follows (see Fig. 19):

24

Note that the power-law regression that produced this value for the world populations series had been performed more than 50 years before a similar regression produced the same value of t* for the Panov series (actually, the first regression was performed before the birth of the author of the present article). Still I would not take too seriously such astonishingly similar values of t* parameter produced by different power-law regressions for very different time series in very different years; of course, there is a very high degree of coincidence here. In any case, as we will see below, there are no grounds at all to expect anything like Doomsday on Friday, November 13, A.D. 2026 25 Note that all the calculations below of the world population are conducted in millions. Note also that the value of parameter С used by us is a bit different from the one used by von Foerster.

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Fig. 19 Correlation between empirical estimates of world population (in millions, 1000–1970) and the curve generated by von Foerster’s Eq. (15). Note black markers correspond to empirical estimates of the world population by McEvedy and Jones (1978) for 1000–1950 and UN Population Division (2020) for 1950–1970. The gray curve has been generated by von Foerster’s Eq. (15). R2 = 0.996

As we see, indeed, Eq. (14) has turned out to be as capable to describe in an extremely accurate way the world population dynamics (up to the early 1970s), as Eq. (5) is capable to describe the overall pattern of global macrodevelopment acceleration. In the Big History context, it is definitely of great significance that Eq. (5) describing the global acceleration of the macroevolutionary development rates and Eq. (14) describing the world population growth are entirely identical. What is more, both empirical and mathematical analyses indicate that there a rather deep substantial connection between those two equations and that they describe two different aspects of the same global macroevolutionary process (see Appendix 1).

On the Formula of Acceleration of the Global Evolutionary Development I must say that I had serious doubts when I first got across calculations of Panov and Modis (and I am not surprised that most historians get very similar doubts when they see their works). I have lots of complaints regarding the accuracy of many of their descriptions of their “canonical milestones,” their selection, and their datings (see, e.g., Korotayev 2015). I have only started taking their calculations seriously,

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49

when I analyzed myself the two respective time series compiled (as we have seen above) entirely independently by two independently working scientists using entirely different sources with a mathematical model not applied to their analysis either by Modis or by Panov, and found out that they are described in an extremely accurate way by an almost identical mathematical hyperbolic function—suggesting the actual presence of a rather simple hyperbolic planetary macroevolution acceleration pattern observed in the Earth for the last 4 billion years. 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 macroevolutions could be described by rather similar simple hyperbolic equations (Korotayev 2005, 2006a, b, 2007a, b, 2008, 2009, 2012, 2013; Korotayev and Khaltourina 2006; Khaltourina et al. 2006; Korotayev et al. 2006a, b; Markov and Korotayev 2007, 2008, 2009; Grinin and Korotayev 2009; Markov et al. 2010; Korotayev and Malkov 2012; Korotayev and Grinin 2013; Korotayev and Markov 2014, 2015; Grinin et al. 2013, 2014; 2015; Korotayev and Malkov 2016; Zinkina et al. 2016; Korotayev et al. 2016; Korotayev and Zinkina 2017; Zinkina and Korotayev 2017), but I must say that even I was really astonished to find such a close fit. To my mind, all these indicate 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, as well as the presence of a global planetary macroevolutionary development acceleration pattern described by a very simple equation: dy y2 ¼ ; dt C1

ð6Þ

where C1 is a parameter in the following hyperbolic equation: yt ¼

C1 ; t  t

ð5Þ

where t* is the singularity date. It is also not without interest that the singularity dates in all the three (rather different) cases under consideration have turned out to be almost entirely identical (2029 CE for Modis–Kurzweil and 2027 CE for both Panov and von Foerster).

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Toward the Singularity Interpretation. The Place of the Singularity in the Big History and Global Evolution But how seriously should we take the prediction of “singularity” contained in such mathematical models? Should we really expect with Kurzweil that around 2029 we should deal with a few orders of magnitude acceleration of the technological growth (indeed, predicted by Eq. (4) if we take it literally26)? I do not think so. This is suggested, for example, by the empirical data on the world population dynamics. As we remember, the global population growth acceleration pattern discovered by Heinz von Foerster is identical with planetary macroevolutionary acceleration patterns of Modis–Kurzweil and Panov, and it is characterized by the singularity parameter (2027 CE) that is simply identical for Panov and has just 2 years difference with Modis–Kurzweil. However, what are the grounds to expect that by Friday, November 13, A.D. 2026 the world population growth rate will increase by a few orders of magnitude as is implied by von Foerster equation? The answer to this question is very clear. There are no grounds to expect this at all. Indeed, as we showed quite time ago, “von Foerster and his colleagues did not imply that the world population on [November 13, A.D. 2026] could actually become infinite. The real implication was that the world population growth pattern that was followed for many centuries prior to 1960 was about to come to an end and be transformed into a radically different pattern. Note that this prediction began to be fulfilled only in a few years after the “Doomsday” paper was published” (Korotayev 2008: 154). Indeed, starting from the early 1970s the world population growth curve began to diverge more and more from the almost ideal hyperbolic shape it had before (see Figs. 19 and 20) (see, e.g., Kapitza 2003, 2006, 2007, 2010; Livi-Bacci 2012; Korotayev et al. 2006a, b; Korotayev et al. 2015; Grinin and Korotayev 2015; UN Population Division 2018), and in recent decades it has been taking more and more clearly logistic shape—the trend toward hyperbolic acceleration has been clearly replaced with the logistic slowdown (see Fig. 20): In some respect, it may be said that von Foerster did discover the singularity of the human demographic history; it may be said that he detected that the human world system was approaching the singular period in its history when the hyperbolic accelerating trend that it had been following for a few millennia (and even a few millions of years according to some) would be replaced with an opposite decelerating trend. The process of this trend reversal has been studied very thoroughly by now (see, e.g., Vishnevsky 1976, 2005; Chesnais 1992; Caldwell et al. 2006; Khaltorina et al. 2006; Korotayev et al. 2006a, b; Korotayev 2009; Gould 2009; Dyson 2010; Reher 2011; Livi-Bacci 2012; Choi 2016; Podlazov 2017) and is known as the “global demographic transition” (Kapitza 1999, 2003, 2006, 2010; Podlazov 2017). Note that in case of global demographic evolution the transition from the hyperbolic acceleration to logistic deceleration started a few decades before the singularity point mathematically detected by von Foerster. 26

This is done, for example, by Nazaretyan (2015a, 2018).

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Fig. 20 World population dynamics (billions), empirical estimates of the UN Population Division for 1950–2015 with its middle forecast till 2100. Data source UN Population Division 2020

There are all grounds to maintain that the deceleration of planetary macroevolutionary development has also already begun—and it started a few decades before the singularity time points detected in both Modis–Kurzweil and Panov. So, how seriously should we take the prediction of “singularity” contained in hyperbolic mathematical models? For example, could we really use the point that our analysis of the Modis–Kurzweil time series reveals a singularity around 2029 CE as an indication to expect that around this time the transition to Big History Threshold 9 could actually start? Note that some big historians take such “mathematically grounded” predictions rather seriously. The most prominent among them is Akop Nazaretyan.27 In his article with a symptomatic title “Megahistory and Its Mysterious Singularity” in the Russian Academy of Sciences flagship journal, he maintains the following: “The solar system formed about 4.6 billion years ago, and the very first signs of life on Earth date back to 4 billion years. Thus, our planet became one of the (most likely, numerous) points on which the subsequent evolution of the metagalaxy was localized. Although its acceleration was noted long ago, a new circumstance has been discovered of late. The Australian economist and global historian G.D. Snooks, the Russian physicist A. D. Panov, and the American mathematician R. Kurzweil compared independently, proceeding from different sources and using different mathematical apparatuses, the time intervals between global phase transitions in biological, presocial, and social evolutions 27

This chapter contains some criticisms of certain views of a great Russian-Armenian big historian Akop Nazaretyan. I have decided to leave them notwithstanding the fact that he passed away just a month before the completion of the initial draft of this monograph, as I have never met a person who would met criticisms of his views more kindly than Akop. Actually, I do not think there is nobody who criticized Akop’s theories more than me (very frequently in Akop’s presence), which never affected our very friendly relations. In fact, I had an impression that our relations became more and more friendly with my new criticisms of his views.

52

A. V. Korotayev (Panov 2005a, 2008; Kurzweil 2005; Snooks 1996; Weinberg 1977). Calculations show that these periods decreased according to a strictly decreasing geometrical progression; in other words, the acceleration of evolution on the Earth followed a logarithmic law” (Nazaretyan 2015a: 356).

Furthermore, in his article in the recent issue of the Journal of Globalization Studies he goes on to claim that “having extrapolated the hyperbolic curve into the future, the researchers have come to a nearly unanimous (ignoring the individual interpretations) and even more striking result: around the mid twenty-first century, the hyperbole turns into a vertical. That is, the speed of the evolutionary processes tends to infinity, and the time intervals between new phase transitions vanish” (Nazaretyan 2017: 32; see also Nazaretyan 2015a: 357).

As we see, Nazaretyan does use the mathematical calculations of the singularity point for the global evolutionary hyperbola to predict the possible timing of Threshold 9 (that according to him should be much more profound than preceding Thresholds 7 (“Agricultural Revolution”) and 8 (“Modern Revolution”). However, do the calculations presented by Panov in 2003–2005, or by us above, really give grounds to expect “the singularity”/onset of Big History Threshold 9 between 2029 and 2050 CE? I do not think so. In fact, as we can see, our paper appears to be the first attempt to “extrapolate the line of the hyperbolic acceleration to the future.”28 Contra Nazaretyan, such an attempt was not undertaken by Donald Snooks (1996), who did not try to calculate any mathematical singularities. No formal attempts to “extrapolate the line of the hyperbolic acceleration to the future” using any mathematical techniques have been undertaken by Ray Kurzweil—at least because he seems to be still sure that he is dealing with exponential (but not hyperbolic) acceleration. Thus, almost the only person who (before us) has conducted any attempts to calculate mathematically the singularity time for the line of the acceleration of the planetary evolution appears to be Alexander Panov (2005a, b; see also Chapter “Singularity of Evolution and Post-singular Development in the Big History Perspective” in this volume (Panov 2020)—though in some respects this can be also said about Sergey Grinchenko [see 2001, 2004, 2006a, b etc., as well as “The Deductive Approach to Big History’s Singularity” in this volume (Grinchenko and Shchapova 2020)], Theodore Modis (2002, 2003), and David LePoire (2013, 2015, 2016 as well as the next chapter in this volume (LePoire 2020)). Panov’s technique was somehow different from the “extrapolation of the line of the hyperbolic acceleration to the future” (this was rather the technique applied by us), but, no doubt, Panov has applied a rather rigorous mathematical technique to identify the singularity of the planetary evolution. But what was the result of these calculations? After Panov applied his mathematical analysis to the time series starting from Phase Transition 0 (emergence of the life on the Earth, 4 billion BP) to Phase Transition 19 (“crisis and collapse of the Communist Block, information 28

While demonstrating that the resultant singularity should be interpreted 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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53

globalization”), he found that the mathematical singularity point for this time series is in no way situated somewhere “around the mid twenty-first century” as is claimed by Nazaretyan, but in 2004 CE29 (Panov 2005a: 130; b: 222). Nazaretyan has even happened to miss that soon after detecting this singularity point, Panov got involved in the study of the processes of the slowdown of the global technological–scientific growth (Panov 2009, 2013; see also his Chapter “Singularity of Evolution and Postsingular Development in the Big History Perspective” (Panov 2020) in the present volume). As LePoire puts it, “Big History trends of accelerating change and complexity with related increases in energy use may not be sustainable. The indications of potential slowdown in the rate of change in economies, technology, and social response were investigated. This is not to say that change will stop, just the rate of change will not accelerate. In fact, at the inflection point in a logistic learning curve only half of the discoveries have been made. Since there were three major phases in life, human, and technological civilization,30 the continuation of the logistic curve would suggest three more phases.31 The direction of the development of technologies points to the next phase including enhanced human technology through advanced biotech and computer integration… A rapid change is not necessarily good. It tends to push systems away from efficiency because there are little long-term expectations…” [(LePoire 2013: 115–116; see the next chapter in this volume for further detail (LePoire 2020)]. As major factors of the starting deceleration, LePoire names “higher costs of energy and limited natural resources, the diminished rate of fundamental discovery in physical sciences, and the need for investment in environmental maintenance” (LePoire 2013: 109). Note that Modis [2002, 2003, 2005, 2012; as well as in his Chapter “Forecasting the Growth of Complexity and Change—An Update” in the present volume (Modis 2020)] also interprets the maximum acceleration of the complexity growth rate that he detects around 2000 CE as an inflexion point after which we will deal with the deceleration of the global complexity growth rate. In fact, the earliest known to me attempt to detect mathematically a singularity in a series of what Modis would call “canonical milestones” of planetary evolution32 was undertaken in 2001 (thus, just a year before Modis’ seminal article in the Technological Forecasting and Social Change) by Sergey Grinchenko [see Grinchenko 2001; see also Grinchenko 2004, 2006a, b; 2007, 2011, 2015; Grinchenko, Shchapova 2010, 2016, 2017a, b; Shchapova, Grinchenko 2017, as well as Chapter “The Deductive Approach to Big 29

Incidentally, this is very close to the singularity of 2005 CE that we detected earlier for Maddison (2001) series of the world GDP estimates (Korotayev et al. 2006a, b; Korotayev and Malkov 2016), and that was detected even much earlier for the same date by Taagepera (Taagepera 1976) in the world GDP estimates available to him by that time. 30 This roughly corresponds to Big History Thresholds 5, 6, and 8. 31 And, thus, at least three more Big History Thresholds. 32 The earliest attempt to detect mathematically the singularity on the basis of data from the human history seems to have been undertaken in 1909 by Henry Adams who found it for year 1921 according to one version of calculations, and, according to the second version of his calculations— for 2025 CE (Adams 1969 (1909): 308)—incidentally not so far at all from 2027 CE detected by Heinz von Foerster in 1960, and by us in the Panov series just above…

54

A. V. Korotayev

History’s Singularity” in this volume (Grinchenko, Shchapova 2020)]; the singularity point was detected by him mathematically33 as 1981 CE, whereas the subsequent period was interpreted by Grinchenko as a period of deceleration of the “metaevolution rate.” Note that this correlates very well with our detection of 1973 CE as an inflection point, after which the hyperbolic acceleration of the world population growth (as well as the quadratic hyperbolic acceleration of the world GDP growth) started to be replaced in the long term by the opposite deceleration trend (Korotayev 2006a; Korotayev et al. 2010; Korotayev and Bogevolnov 2010; Akaev et al. 2014; Sadovnichy et al. 2014; Korotayev and Bilyuga 2016). This is well supported by the growing body of evidence suggesting the start of the long-term deceleration of the global techo-scientific and economic growth rates in the recent decades (see, e.g., Krylov 1999, 2002, 2007; Huebner 2005, Khaltourina and Korotayev 2007; Maddison 2007; Korotayev and Bogevolnov 2010; Korotayev et al. 2010; Modis 2002, 2005, 2012; Akaev 2010; Gordon 2012; Teulings and Baldwin 2014; Piketty 2014; LePoire 2005, 2009, 2013, 2015; Korotayev and Bilyuga 2016; Summers 2016; Taylor and Tyers 2017; Cervellati et al. 2017; Jones 2018; Popović 2018 etc.; see also Chapter “Forecasting the Growth of Complexity and Change—An Update” (Modis 2020), Chapter “Energy Flow Trends in Big History” (LePoire and Chandrankunnel 2020), Chapter “Near-Term Indications and Models of a Singularity” (LePoire and Devezas 2020), and Chapter “The TwentyFirst-Century Singularity: The Role of Perspective and Perception” (Widdowson 2020) in this volume).

Conclusion Thus, the analysis above appears to indicate the existence of sufficiently rigorous global macroevolutionary regularities (describing the evolution of complexity on our planet for a few billion years), which can be surprisingly accurately described by extremely simple mathematical functions. At the same time, this analysis suggests 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.

33

Note that for the detection of the singularity in his series Grinchenko applied a methodology that was somehow different from the methodologies used either by Panov or by me above.

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Appendices34 Appendix 1: Relationship Between the Pattern of Acceleration of the Planetary Complexity Growth and the Equation of the World Population Hyperbolic Growth As we could see above, the pattern of the acceleration of the planetary complexity growth (5) has turned out to be virtually identical with the equation discovered by von Foerster et al. (1960) to describe almost perfectly the hyperbolic growth of the global population (14). Indeed, concerning the Panov series, the equation describing the acceleration of the planetary complexity growth looks as follows (cf. Formula 11): yt ¼

C1 : 2027  t

ð16Þ

It is not difficult to see that this formula is virtually identical with the law of the hyperbolic growth of the Earth population discovered by von Foerster well in 1960 (see Eq. 15): Nt ¼

C2 : 2027  t

ð15Þ

It is easy to see that these two equations only differ with respect to the value of parameter C in the numerator. Note, however, that this acceleration pattern is not trivial at all. In the meantime, it appears important to note that, notwithstanding some fundamental similarity, the pattern of the planetary macroevolutionary acceleration (that can be traced in the Panov and Modis–Kurzweil series) differs substantially from the pattern discovered by von Foerster with respect to the world population growth. The point is that y of Eq. (16) is the global complexity growth rate, that is why equation y = C1/(2027 − t) does not describe the growth of the global complexity; it describes precisely the increase in the global complexity growth rate. And, that is why y of Eq. (16) does not correspond to the world population (N) of Eq. (15); it corresponds to the world population growth rate, whereas the equation describing the growth of the world population (N) differs substantially from the equation describing the dynamics of the world population growth rate (dN/dt). Indeed, as we remember, algebraic equation of type yt ¼

34

t

C t

ð5Þ

I would like to express my deep gratitude to Sergey Shulgin and Alexey Fomin for their invaluable help with the calculations contained in Appendices 1 and 2

56

A. V. Korotayev

can be regarded as the solution of a differential equation of type dy y2 ¼ : dt C

ð6Þ

Thus, if the world population grows according to the following law: N = C2/ (t* − t) (14), its growth rate will follow a rather different law: dN N 2 ¼ : dt C2

ð17Þ

On the other hand, substituting N with C/(t* − t) in dN/dt = N2/C we get dN ¼ dt



C  t t

2

=C ¼

C2 ðt

 tÞ

2

=C ¼

C ðt

 tÞ2

:

Thus, the world population grows35 following the simple hyperbolic law Nt ¼

C2 ; 2027  t

ð15Þ

whereas the world population growth rate increases following the quadratic hyperbolic law: dN C2 ¼ : dt ð2027  tÞ2

ð18Þ

Compare this now with equations describing the growth of global complexity. Let us (with Fomin (2020) and Panov (2004, 2005a, b)) denote the global complexity level as n.36 With such an approach, the abovementioned variable y may be denoted as dn/dt. As we remember, the global complexity growth rate (y = dn/ dt) increases in the Panov series37 following the law that is substantially different from the equation describing the dynamics of the world population growth rate (18): y¼

dn C1 ¼ : dt 2027  t

ð11Þ

Note that the solution of differential Eq. (11) looks as follows: 35

Or, to be more exact, it grew this way till the early 1970s. Note that within this perspective the level of planetary complexity at a given time will be calculated by the number (n) of “biospheric revolutions” (according to Panov–Fomin) or “complexity jumps” (according to Modis)—based on the assumption that every “complexity jump” adds to the present n one more level of complexity. 37 Note, however, that within the Modis–Kurzweil series the global complexity growth rate increases following the same law (with a slightly different value of parameters С1 and t*). 36

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Table 4 Comparison between equations describing the planetary complexity growth, on the one hand, and the world population growth, on the other Equations describing the global Equations describing the world complexity (n) growth (for the Panov population (N) growth (for the series) von Foerster–Kapitza series) Growth of global nt ¼ A  C1  lnð2027  tÞ complexity/world population Increase in the growth dn ¼ C1 ð11Þ dt 2027t rates of global complexity/world population

C2 ð19Þ Nt ¼ 2027t

dN ¼ C2 dt ð2027tÞ2

nt ¼ A  C1  lnð2027  tÞ;

ð15Þ

ð18Þ

ð19Þ

where A is a constant.38 Thus, the growth of planetary complexity (n) follows the law that is rather different from the one followed by the world population (N) growth (see Table 4): As we see, the world population (N) grew (until the early 1970s) following a simple hyperbolic law (Nt = C/t* − t), whereas the global complexity was increasing following a logarithmic hyperbolic law ðnt ¼ const  C  lnðt  tÞÞ. On the other hand, the world population growth rate (dN/dt) changed (until the early 1970s) following a quadratic hyperbolic law (dN/dt = C/(t*–t)2), whereas the global complexity growth rate was increasing following a simple hyperbolic law (dn/dt = C/t*–t). Nevertheless, the question remains—is this a coincidence that (until the early 1970s) the global complexity growth rate (dn/dt) in the Panov series and the world population (N) were increasing following the same law: xt = C/(2027 − t)? Note that calculations performed below by Alexey Fomin (2020) suggest that this might not be a mere coincidence. Indeed, Alexey Fomin (2020), in Chapter “Hyperbolic Evolution from Biosphere to Technosphere” below, brings our attention to the point that during the social phase of the Big History/Universal Evolution, the population of the Earth between each pair of “biospheric revolutions” increased about the same number of times (somewhere around 2.8) (In fact, Sergey Kapitza (1996a, b) appears to be the first to have noticed this regularity). Moreover, Fomin (2020: **) demonstrates mathematically that against this background “the increase of the world population by a factor of a is accompanied by the reduction of duration between phase transitions by the same 38 Incidentally, the calculations performed by Alexander Fomin (2020) below in Chapter “Hyperbolic Evolution from Biosphere to Technosphere” allow to identify the value of this constant for the Panov series. It turns to be equal to lnT/lna, where T is the period of the existence of life on the Earth (that can be estimated as 4 billion years) and a is “a coefficient of acceleration of historical time” (Panov 2005a: 128)/“a coefficient of reduction of the duration of each subsequent evolution phase” (Panov 2005b: 222). For more detail on the coefficient a, see below (in particular, Appendix 2).

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A. V. Korotayev

factor of a” (see also Kapitza 1996a, b). That is, if between the biospheric revolutions the population on average increases by a factor of a, then (against the background of hyperbolic growth of the world population) the intervals between each subsequent pair of biospheric revolutions will be reduced by a factor of a (it appears appropriate to recollect at this point that this coefficient a is nothing else but what Panov (2005a: 128) denotes as “a coefficient of acceleration of historical time” and “a coefficient of reduction of the duration of each subsequent evolution phase39” (Panov 2005b: 222)). At the same time, Fomin’s (2020) empirical calculations confirm that the average value of the increase in population between biospheric revolutions is approximately equal to the average value of the shortening of the time periods between biospheric revolutions. Fomin’s (2020) calculations show that both values are located within the interval 2.5–2.8, which is close enough to the value of a, empirically calculated by Panov (2.67, see, e.g., Panov 2005a: 130; 2005 b: 222). However, Fomin’s (2020) own explanation why “the increase of the world population by a factor of a is accompanied by the reduction of duration between phase transitions by the same factor of a” seems to be a bit difficult to comprehend (though in no way it can be called wrong). So, below I will try to explain the respective regularity in a simpler way. The hyperbolic growth of the world population (observed till the early 1970s) meant that it grew according to the following law: Nt ¼

C2 ; 2027  t

ð15Þ

C2 ; x

ð15’Þ

that can be also expressed as Nt ¼

where x is the time until the singularity (x = 2027 − t). The very nature of the hyperbolic growth implies that in order that the world population (N) could increase by a factor a (e.g., 3 times), the time till the Singularity should decrease precisely by the same factor a (that is, the same 3 times in our case). As a result, each new period of multiplication of N by a factor a (e.g., population tripling) will be shorter than the previous multiplication period (e.g., the previous period of population tripling) by the same factor of a (in our case—three times). However, if each period of multiplication of the world population by some factor a is accompanied by a “complexity jump/phase transition” [as has been demonstrated by Fomin (2020)], then the length of this period turns out to be just the reciprocal of the global macroevolution rate (that is defined as the frequency of phase transition per unit of time)—thus, each increase in the size of the world population N by the factor of a should be accompanied by the increase in the global complexity growth rate (y = dn/dt) by the same factor of a. Thus, we find that, against the background specified above, the dynamics of the world population (N) and the global That is a period between “biospheric revolutions”/“complexity jumps”—A.K.

39

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59

complexity growth rate (dn/dt) should be described by the same Eq. (5) (albeit, of course, with different values of parameter C). In other words, already from the fact that the average value of the population increase between biospheric revolutions is approximately equal to the average value of the shortening of time between biospheric revolutions, it follows that the growth rate of global complexity (dn/dt) should be proportional to the population of the Earth (N), and therefore N and dn/dt must grow according to one law. Indeed, as has been shown above, if N has increased by a factor of a, then the distance to the next biospheric revolution must be reduced by a factor of a too. But we calculate the growth rate of global complexity (dn/dt) just as “1” divided by the number of years between biospheric revolutions (which gives us “the number of biospheric revolutions per year”). Thus, the reduction of time between biospheric revolutions by a factor of a means by definition that the intensity of the global macroevolution rate (dn/dt) should increase by the same factor of a. This means that if the increase of N by a factor of a is accompanied by a reduction in the time between biospheric revolutions by a factor of a, and the reduction of the time between biospheric revolutions by a factor a increases the intensity of the global macroevolution (dn/dt) by a factor a, then the increase of N by a times should be accompanied by an increase in dn/dt by a factor of a, which means that N is proportional to dn/dt, and they grow according to one law. Now, let us demonstrate this more formally. Since the movement from one biospheric revolution to another is accompanied by an increase in population N by the same factor of a and an increase in the index of global complexity n by one unit, we obtain: N ¼ k  an ;

ð20Þ

where k is a coefficient of proportionality between N and an.40 Taking into account that Nt ¼

C2 ; 2027  t

ð15Þ

we arrive at: k  an ¼

C2 : 2027  t

ð21Þ

This implies the following:  C2 lnðk  a Þ ¼ ln ; 2027  t n



ð22Þ

Note that an empirical test performed by Alexey Fomin in Chapter “Hyperbolic Evolution from Biosphere to Technosphere” below (Fomin 2020) supports the hypothesis of the presence of this non-trivial relationship. 40

60

A. V. Korotayev

 lnðkÞ þ lnðan Þ ¼ ln

 C2 ; 2027  t

 lnðkÞ þ n lnðaÞ ¼ ln

n¼

ln

C2 2027t

 C2 ; 2027  t

ð23Þ ð24Þ




 lnðkÞ : lnðaÞ

ð25Þ

Differentiating expression (25), we obtain: dn 1 1 ¼  ; dt lnðaÞ 2027  t

ð26Þ

dn C1 ¼ ; dt 2027  t

ð11Þ

or

where C1 = 1/ln (a).41 Thus, we obtain analytically that if the world population (N) grows hyperbolically according to the law Nt = C2/2027 − t, whereas the ratio N = k∙an is observed between the index of global complexity (n) and the population of the Earth (N), and then the global complexity growth rate (dn/dt) will increase according to the same hyperbolic law (x = C/2027 − t) as the population of the Earth. The tests whose results are presented in this chapter demonstrate that these theoretical expectations find an unexpectedly strong empirical support (at least, I myself did not expect it to be so strong). So, the calculations suggest that the fact that, up to the beginning of the 1970s, the world population size (N) and the global complexity increase rate (dn/dt) in the Panov series grew following the same law (xt = C/2027 − t) is by no means a coincidence; it is rather a manifestation of a fairly deep pattern of the global evolution. Thus, at the social phase of universal and global history, the hyperbolic growth of the rate of increase in global complexity and the hyperbolic growth of the Earth’s population are two closely related aspects of a single process. It should be noted that this is not in bad agreement with many mathematical models of hyperbolic growth of the world population,42 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 41

Note that, among other things, our calculations allow us to establish analytically the value of the parameter C1 in Eq. (11). 42 See, e.g., (Korotayev et al. 2006a, b; Taagepera 1976; Kremer 1993; Podlazov 2000, 2001, 2002; Tsirel 2004; Korotayev and Malkov 2012; Korotayev 2012, 2013; Korotayev and Malkov 2016; Grinin et al. 2013, 2014, 2015).

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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”43) through collective learning mechanisms accelerated onset of each successive “biospheric revolution” (that usually corresponded to a new major technological breakthrough). In particular, this correlates very well with an idea that was developed long ago by Taagepera (1976, 1979), Kremer (1993), Podlazov (2000, 2017), and Tsirel (2004) who demonstrated that the global technological growth rate is to be proportional to the global population and who explained the hyperbolic growth of the world population through this point. For example, Michael Kremer notes that the “high population spurs technological change because it increases the number of potential inventors….44 All else equal, each person’s chance of inventing something is independent of population. Thus, in a larger population there will be proportionally more people lucky or smart enough to come up with new ideas” (Kremer 1993: 685); thus, “the growth rate of technology is proportional to total population” (Kremer 1993: 682). We have already mentioned that for the human part of the Big History the “complexity jumps/biospheric revolutions” identified by Modis and Panov correspond rather closely to the major technological breakthroughs in the human history (see Chapter “Dynamics of Technological Growth Rate and the Forthcoming Singularity” (Grinin et al. 2020) below for more detail); hence, for the human part of the Big History the global evolutionary macrodevelopment rate detected in their series can well be regarded as a proxy for the global microtechnological development. Thus, already the theory developed by Taagepera, Kremer, Podlazov, and Tsirel would allow to expect that for the human part of the Big History we should find a rather high correlation between the size of the world population and the global evolutionary macrodevelopment rate. However, I am sure that Taagepera, Kremer, Podlazov, and Tsirel themselves will be a bit surprised to see that their theoretical expectation finds such a strong support (r = 0.997, p < 0.001) for a test employing an apparently rather imperfect proxy of the global technological growth rate (see Fig. 21): 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. Thus, holding constant the share of resources devoted to research, an increase in population leads to an increase in technological change” (Kremer 1993: 681). Note that we are dealing here with a mechanism that is actually identical with what David Christian denotes as “collective learning” effect (Christian 2005). 44 Kremer 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. Thus, holding constant the share of resources devoted to research, an increase in population leads to an increase in technological change” (Kremer 1993: 681). Note that what is described by Kremer is virtually identical with what David Christian calls “collective learning” (Christian 2005: 146–148; 2014, 2015; Baker 2014, 2015a, b). 43

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Fig. 21 Correlation between the world population and the global macrodevelopment rate in the Panov series, scatterplot with a fitted regression line, natural scales. Source of data on the historical world population estimates: Kremer 1993: 683

In the double logarithmic scale, this correlation looks as follows (see Fig. 22): Note that we still obtain rather similar results when we use estimates developed more directly to measure the global technological growth rate. Below (see Chapter “Dynamics of Technological Growth Rate and the Forthcoming Singularity”), Grinin et al. (2020) attempt to estimate specifically the dynamics of the global technological growth rate by identifying the main phase transitions in the specific technological macrodevelopment (see also Grinin 2006). It is highly remarkable that the resultant series of estimates of the global microtechnological growth rates turn out to be described with very high accuracy by an equation of type (5) that describes so well both the macrodynamics of the world population and the planetary complexity growth rate [see below Chapter “Dynamics of Technological Growth Rate and the Forthcoming Singularity” (Grinin et al. 2020)]. Against this background, it is hardly surprising to see that this series of specific estimates of the global technological growth rates demonstrates a comparably high correlation with the world population size (r = 0.992, p < 0.001), especially for the period since the start of more reliable estimates of both the world population and global technological growth rates and till the beginning of the systematic decline of the world population growth rates (see Fig. 23). This correlation with double logarithmic scale is presented in Fig. 24.

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Fig. 22 Correlation between the world population and the global macrodevelopment rate in the Panov series, scatterplot with a fitted regression line, double logarithmic scale. Source of data on the historical world population estimates: Kremer 1993: 683

Global macrotechnological growth rate = frequency of phase transitions (per year)

4.0E-02

y = 2E-05x - 0,001 R² = 0,983

3.5E-02 3.0E-02 2.5E-02 2.0E-02 1.5E-02 1.0E-02 5.0E-03 0.0E+00

0

250

500

750 1000 1250 1500 1750 2000

World population, millions Fig. 23 Correlation between the world population and the global macrotechnological growth rate, 8,000 BCE–1950 CE, scatterplot with a fitted regression line, natural scales. Source of data on the historical world population estimates: Kremer 1993: 683; Source of data on the historical estimates of the global macrotechnological growth rate: Grinin 2006; Grinin et al. 2020 [Chapter “Dynamics of Technological Growth Rate and the Forthcoming Singularity” below]

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Fig. 24 Correlation between the world population and the global macrotechnological growth rate, 8,000 BCE–1950 CE, scatterplot with a fitted regression line, double logarithmic scale. Source of data on the historical world population estimates: Kremer 1993: 683; Source of data on the historical estimates of the global macrotechnological growth rate: Grinin 2006; Grinin et al. 2020 [Chapter “Dynamics of Technological Growth Rate and the Forthcoming Singularity” below]

It is of a special interest that Grinin’s series [see below Chapter “Dynamics of Technological Growth Rate and the Forthcoming Singularity” (Grinin et al. 2020)] demonstrates such properties that are rather similar to the ones that were found by Fomin below [see Chapter “Hyperbolic Evolution from Biosphere to Technosphere ” (Fomin 2020)] with respect to Panov’s series—the population of the Earth between each pair of phase transition tended to increase about the same number of times (a), whereas the periods between technological phase transitions tended to decrease by the same factor of a. Note, however, that Panov singled out primary phase transitions, whereas Grinin’s list includes some secondary phase transitions. Consequently, for the period since the Agrarian (Neolithic) Revolution Grinin identifies almost twice as many phase transitions as Panov. As a result, for the Panov series the value of a turns out to be close to Euler’s number (e), whereas for the Grinin’s series it appears closer to the square root of Euler’s number (√e).

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Appendix 2: On Some Patterns on Global Macroevolutionary Acceleration—Additional Calculations As has been shown by Alexander Panov45, for his series of “biospheric revolutions” one can observe the following regularity: tn ¼ t  

T ; an

ð27Þ

where “the coefficient a > 1 is a coefficient of reduction of the duration of each subsequent evolution phase comparing with the corresponding preceding one. T is a duration of the whole period of time under consideration,46 n is a number of phase transition, and t* is the limit of the geometrical progression {tn} and t* may be called as singularity of the evolution” (Panov 2005b: 222; see also Panov 2005a: 128). Note that, as we have shown above, n can also be well interpreted as a global complexity index. For further calculations, Panov (2005a: 129; b: 222) transforms Eq. (27) along the following lines: lgðt  tn Þ ¼ lgðT Þ  n  lgðaÞ:

ð28Þ

However, below Alexey Fomin in Chapter “Hyperbolic Evolution from Biosphere to Technosphere” (Fomin 2020) shows that for a further analysis of the Panov model it is better to use a slightly different version of the transformation of Eq. (27): lnðt  tn Þ ¼ lnðT Þ  n  lnðaÞ:

ð29Þ

Indeed, Eq. (29) can be rewritten as follows: n  lnðaÞ ¼ lnðT Þ  lnðt  tn Þ;

ð30Þ

lnðT Þ 1   lnðt  tn Þ; lnðaÞ lnðaÞ

ð31Þ

n¼

nt ¼ A  C1  lnðt  tÞ;

ð19Þ

where A = ln (T)/ln (a) and a C1 = 1/ln (a). At the same time, as we recall, the algebraic Eq. (19) is a solution of the following differential equation:

See, e.g., Panov 2005a, b and Chapter “Singularity of Evolution and Post-singular Development in the Big History Perspective” (Panov 2020) below. 46 As mentioned above, T can be considered as the time of existence of life on Earth and equated to 4 billion (years). 45

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dn C1 ¼  : dt t  t

ð11Þ

Thus, we obtain the same Eqs. (19) and (11), which were obtained by us earlier in a somewhat different way. Note that Panov’s calculations indicate that the value of a equals 2.67, which, as Panov notes, turns out to be very close to the numeric value of the mathematical constant e/Euler’s number (2718…), and one cannot exclude the “coefficient of acceleration of historical time” could turn out to be actually so close to Euler’s number that the parameter a in Eqs. (11), (31), and (20) may be replaced with e. In this case, the set of equations describing the hyperbolic acceleration of global macroevolutionary development rate appears particularly elegant in its simplicity. Indeed, taking into consideration the point that in the equation nt ¼ A  C1  lnð2027  tÞ

ð19Þ

A = ln (T)/ln (a) and C1 = 1/ln (a), when substituting e, instead of a, we arrive at nt ¼ ln ðT Þ  ln ð2027  tÞ:

ð32Þ

Taking into account the point that in the equation dn C1 ¼ dt 2027  t

ð11Þ

C1 = 1/ln (a), when substituting e, instead of a, we arrive at47 dn 1 ¼ : dt 2027  t

ð33Þ

N ¼ k  an ;

ð20Þ

In addition, the equation

when substituting e, instead of a looks as follows: N ¼ k  en ;

ð34Þ

Note that Fomin’s calculations in Chapter “Hyperbolic Evolution from Biosphere to Technosphere” below (Fomin 2020) indicate that if, in calculating with the help of Eq. (11), t is taken not as the moment of the beginning of the period by which the derivative is calculated, but as its middle, then the value of the parameter C1 turns out to be closer to 1 rather than to 2. See also Chapter “The Twenty-First-Century Singularity: The Role of Perspective and Perception” (Widdowson 2020) in this volume. 47

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from which it follows that n ¼ lnðN Þ  lnðkÞ:

ð35Þ

As a result, the set of equations describing the hyperbolic acceleration of the global macroevolutionary development rate turns out to be especially elegantly simple48: nt ¼ lnðT Þ  lnð2027  tÞ;

ð32Þ

dn 1 ¼ ; dt 2027  t

ð33Þ

N ¼ k  en ;

ð34Þ

n ¼ lnðN Þ  lnðkÞ;

ð35Þ

where, let us recollect, n denotes the global complexity index, T is the period of the existence of the life on the Earth (*4 billion years), N is the world population, and k is a constant. However, it appears difficult not to agree with Alexander Panov (2005a: 130) that “the question whether the point [that the value of coefficient a is so close to e] has any deep sense remains open.”

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Korotayev AV (2007b) Secular cycles and millennial trends: a mathematical model. In: Dmitriev M, Petrov A, Tretyakov N (eds) Mathematical modeling of social and economic dynamics. RUDN, Moscow, pp 118–125 Korotayev AV (2008) Globalization and mathematical modeling of global development. In: Grinin L, Beliaev D, Korotayev AV (eds) Hierarchy and power in the history of civilizations: political aspects of modernity. LIBROCOM/URSS, Moscow, pp 225–240 Korotayev AV (2009) Compact mathematical models of the world system development and their applicability to the development of local solutions in third world countries. In: Sheffield J (ed) Systemic development: local solutions in a global environment. ISCE Publishing, Litchfield Park, pp 103–116 Korotayev AV (2012) Globalization and mathematical modeling of global development. Glob Glob Stud 1:148–158 Korotayev AV (2013) Globalization and mathematical modeling of global evolution. Evolution 3:69–83 Korotayev AV (2015) Singular points of big history. Archimedes singularity. Paper presented at the 2nd international symposium ‘big history and global evolution’, 27–29 Oct 2015, Lomonosov Moscow State University. https://www.academia.edu/39090913/Korotayev_A_ 2015_Singular_Points_of_Big_History._Archimedes_Singularity._Paper_presented_at_the_ 2nd_Symposium_Big_History_and_Global_Evolution_October_27_29_2015_Moscow_ State_University._SHORT_VERSION Korotayev AV, Bilyuga S (2016) O nekotorykh sovremennykh tendentsiyakh mirovogo ekonomicheskogo razvitiya. Vestnik Instituta ekonomiki Rossiyskoy akademii nauk 4:20–39 Korotayev AV, Bogevolnov J (2010) Nekotoryye obshchiye tendentsii ekonomicheskogo razvitiya Mir-Sistemy. In: Akaev A, Korotayev AV, Malinetsky G (eds) Prognoz i modelirovaniye krizisov i mirovoy dinamiki. LKI/URSS, Moscow, pp 161–171 Korotayev AV, Goldstone J, Zinkina J (2015) Phases of global demographic transition correlate with phases of the great divergence and great convergence. Technol Forecast Soc Chang 95:163–169. https://doi.org/10.1016/j.techfore.2015.01.017 Korotayev AV, Grinin L (2013) Urbanization and political development of the World System. Entelequia. Revista interdisciplinar 15:197–254 Korotayev AV, Khaltourina D (2006) Introduction to social macrodynamics: secular cycles and millennial trends in Africa. KomKniga/URSS, Moscow Korotayev AV, Khaltourina D, Malkov A, Bogevolnov J, Kobzeva S, Zinkina J (2010) Zakony istorii. Matematicheskoye modelirovaniye i prognozirovaniye mirovogo i regional’nogo razvitiya. LKI/URSS, Moscow Korotayev AV, Malkov A (2016) A compact mathematical model of the world system economic and demographic growth, 1 CE–1973 CE. Int J Math Model Methods Appl Sci 10:200–209 Korotayev AV, Malkov A, Khaltourina D (2006a) Introduction to social macrodynamics: compact macromodels of the world system growth. KomKniga/URSS, Moscow Korotayev AV, Malkov A, Khaltourina D (2006b) Introduction to social macrodynamics: secular cycles and millennial trends. KomKniga/URSS, Moscow Korotayev AV, Malkov S (2012) Mathematical models of the world-system development. In: Babones S, Chase-Dunn C (eds) Routledge handbook of world-systems analysis. Routledge, London, pp 158–161 Korotayev AV, Markov A (2014) Mathematical Modeling of Biological and Social Phases of Big History. In: Grinin L, Baker D, Quaedackers E, Korotayev AV (eds) Teaching and researching big history: exploring a new scholarly field. Uchitel, Volgograd, pp 188–219 Korotayev AV, Markov A (2015) Mathematical modeling of biological and social phases of big history. Glob Glob Stud 4:319–343 Korotayev AV, Zinkina J (2017) Systemic boundary issues in the light of mathematical modeling of world-system evolution. J Glob Stud 8(1):78–96 Korotayev AV, Zinkina J, Andreev A (2016) Secular cycles and millennial trends. Cliodynamics 7 (2): 204–216. https://doi.org/10.21237/C7CLIO7230484

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Panov A (2017) Singularity of evolution and post-singular development. In: Rodrigue B, Grinin L, Korotayev AV (eds) From Big Bang to galactic civilizations. A Big History anthology, Volume III. The ways that Big History works: cosmos, life, society and our future. Primus Books, Delhi, pp 370–402 Panov A (2020) Singularity of evolution and post-singular development in the Big History perspective. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 439–465. https://doi.org/10.1007/9783-030-33730-8_20 Piketty T (2014) Capital in the twenty-first century. The Belknap Press of Harvard University Press, Cambridge, MA Podlazov A (2000) Teoreticheskaya demografiya kak osnova matematicheskoy istorii. IPM RAN, Moscow Podlazov A (2001) Osnovnoye uravneniye teoreticheskoy demografii i model’ global’nogo demograficheskogo perekhoda. IPM RAN, Moscow Podlazov A (2002) Teoreticheskaya demografiya. Modeli rosta narodonaseleniya i global’nogo demograficheskogo perekhoda. In: Malinetskiy G, Kurdyumov S (eds) Novoye v sinergetike. Vzglyad v tret’ye tysyacheletiye. Nauka, Moscow, pp 324–345 Podlazov A (2017) A theory of the global demographic process. Her Russ Acad Sci 87(3):256– 266. https://doi.org/10.1134/S1019331617030054 Popović M (2018) Technological progress, globalization, and secular stagnation. J CentL Bank Theory Pract 7(1):59–100. https://doi.org/10.2478/jcbtp-2018-0004 Ranj B (2016) Google’s chief futurist Ray Kurzweil thinks we could start living forever by 2029. Business Insider 20 Apr 2016. http://www.techinsider.io/googles-chief-futurist-thinks-wecould-start-living-forever-by-2029–2016-4 Reher D (2011) Economic and social implications of the demographic transition. Popul Dev Rev 37:11–33. https://doi.org/10.1111/j.1728-4457.2011.00376.x Rozanov A (1986) Chto proizoshlo 600 millionov let nazad. Nauka, Moscow Rozanov A (2003) Iskopayemyye bakterii, sedimentogenez i ranniye stadii evolyutsii biosfery. Paleontologicheskiy zhurnal 6:41–49 Rozanov A, Zavarzin G (1997) Bakterial’naya paleontologiya. Vestnik RAN 67(3):241–245 Sadovnichy V, Akaev A, Korotayev AV, Malkov S (2014) Kompleksnoye modelirovaniye i prognozirovaniye razvitiya stran BRIСS v kontekste mirovoy dinamiki. Nauka, Moscow Sagan S (1989) The dragons of Eden: speculations on the evolution of human intelligence. Ballantine Books, New York, NY Schopf JW (ed) (1991) Major events in the history of life. Jones and Bartlett Publishers, Boston, MA Shanahan M (2015) The technological singularity. MIT Press, Cambridge, MA Shantser E (1973) Kaynozoyskaya gruppa (era). Bol’shaya sovetskaya entsiklopediya. T. 11. Sovetskaya entsiklopediya, Moscow Shchapova Y, Grinchenko S (2017) Vvedeniye v teoriyu arkheologicheskoy epokhi: chislovoye modelirovaniye i logarifmicheskiye shkaly prostranstvenno-vremennykh koordinat. Moscow University, Moscow, Faculty of History Snooks GD (1996) The dynamic society: exploring the sources of global change. Routledge, London Snooks GD (2005) Big history or big theory? Uncovering the laws of life. Soc Evol Hist 4(1):160– 188 Snooks GD (2020) Is singularity a scientific concept, or the metaphysical construct of historicism? Implications for Big History. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 225–263. https://doi.org/10. 1007/978-3-030-33730-8_12 Summers LH (2016) The age of secular stagnation: what it is and what to do about it. Foreign Aff 95(2):2–9

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TK (1975) Paleozoic era, lower. In: The new encyclopedia Britanica, 15th edn, vol 13. Encyclopedia Britanica, Inc., Chicago, pp 916–920 Taagepera R (1976) Crisis around 2005 AD? A technology-population interaction model. Gen Syst 21:137–138 Taagepera R (1979) People, skills, and resources: an interaction model for world population growth. Technol Forecast Soc Chang 13:13–30. https://doi.org/10.1016/0040-1625(79)90003-9 Taylor G, Tyers R (2017) Secular stagnation: determinants and consequences for Australia. Econ Rec 93(303):615–650. https://doi.org/10.1111/1475-4932.12357 Teulings C, Baldwin R (eds) (2014) Secular stagnation: facts, causes, and cures. CEPR, London Tsirel S (2004) On the possible reasons for the hyperexponential growth of the earth population. In: Dmitriev MG, Petrov AP (eds) Mathematical modeling of social and economic dynamics. Russian State Social University, Moscow, pp 367–369 UN Population Division (2020) United Nations population division database. United Nations, New York. http://www.un.org/esa/population Vishnevsky A (1976) Demograficheskaya revolyutsiya. Statistika, Moscow Vishnevsky A (2005) Izbrannyye demograficheskiye trudy, vol 1. Demograficheskaya teoriya i demograficheskaya istoriya, Nauka, Moscow Weinberg S (1977) The first three minutes: a modern view of the origin of the universe. Basic Books, New York, NY Widdowson M (2020) The 21st century Singularity: the role of perspective and perception. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 489–516. https://doi.org/10.1007/978-3-030-33730-8_22 Wong K (2003) U kolybeli Homo sapiens. V mire nauki 11:9–10 Wood B (1992) Origin and evolution of the genus homo. Nature 355:783–790. https://doi.org/10. 1038/355783a0 Zavarzin G (2003) Stanovleniye sistemy biogeokhimicheskikh tsiklov. Paleontologicheskiy zhurnal 6:16–24 Zaytsev A (2001) Kul’turnyy perevorot v Gretsii VIII–V vv. do n.e. Petropolis, Saint Petersburg Zinkina J, Korotayev AV (2017) Sotsial’no-demograficheskoye razvitiye stran Tropicheskoy Afriki: Klyuchevyye faktory riska, modifitsiruyemyye upravlyayushchiye parametry, rekomendatsii. Lenand/URSS, Moscow Zinkina J, Shulgin S, Korotayev AV (2016) Evolyutsiya global’nykh setey. Zakonomernosti, tendentsii, modeli. Lenand/URSS, Moscow

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 Center 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.

Exploring the Singularity Concept Within Big History David J. LePoire

Basic Questions Basic questions concern definitions related to singularities, fundamental causes, behaviors of trends that might lead to its occurrence, and possible substructures or processes leading to a singularity including the interplay between energy, information, and entropy. We will also determine if the pattern of growth leading to and predicting a singularity can be based on a mathematical model. Importantly, the assertion that a singularity is happening or about to happen is not claimed. Instead, a description of what might be happening is explored with simple models and empirical data. These general topics are not usually found in an analysis of historical events (Christian et al. 2014), but as later described, this singularity trend might be viewed in physical terms as a complex adaptive system (Jantsch 1980; Chaisson 2004) far from thermal equilibrium. This means that useful energy continually flows through the system (from the sun) which can be used to maintain, reproduce, and evolve the system over time, while also effectively managing its associated waste (entropy).

What Is the Definition of a Singularity? The pattern of accelerating rates of change from the beginning of life on Earth to the present state of ever more rapid technological change has motivated various interpretations [(Panov 2011, Modis 2002, Kurzweil 2005, LePoire 2015; Korotayev 2018; see also Chapter “The Twenty-First Century Singularity in the Big History Perspective. A Re-Analysis” (Korotayev 2020), Chapter “Forecasting the D. J. LePoire (&) Argonne National Laboratory, Lemont, IL, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 A. V. Korotayev and D. J. LePoire (eds.), The 21st Century Singularity and Global Futures, World-Systems Evolution and Global Futures, https://doi.org/10.1007/978-3-030-33730-8_3

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Growth of Complexity and Change—An Update” (Modis 2020), Chapter “Hyperbolic Evolution from Biosphere to Technosphere” (Fomin 2020), Chapter “Big History and Singularity as Metaphors, Hypotheses and Predictions” (Tsirel 2020a), Chapter “Big History Trends in Information Processes” (Solis and LePoire 2020), Chapter “Dynamics of Technological Growth Rate and the ForthComing Singularity” (Grinin et al. 2020), Chapter “The Twenty-First Century’s “Mysterious Singularity” In the Light of the Big History” (Nazaretyan 2020), Chapter “Singularity of Evolution & Post-Singular Development in the Big History Perspective” (Panov 2020), Chapter “The Twenty-First Century Singularity: The Role of Perspective and Perception” (Widdowson 2020), Chapter “About the Singularity in Biological and Social Evolution” (Malkov 2020), Chapter “The Transition to Global Society as a Singularity of Social Evolution” (Dobrolyubov 2020), and Chapter “Evolution, the ‘Mechanism’ of Big History, Predicts the Near Singularity” (Torday 2020) in this volume]. These interpretations include a continuing of the acceleration with a rapid advent of artificial intelligence machines and or technologically enhanced human capabilities. Others argue that while progress to these technologies continues to occur, it might happen at a slower pace after the rate of change reaches a peak. These interpretations are based on the different ways the current pattern might continue. The acceleration pattern seems to follow a simple mathematical form [(Kremer 1993; see also Chapter “The Twenty-First Century Singularity in the Big History Perspective. A Re-Analysis” (Korotayev 2020) and Chapter “Hyperbolic Evolution from Biosphere to Technosphere” (Fomin 2020) in this volume] with the progress being proportional to 1/(ts – t) where ts = time of the singularity and ts – t is the time until the singularity. The mathematical continuation of this pattern toward the ts predicts ever-increasing rates of change which becomes infinite at the time of the singularity. While this is not physically possible, some expect the trend to continue to rates of change much more rapid than today [see, e.g., Chapter “The Twenty-First Century’s “Mysterious Singularity” In the Light of the Big History” (Nazaretyan 2020) of this volume]. However, other limits such as energy and rate of social adaptability might already be curtailing the rate of change (Linstone 1996), so that although change will continue, it will be at a slower, perhaps even much slower rate [see, e.g., Chapter “The Twenty-First Century Singularity in the Big History Perspective. A Re-Analysis” (Korotayev 2020), Chapter “Forecasting the Growth of Complexity and Change—An Update” (Modis 2020), Chapter “The Deductive Approach to Big History’s Singularity” (Grinchenko and Shchapova 2020), Chapter “Singularity of Evolution & Post-Singular Development in the Big History Perspective” (Panov 2020), and Chapter “The Twenty-First Century Singularity: The Role of Perspective and Perception” (Widdowson 2020) of the present collective monograph].

What Type of Simple Model Has a Singularity Behavior? As more is known and applied in the computer sciences and other relevant technological and scientific fields, more combinatorial and complex technologies

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become ever more possible to construct new devices to learn even more. For example, the modern smartphone is an amalgamation of telephone, camera, video recorder, and computer that can be carried in one’s pocket, whereas only a few decades ago, a much less advanced computer alone was the size of a room. This is an example of technological positive feedback loops of innovation, where one discovery and implementation led to more discoveries and implementations. The interest on a savings account is a similar example of a positive feedback loop, and the more money in an account the greater the interest payment and the quicker the account balance rises. This can be captured mathematically as dy/dt = ky (i.e., the rate of increase of money in the account (dy/dt) is proportional to the interest rate (k) and the current amount of money in the account (y) which leads to exponential growth. With this type of growth, the amount doubles in a fixed duration. For example, at 7% annual interest the money doubles about every 10 years. However, while the recent exponential rate of computer innovation, e.g., Moore’s law—doubling of computing power every 2 years, might continue (Kurzweil 2005), it does not lead to a singularity where the growth is unlimited within a finite time. To obtain this type of growth, there must be another component to the feedback. For example, if the interest rate also increases with the amount in the account, then the equation for growth would be dy/dt = (ky) y = ky2. The solution to this is very simple: y = A/(ts – t) with a singularity at time ts. In the case of human population growth, one hypothesis is that population growth rates are proportional to the product of the current population and the current technology level (Kremer 1993). If the technology level is considered to be proportional to the number of people, the resulting model is similar to the savings account with interest rate being dependent on the size of the account, i.e., leading to a singularity trend. The historical population shows such a pattern over a long period of time with deviations due to famine, disease, war, and natural disasters [see Chapter “The Twenty-First Century Singularity in the Big History Perspective. A Re-Analysis” (Korotayev 2020), Chapter “Hyperbolic Evolution from Biosphere to Technosphere” (Fomin 2020), Chapter “Dynamics of technological growth rate and the forth-coming Singularity” (Grinin et al. 2020), and Chapter “About the Singularity in Biological and Social Evolution” (Malkov 2020) in this volume for more detail]. There are some other related simple models that might be useful to understand the growth patterns seen in other systems. In business, the transition from an older product to a new, improved product is often described by a logistic curve (Marchetti 1980). With this example, the new product’s initial growth in the market is exponential because its market share is small and there are many potential new customers. However, the growth rate slows as the market becomes saturated with the new product. This type of growth curve is called a logistic curve, or because of its shape, the “S” curve. Because it describes the transition in a system as information about the product is distributed or learned, it is also called a “learning curve.” Another example is how gossip is spread among a group of people. If one person has the information they can initiate a quick chain of gossip spreading as one person tells two, those two each tell two others to make 4 and so on in an exponential manner. Eventually, someone will try to spread the gossip, only to find that

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they are telling people that already know the information. The rate of the spread of the gossip is proportional to the product of the fraction of people that do not know and the fraction of people who already know. This slows down the spread of the gossip such that the equation is now dy/dt = ky(1 – y). We see that this formula is quite similar to both the exponential growth and singularity growth equations.

What Is Driving the Rate of Change and Complexity Increase? An essential resource that drives the growth in an individual is food. Food provides the energy captured, at least initially, from the sun by plants that in turn helps keep the biological systems operating and to forestall the natural tendencies of non-living systems to become more disordered with time due to entropy. Of course, edible food is but one form of useful energy. In a technological civilization, energy from many other sources such as fossil fuels, wind power, fast-flowing water, and nuclear fission (Smil 2010) is also used in the same way—to grow, to maintain, and to organize societies. High energy flow density was identified as a major driver in biological and cultural systems by Chaisson (2004) and others [(Ayres et al. 2007; Kummel et al. 2010; Fox 1988; Niele 2005; see also Chapter “Energy Flow Trends in Big History” (LePoire and Chandrankunnel 2020) in this volume). The hypothesis that complex systems evolve by capturing more energy flow, growing, and periodically reorganizing to mitigate the effects of environmental degradation is consistent with thermodynamics (Schneider and Kay 1994) where there is an external energy source (e.g., the sun). This growth requires the capture and utilization of the energy flowing from the sun before it is reradiated out into space at a lower temperature, which has the requisite higher degree of entropy. This energy flow is utilized by biological systems in the environment to periodically reorganize to a higher complexity. This non-equilibrium organization, however, also contains the seeds of its own destruction since eventually greater energy flow leads to nonlinear problems caused by limited resources and environmental challenges like disease, pollution, and resource depletion (Chase-Dunn and Hall 1997; Homer-Dixon 2006; Tainter 1996). This perhaps is resolved by continuing the process of growing, capturing more energy flow, and reorganizing.

What Is the Role of Energy, Information, and Entropy? As already noted, systems that evolve to greater complexity require ever larger energy flows to maintain the organization and growth. These larger energy flows often require new sources of energy to be identified and controlled (by applying information in the form of experience and reasoning to decisions). Initially, the new energy source’s wastes (entropy) are easily handled, often by distributing them among the environment (Smil 2010; Ponting 2007). However, as the system grows in numbers, new environmental impacts of the increased energy flow are no longer easily handled. This quantitative shift results in a limited capacity for system

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growth as any attempts to easily modify one part of the system lead to nonlinear side effects in other aspects (Grübler et al. 2002; Kummel et al. 2010; Tainter 1996). As the growth of the system is slowed, solutions (based on new technology, energy, and information) and organizational patterns are sought to solve the problems. A variety of solutions are proposed and tested by nature, organisms, and eventually, humans (Morowitz 2002). Ultimately, one system is identified that has the best prospect for growth (natural selection). This continues the development process into the next phase. For example, in the transition from hunter-gatherer to agriculture (Diamond 2005), hunting required more land but as the population slowly grew alternatives to hunting were explored especially in stressful situations (e.g., sudden climate change). Through many years, the groups identified plants and animals for domestication and selection which allowed a higher energy flow (cultivated food) and subsequently increased population density. Since the new agricultural lifestyle produces more food for higher growth, the pressure on the hunter-gatherer lands increased, leading more people to switch to agriculture. However, as agriculture villages grew, new problems arose such as disposal of the waste, storage and protection of the excess, recording property and contracts, and maintaining sustainable soil to name a very few of the newly created challenges. Eventually, as more villages are founded, conflicts over land and access to water and resources increased. The organization reached the limit of resources and environment. The events in this transition follow a logistic pattern as seen in the graph below (LePoire 2020a) (Fig. 1). This led to the next step of energy, organization, experience (information), and environmental modifications as some villages group and reorganize with a hierarchy to support new functions such as rules, defense, and common understanding (e.g., religions, common myths) which starts the next subphase of civilization with some of the energy now supplied by forced labor of captured villagers who had not formed a higher level of organization.

Fig. 1 Example of logistic transition based on empirical evidence

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Is There Substructure in the Trend Leading to the Singularity? One interpretation of Big History (Spier 2010; Snooks 2005) is that the three major stages discussed before—life, humans, and civilization—form the first half of an accelerated learning (or logistic or “S”) growth pattern (LePoire 2015). These three major stages started at about 5 billion, 5 million, and 5 thousand years ago. (While more precise times are known for the beginning of the universe at 13.8 billion years ago, and the formation of the Earth at 4.54 billion years ago, this paper works with geometric factors, so an approximation on a logarithmic scale is used. The approximations are within 10% of the more precise values. Also, the beginning of each of the stages is uncertain and often not well defined, so the times chosen are close to the Earth formation, the splitting of the evolutionary branch that would lead to humans from the other apes, and the formation of multi-city states with hierarchy.) Each stage developed over 6 (nested) steps with each subsequent step being about a third the duration of the previous [(LePoire 2018); note here some striking parallels with Panov’s findings—see Chapter “Singularity of Evolution & PostSingular Development in the Big History Perspective” (Panov 2020) in this volume]. These 6 steps then make the stage’s geometric acceleration factor the sixth power of 3, which is about 1,000, as seen in the pattern of stages above (actually, the step factor would be the square root of 10 which is about 3.14, but it is rounded to 3 for convenience). Furthermore, the duration of the universe from the Big Bang to the present is approximately one step factor (3) larger than the history of the Earth, although this step is quite different in that the evolution takes place through cooling and gravitational attraction rather than through natural selection evolution. One perspective is that the 4 stages occur sequentially with each stage starting with an expansion phase followed by a focusing phase (Fig. 2). The expansion phase concerns exploration a new environment by building larger units (e.g., from unicellular to multi-cellular life-forms). The remaining half of the stage can be viewed as focusing major change within a unique part of that environment (e.g., planets, forests). These stages have some overlap in time but can be viewed as happening sequentially. To gain a perspective on these factors, if the time values of the 3 major stages are plotted on a line (i.e., 5 billion, 5 million, 5 thousand) with the line being 1 km long which represents the age of Earth, then the development of humans would start at 1 m from the end. All of written civilization history would occur in the last 1 mm. If the time between the Big Bang and Earth formation was added, the line would be about 3 km. A human generation scale of 50 years would be 10 micrometers, less than the width of a hair.

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Fig. 2 Expansion and focusing phases of evolution (LePoire 2020b)

Detailed Questions What Are the Potential Indicators of How the Singularity Will Behave? While the trend leading up to the singularity is long, the determination of the possible singularity scenarios (e.g., ever accelerating, slowing down, stabling at

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constant pace) should be known relatively soon, within a generation. This is because the rate of change is already at that of a generation, so comparing the rate of change in this generation to the next would give an indication of possible long-term behavior (Devezas et al. 2005). Some leading indicators, i.e., those areas which are needed to cause change in further developments, should start to show different patterns before the singularity. One such field is scientific understanding. While the biological discovery rate seems to be accelerating, the discoveries in fundamental physics seem to be slowing and might be demonstrating a logistic growth pattern starting from the early controlled experiments of Galileo to the peak change of physics in the 1920s and 1930s with the developments in general relativity, nuclear science, and quantum mechanics, followed by slower progress in particle physics and the current uncertainty in research directions (LePoire 2005). Indicators would also include the major factors in the system driving the singularity trend, i.e., energy use, population, economics, and environment. Transitions are well underway in many of these. In energy use, the transition from fossil fuels to sustainable energy (renewable and nuclear) (LePoire 2004, Devezas et al. 2008) is coupled with the first major global environmental impact of potential climate change. A related trend is the slowing of the population growth rate (Korotayev et al. 2006). This is important because greater economic benefits tend to decrease the birthrate, and it also causes higher energy consumption. A fundamental correlation between the rate of population growth and economic growth was recently discovered (Korotayev et al. 2015). As the rate of new innovations slows down, there is more opportunity for the technology to diffuse to other regions. If the rate of innovation continually increased, it would tend to occur at the location of previous innovations, since there would be little time for diffusion. This relative rate of innovation and diffusion in fundamental R&D seems to be diffusing as many countries contribute higher fractions of discoveries (Global Sherpa 2011). However, the concentration of innovation in electronics and Internet technologies in the Silicon Valley demonstrate that these fields seem to still have a greater innovation rate than diffusion.

When Might the Singularity Occur? The earlier chapter by Korotayev in this volume (Korotayev 2020; see also Korotayev 2018) reviews many of the predictions over time when a singularity might occur. However, there are some cases where multiple singularities might be happening (Magee and Devezas 2011; Devezas et al. 2008). Also with the definition used in this chapter, a singularity might be hardly noticeable at the time because it may just be a peak of innovation rate (an inflection in technology). There might be other ways to define the innovation change rate, such as the relative rate of change versus the absolute change rate. For example, Aunger (2007) identified the early twentieth century with a peak of patents per person. During this time, the qualitative change rate was large with the introduction of innovations that

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fundamentally change the way of life such as cars, planes, household appliances, and distance public communication such as radio. While we might be able to investigate trends (as above) to get some indications of how the singularity will behave, it might take much longer to analyze the details of the characteristics of the singularity, for example, analysis of the number, the times, and the negative feedback mechanisms that limit the rate of change.

What Models and Metaphors Apply to the Singularity and Associated Transitions? While detailed complex adaptive system models might eventually reproduce details of transitions, simpler more qualitative models might provide more insights. For example, simple analogies and models can provide insights into the historical human civilization transition sequence of hunting/gathering, farming, cities/ civilizations, global commerce, industrial, and potential future sustainability (LePoire 2018). It was hypothesized that the overall logistic trend is composite, formed by nested logistic growth in phases indicative of progressive learning (LePoire 2015). This growth might also be viewed as a behavior exhibited by a complex adaptive system (Kauffman 1995). As these systems develop further from equilibrium toward critical states, the systems spontaneously may bifurcate into two potential discrete states. The growth between the bifurcations might exhibit recursive logistic growth (Fig. 3). In the evolution of civilization, it seems like one period which solves a problem of the previous, then grows, and is prosperous until some limit is reached causing problems. Searches then begin for alternative ways of organizing, leading to the end of the period and the beginning of the next. Some of these problems are due to the larger populations with corresponding issues in providing and controlling energy and wastes. The old solutions no longer work, so this demands reform,

Fig. 3 Relationship to bifurcations in complex adaptive systems

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reorganization, and new understanding [(Morowitz 2002; Perry 1995; Tainter 1996; Gunderson 2002); see also Chapter “The Twenty-First Century’s “Mysterious Singularity” In the Light of the Big History” (Nazaretyan 2020) and Chapter “Singularity of Evolution & Post-Singular Development in the Big History Perspective” (Panov 2020) in this volume]. For example, many energy sources can be very dangerous without proper control such as (1) early humans figured out how to control natural fires which could have easily destroy their environment without proper care, (2) agricultural villages enabled greater food production but generated larger environmental issues in human waste disposal and diseases, and (3) current energy sources generate large amounts of pollution such as CO2 and nuclear waste. Various qualitative models have been suggested in for major historical social and technological transitions (Diamond 2005). Many of these transitions still have puzzling aspects such as the early transition from hunter-gatherer to agriculturally based society which required dramatically increased work expenditure. Explorations of simple models might lead to insights of the unique aspects of each transition. Topics include the transitions between hunter-gatherers, agricultural societies, early civilizations, market development, industrialization, and sustainable societies using analogies to raindrop formation, market consolidation, prairie fires, chain reactions, and rocket launching (LePoire 2018). An evolving technological society might be viewed as a launching of a rocket into orbit. A rocket, once launched, needs to reach a critical velocity and height before obtaining a sustainable orbit. Once a stable orbit is attained, there are many further beneficial options such as space observations or facilitating further space exploration. The basis for the metaphor is that there are two stationary states for the rocket—the ground and a stable orbit. The ground is analogous to the historical situation of a society based on traditional solar energy for crop growth, warmth, wind, and water. The stable orbit is analogous to an improved situation of an advanced society with more freedom, comforts, and fulfillment, which is also stable through technologically capturing a larger fraction of the solar energy (or supplementing it with nuclear fission or fusion).

Why Does the Substructure Follow a Mathematical Pattern? So, what is the origin of the factor of 1,000? The answer should lie within the capacity of the information system to support the needed organizational changes. This can be seen in the three previous information systems of DNA, brain, and writings/culture. The genetics of animals evolved to fit their environment. It was not an active part of the animal (Lamarckian evolution although some aspects, like epigenetics, might be valid). Instead, it seems like random mutations which are formed and tested with natural selection. This is good to develop advantages in speed, armor, teeth, and claws but not too helpful in developing collaborative strategies which require collective memory, communication, and predictive planning. A more volatile but responsive information system developed with the brain, especially in humans, which required a long period of time for guided development

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of newborns. Also, employing a generalist approach to food gathering led to an approach to collaborate by using the available resources in the environment including tools such as plants, stones, bones, and clay. Later writing and technological development occurred when agricultural villages required greater collective learning over a wider area (Devezas and Modelski 2003). An early estimate (Sagan 1977) was that the information available from DNA peaked and was supplemented by the higher capacity brain system in animals leading to human development. This peaked later leading to further supplementation by writing. The limits of the information capacity seemed to be a factor of 1,000 between the DNA and brain systems. However, capacity is but one aspect of information processing. There is also the speed of information transfer (e.g., DNA transcription vs. neuronal firing rate) and qualitative differences (e.g., syntactical vs. semantic information processing). A few recent approaches to applying thermodynamics to evolving systems might supply insights to these factors. Bejan (2011) developed the constructal law and constructal theories to explain how systems out of equilibrium, i.e., energy flowing through the systems, evolve to best intercept the useful energy before the energy is completely converted into heat. This was applied to animal dynamics, sports, economics, river flow, and conventional engineered systems. As their energy flow increased, the systems periodically change in organization with increased ability to deal with the entropy caused by the increased energy flow. Another approach to explain the factor of three is given by Jose Faixat (2011) who considers that the first step sets the timescale. The logistic development of this phase consists of the initial rapid growth followed by a similar duration phase of slower growth limited by the capacity of the system. He then considers what would happen if this cycle period was continued in a fractal manner, i.e., a second harmonic of the initial phase. This leads to the factor of 3 found here and by others [e.g., Panov 2011; Snooks 1998; see also Chapter “Singularity of Evolution & Post-Singular Development in the Big History Perspective” (Panov 2020)]. The factor of 3 in each step along with the number of nested steps (6) found in the history of physics development would be consistent with the stage time factor of 1,000. The growth of energy flow (Niele 2005) in the evolving system should increase faster than the population since it is expected that the energy intensity (energy flow per unit) increases. For example, warm-blooded animals need more energy flow to regulate temperature at night. In human development, the use of fire allowed the energy of modern humans to be directed more toward the brain than the digestive system since the cooking did a large part of the energy-intensive digestion process. While others have focused on the energy flow per mass of material and successfully applied it to the complexity classification of natural and engineered systems (Chaisson 2004), an alternative measure is the amount of energy (free energy, exergy, or useful energy) that flows through the evolving system. At first, the system was relatively small. For example, a hydrothermal vent is one location identified as a possible place for life to first develop. One typical vent has a chemical potential energy flow of a few kilowatts of which only a small fraction is

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used by life-forms. The amount of power used in the world today (2  1013 W) is about 10 billion times larger than a typical hydrothermal vent. Another insight might be gained by comparing the base human metabolism (roughly 100 W) to the average energy intensity (energy per person) today in the USA (10 kW) which is 100 times larger. With this factor, the energy per person would have to expand by about 1.5 times faster than the population over the 11 steps during the evolution of humans and civilization. Since the population growth factor is about 3 per step, the overall energy flow from increasing population and energy per person would be about 4.5. This gives a possible indication that the system is a complex adaptive system (CAS) (Jantsch 1980) since the universal constant for their ratio of driving parameter is the Feigenbaum number of about 4.67. This could indicate that the system is behaving like an evolving CAS, where the steps occur when the overall energy flow in the system increases by about 4.5, but then accounting for the increase in energy intensity, the population grows by a smaller factor of 3 for each step.

Extension Questions What Is the Near-Term Impact of the Singularity Trend? One extension of the pattern is that the rate of change starts to reverse itself after the singularity as a logistic growth pattern does near the middle of the phase, i.e., instead of an accelerating rate of change, the rate of change might stall (although the change continues at first at a rapid pace) and then might slow (Nazaretyan 2017; Ausubel 1996; Linstone 1996). Besides the logistic pattern, there are natural systems with limited capacities that tend to follow a pattern of increasing complexity but then reverse the complexity before going into chaos (Stone 1993). This would mean a period of simplification. Just slowing down the rate of change would be a simplification since products and training would last longer. For example, the increasing introduction of IT systems now barely gives the users enough time to learn the new features and idiosyncrasies of new systems before they are replaced with another to be learned. One way to project what a logistic world would look like after the inflection point would be to mirror past rates of change. For example, if 2000 was the inflection point, meaning that technological change continues for a while at the same rapid progress but does not accelerate, then the twentieth century might be a good indication of the level of changes we might expect in the twenty-first. In the twentieth century, there was such growth in population and resource use to move the world beyond sustainability. The major energy supply was from non-renewable fossil fuels. The expansion was driven by relatively inexpensive energy, new insights from physics leading to electrical, aerodynamic, and material technologies. These innovations led to creative destruction in capital formation and development as exemplified by the semiconductor industry which followed Moore’s law where

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they had to foresee 3 generations of electronic advances (about 6 years) to maintain continual revamping their manufacturing and design technique to maintain competitiveness. The technology also caused problems such as arms races and environmental impacts. The twenty-first century might adjust to the slowing down to a more sustainable society with more efficient energy use, a stable or declining population, reduction in the gap between incomes, and exploration of ways to mitigate global environmental impacts while maintaining robust fair trade.

What Might the Far-Future Look like if the Trend Continues? A possible overall trend of the Big History might be viewed as consisting of three spirals on one side of a double cone representing the evolution of life, mind, and human civilization (Fig. 4) (LePoire 2015). Each spiral would consist of six to seven nested smaller logistic growth phases with time durations decreasing by about a factor of three. The astronomical period before life began (i.e., 13.8 billion to 5 billion years ago) is a factor of three times the duration represented in the cone. This period was driven by gravitation and expansion as the universe’s temperature dropped, at first quickly but then slowing down. This can be represented by a cone pointed in the opposite direction. After the inflection point, a reflection in the duration of phases might occur. For example, the next hundred years after the inflection would have a technological development rate about the same as preceding century. However, after that the rate of change would slow. Instead, one of the next phases after achieving sustainability would be to integrate biological and computer technology in order to extend our capacity to learn, discover trends in complex systems, and solve problems. If the slowdown does take place, part of its reason is because the issues become too complex, but the process of slowing down actually helps simplify the problems since there is less need to account for the effects of obsolescence and changing environment.

Fig. 4 Speculative cone of history (left) with possible symmetric extension on right. After the Big Bang, events started to slow down (widening). After life formation, events started to speed up (narrowing) in three phases

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But in the longer-term future of millions and billions of years, what would people be doing for such a long time (Vidal 2008)? Well, perhaps evolution will continue with the artificial intelligence in which time passage is more easily handled. Panov (2011); see also Chapter “Singularity of Evolution & Post-Singular Development in the Big History Perspective” (Panov 2020) in this volume) considers galactic communication as a next stage; however, this would not be true interactive communication since the time between sending and receiving a message across the galaxy would require a few hundred thousand years.

Are There Trends in Worldviews? Historical trends in worldviews have been articulated by Clare Graves among others (Beck 1996). The general trend is for the worldviews of groups to evolve emphasis with societal changes and knowledge. The sequence identified was assigned colors starting with the beige survival strategies, to red power-based empire worldviews, to the more encompassing flexible nature-based worldview. The changes in worldviews tend to be slow often requiring generations of slow change to be accepted. At any one time, there is a mixture of worldviews among various groups and its dynamics are very organic. But the whole population does not change at once and even individuals might display characteristic of a variety of worldviews in different situations. Interpretations of the trends vary, but it is expected that worldviews evolve by incorporating new knowledge along with uncertainties.

Did the Far-Past of Cosmological History (Before Earth) Show Similar Trends? To address the attempt in Big History to integrate all aspects of history, we also need to explore the timescale and development of the universe from the Big Bang. The characteristics of the timescale and structure formation are quite different. The geometric acceleration of evolution on Earth was previously discussed; however, the majority of time occurred between the Big Bang and the Earth formation is not included in this pattern. Many of the important events happened early after the Big Bang, followed by a long period of structure formation due to gravity. Is there a pattern in this contrasting deceleration rate of events? Life’s evolution required a supporting physical environment provided through cosmic events starting from the Big Bang. An example is the formation of the Earth in a solar system in the middle of the galaxy’s arm. This area provided an appropriate gravity, chemistry mixture, including water, sunlight, and rotational and orbital stability, enhanced by the effects of a large moon, while it enabled Earth to maintain a safe distance from more chaotic and dangerous galactic objects near the galactic center. The ability to form more complex structures was enabled by free energy left over from the Big Bang in the form of gravity and nuclear forces which

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did not have the time to reach equilibrium—that is, energy was still available in the gravitational attraction and in the hydrogen that did not fuse into helium during the Big Bang. The development of universe structure to support life on Earth took about 10 billion years from the Big Bang. The long period was needed for gravity to form structures of galaxies and stars and for generations of stars to process some of the hydrogen into heavier elements such as oxygen, carbon, silicon, and iron (Royal Astronomical Society 2012). Things happened very fast from the universe’s beginning. Steven Weinberg’s book The First Three Minutes (Weinberg 1993) highlights how much of the universe’s form and structure was determined early after the Big Bang. However, from a relative time view, the major events summarized below were separated in time by factors of a million—that is, between events, the universe aged by factor of a million. The Big Bang starts with the formation of space-time within the fundamental Planck time of 10−43 s. It then soon undergoes inflation, generating a smooth, very hot universe such that the forces are indistinguishable and no particles can bind together. Then as temperature drops, the forces tend to freeze, resulting in their current properties, with gravity first followed by nuclear, electromagnetism, and the weak force. All this is currently believed to have happened within the first fraction of a nanosecond of the universe. Once the temperature drops such that the binding forces cannot be broken, particles can form structures that are more complicated. For example, quarks combine into protons and neutrons, which in turn combine to form nuclei, which combine with electrons to finally form atoms 380,000 years after the Big Bang. The timescale of these events seems to increase by a factor of a million with the exception of primordial nucleosynthesis (the event near three minutes) and a large energy gap between the grand unification and electroweak transitions (the Hierarchy Problem) (Hossenfelder 2018), although there are many speculations about what might occur in this corresponding energy range. The slowdown continued. As the universe expanded, the temperature rapidly decreased. It then took about 400,000 years for the universe to cool off enough for stable atoms to form, disentangling light from matter. It then took a much longer time for the small force of gravity to enhance the small differences in density into clumps of matter that would form early galaxies and stars at least by 1 billion years after the Big Bang. As the universe cooled, more subtle and delicate phenomena emerged, such as planets and life.

What Are the Conditions (e.g., on Other Worlds) that Lead to a Singularity Trend? Panov (2011); see also Chapter “Singularity of Evolution & Post-Singular Development in the Big History Perspective” (Panov 2020) in this volume) has written on the possibility of civilization after the inflection (or singularity). He also sees the need for civilization to follow a different path toward sustainability and slowdown. He describes the period as a polyfurcation in which many paths are identified and tested. He describes the scenario of an intensive development of

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humans, for example, developing and adapting to the new technology in a more peaceful and fair way but also the limits of science to generate knowledge at the rate we have been experiencing. He offers the specific scenario of participating in a galactic communication. His thinking on this is that the trends so far explored work well from the prokaryotic life on Earth. However, a major event of the development of life from chemicals wither happened very fast on Earth or was part of a much longer development through the galaxy. Only the second scenario would fit in the trend, leading to life developing over about 6 billion years before the Earth formed. (Another potential indication of life forming on other places besides Earth is the analysis of DNA mutation rate. Based on the rate and length needed to support various animals throughout evolution, the extrapolation back to the first short segment of DNA should extend back billions of years before the Earth formed (Markov et al. 2010; Sharov 2013). If it takes this long for life to develop on a planet, then it might be dispersed through the galaxy from a supernova near the planet, dispersing life into the galactic dust. The time for this to spread throughout the galaxy might be estimated based on the galactic rotation of stars through the gas which takes about 200 million years, which is consistent with the time from the formation of Earth to the earliest fossils. The life material would fall on a large range of potential planets and continue development. Some planets would only be able to support to a certain level, but others like Earth would be able to evolve to intelligent beings and a technological civilization. If the time periods follow the same laws as on Earth, then the planets would be synchronized to within 200 million years. Two hundred million years is still quite a long time especially with the technological progress made in the last couple of centuries. However, if the progress rate slows down, it might take an equivalent amount of time to discover technologies to collaborate among the various galactic civilizations. Some of the major events to be accomplished are the transition to sustainability, the inclusion of computer technology along with humans for physical, logical, and memory in decision making. What would people be doing for such a long time? Well, perhaps the evolution will continue with the AI in which time passage is more easily handled. Panov considers galactic communication as a next stage in which we might be able to tap into thin beam transmissions and participate by sending our information out. However, this would not be true interactive communication since the time between sending and receiving a message across the galaxy would require a few hundred thousand years (about double the diameter of the galaxy measured in light-years). Instead, one of the next phases after achieving sustainability would be to integrate biological and computer technology in order to extend our capacity to learn, discover trends in complex systems, and solve problems. If the slowdown does take place, part of its reason is because the issues become too complex, but the process of slowing down actually helps simplify the problems since there is less need to account for the effects of obsolescence and changing environment. Other questions deal with the situation where the transitions might not have been possible given the resources in the environment. For many of the transitions, there

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were many independent trials being tested. Again, in evolution, the trial that succeeds is the one that can propagate the best. This could be seen in the transitions to civilization—many early successes have been documented although many in the New World such as the Mayans and the Mississippian civilizations seemed to collapse after a long successful development (Tainter 1996). This could be a bit disconcerting in that the major transition now, there seems to be only one system left, the global system. If there is only one attempt at this transition, then missing it through lack of learning or resources might cause the process to stop. For example, much of the progress of the past century has been supported by the use of easily extracted fossil fuels. If the transition to a new sustainable society is not achieved before either the fossil fuel resources are too diminished or their use has caused irreparable harm to the environment, a second chance might not be an option. The nonlinear aspects of the global system are seen in the global intertwined issues of environment, energy, population demographics, potential epidemics, technology development, and terror risk (LePoire 2004, 2010). It seems each issue cannot be independently solved but must include some systemic reorganization of global cooperation.

How Might This Inform Us About Potential Explanations of the Fermi Paradox? Soon after World War II, the Nobel Prize winning Italian physicist, Enrico Fermi was pondering the quickening technological changes of the time (Popoff 2016). During World War II, advances were made in nuclear, rocket, jet, electronics, radar, and computer technologies. With such advances, it might have seemed like space travel to other solar systems might be accessible. Given the billions of years it took life to evolve on Earth to this level of technology, it seemed very possible that life on other solar systems might have advanced a bit faster, hundreds, thousands, or even millions of years faster. This might have led to their capabilities for space travel or communications long ago. This prompted Fermi to ask “Where are they?” Possibly other intelligences have evolved to our level and beyond, but the technological level necessary to travel and communicate requires technology and energy levels far beyond our current means. We saw here that a technological advance might initially accelerate but then slow down. If the technology needed to interact with other civilizations requires advances well beyond our current inflection point, the current wide technological lead that we expect of other worlds that started earlier than ours might not be sustained. Consider that the expansion of energy use to one where the complete energy of the sun is captured (e.g., a Dyson sphere). This would require another 3 major sets of extended evolution phases. It is very difficult to identify what these emergent phases might be; however, they may be related to the emergence of a symbiosis of humans and artificial intelligence.

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Conclusions There are many open questions concerning the nature, cause, and impact of a potential singularity (a unique event suggested by a long-term trend in increasing rates of complexity and energy use). Its nature might be realized soon as rates of change either continue to accelerate, slow down, or remain fixed. The cause of this trend requires interdisciplinary research into the areas such as evolution, history, complex systems, and energy use. The potential impact might be the most valuable research in preparation and reaction to the changes in technological advances. A slowdown might lead to greater diffusion of technology and a mitigation of stress due to rapid change. An acceleration might lead to great benefits or to an unstable system as the technology outpaces the rate of social change.

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Grinin L, Grinin A, Korotayev AV (2020) Dynamics of technological growth rate and the 21st century singularity. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 287–344. https://doi.org/10.1007/9783-030-33730-8_14 Grübler AN, Nakicenovic N, Nordhaus WD (2002) Technological change and the environment. Int Inst Appl Syst Anal, Laxenbourg Gunderson LH, Holling CS (2002) Panarchy: understanding transformations in human and natural systems. Island Press, Washington DC Grinchenko S, Shchapova Y (2020) The deductive approach to Big History’s Singularity. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 201–210. https://doi.org/10.1007/978-3-030-33730-8_10 Homer-Dixon TF (2006) The upside of down: catastrophe, creativity, and the renewal of civilization. Island Press, Washington DC Hossenfelder S (2018) Lost in math: how beauty leads physics astray. Basic Books, New York Jantsch E (1980) The self-organizing universe: scientific and human implications of the emerging paradigm of evolution. Pergamon, Oxford Kauffman SA (1995) At home in the universe: the search for laws of self-organization and complexity. Oxford University Press, New York Korotayev A (2018) The 21st century singularity and its big history implications: a re-analysis. J Big Hist 2(3):71–118. http://dx.doi.org/10.22339/jbh.v2i3.2320 Korotayev AV (2020) The 21st century Singularity in the Big History perspective. A re-analysis. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 19–75. https://doi.org/10.1007/978-3-030-33730-8_2 Korotayev A, Goldstone JA, Zinkina J (2015) Phases of global demographic transition correlate with phases of the great divergence and great convergence. Technol Forecast Soc Chang 95:163–169. https://doi.org/10.1016/j.techfore.2015.01.017 Korotayev A, Malkov A, Khaltourina D (2006) Introduction to social macrodynamics: compact macromodels of the world system growth. KomKniga/URSS, Moscow Kremer M (1993) Population growth and technological change: one million B.C. to 1990. Q J Econ 108:681–716. https://doi.org/10.2307/2118405 Kummel R, Ayres RU, Lindenberger D (2010) Thermodynamic laws, economic methods and the productive power of energy. J Non-Equilib Thermodyn 35(2):145–179. https://doi.org/10. 1515/jnetdy.2010.009 Kurzweil R (2005) The singularity is near: when humans transcend biology. Viking, New York LePoire DJ (2005) Application of logistic analysis to the history of physics. Technol Forecast Soc Chang 72(4):471–479. https://doi.org/10.1016/S0040-1625(03)00044-1 LePoire DJ (2004) A ‘Perfect Storm’ of Social and Technological Transitions. Futures Research Quarterly, Fall LePoire DJ (2010) Long-term population, productivity, and energy use trends in the sequence of leading capitalist nations. Technol Forecast Soc Chang 77(8):1303–1310 LePoire DJ (2015) Interpreting big history as complex adaptive system dynamics with nested logistic transitions in energy flow and organization. Emerg Complex Organ 17(1):1–16 LePoire DJ (2018) Rocketing to energy sustainability. J Big Hist 2(2):103–114. https://doi.org/10. 22339/jbh.v2i2.2304 LePoire DJ (2020a) An exploration of historical transitions with simple analogies and empirical event rates. J Big Hist 3(2):1–16. https://doi.org/10.22339/jbh.v3i2.3210 LePoire DJ (2020b) Major expansion and integration phases in the major stages of big history. Evolution 6 (fourthcoming) LePoire DJ, Chandrankunnel M (2020) Energy flow trends in Big History. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 185–200. https://doi.org/10.1007/978-3-030-33730-8_9 Linstone HA (1996) Technological slowdown or societal speedup: the price of system complexity. Technol Forecast Soc Chang 51:195–205. https://doi.org/10.1016/0040-1625(95)00253-7

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Magee CL, Devezas TC (2011) How many singularities are near and how will they disrupt human history? Technol Forecast Soc Chang 78(8):1365–1378. https://doi.org/10.1016/j.techfore. 2011.07.013 Malkov S (2020) About the singularity in biological and social evolution. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 517–534. https://doi.org/10.1007/978-3-030-33730-8_23 Marchetti C (1980) Society as a learning system: discovery, invention, and innovation cycles revisited. Technol Forecast Soc Chang 18:267–282. https://doi.org/10.1016/0040-1625(80) 90090-6 Markov A, Anisimov V, Korotayev A (2010) Relationship between genome size and organismal complexity in the lineage leading from prokaryotes to mammals. Paleontol J 44(4):363–373. https://doi.org/10.1134/S0031030110040015 Modis T (2002) Forecasting the growth of complexity and change. Technol Forecast Soc Chang 69:377–404. https://doi.org/10.1016/S0040-1625(01)00172-X Modis T (2020) Forecasting the growth of complexity and change—an update. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 101–104. https://doi.org/10.1007/978-3-030-33730-8_4 Morowitz HJ (2002) The emergence of everything: how the world became complex. Oxford University Press, New York Nazaretyan AP (2017) Mega-history and the twenty-first century singularity puzzle. Soc Evol Hist 16(1):31–52 Nazaretyan A (2020) The 21st century’s “mysterious singularity” in the light of the Big History. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 345–362. https://doi.org/10.1007/978-3-030-337308_15 Niele F (2005) Energy: engine of evolution. Elsevier, Amsterdam and Boston Panov AD (2011) Post-singular evolutions and post-singular civilizations. Evolution 2:212–231 Panov A (2020) Singularity of evolution and post-singular development in the Big History perspective. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 439–465. https://doi.org/10.1007/9783-030-33730-8_20 Perry DA (1995) Self-organizing systems across scales. Trends Ecol Evol 10(6):241–244. https:// doi.org/10.1016/S0169-5347(00)89074-6 Ponting C (2007) A new green history of the world: the environment and the collapse of great civilizations. Penguin Books, New York Popoff A (2016) The fermi paradox: 100 solutions and the survival of mankind. CreateSpace, New York Royal Astronomical Society (2012) Star formation slumps to 1/30th of its peak. ScienceDaily 06.11.2012. https://www.sciencedaily.com/releases/2012/11/121106114141.htm Sagan C (1977) The dragons of eden: speculations on the evolution of human intelligence. Random House, New York Schneider ED, Kay JJ (1994) Life as a manifestation of the second law of thermodynamics. Math Comput Model 19(6–8):25–48. https://doi.org/10.1016/0895-7177(94)90188-0 Sharov A, Gordon R (2013) Life before earth. https://arxiv.org/abs/1304.3381 Smil V (2010) Energy transitions: history, requirements, prospects. Praeger, Santa Barbara, California Snooks GD (1998) The laws of history. Routledge, London Snooks GD (2005) Big history or big theory? Uncovering the laws of life. Soc Evol Hist 4(1):160– 188 Solis K, LePoire DJ (2020) Big History trends in information processes. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 145–161. https://doi.org/10.1007/978-3-030-33730-8_7 Spier F (2010) Big history and the future of humanity. Wiley, Chichester, UK

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Stone L (1993) Period-doubling reversals and chaos in simple ecological models. Nat Cell Biol 365:617–620. https://doi.org/10.1038/365617a0 Tainter JA (1996) Complexity, problem solving, and sustainable societies. In: Constanza R, Segura O, Martinez-Alier J (eds) Getting down to earth. Island Press, Washington, DC, pp 61–76 Torday J (2020) Evolution, the ‘mechanism’ of Big History, predicts the near Singularity. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 559–570. https://doi.org/10.1007/978-3-030-33730-8_25 Tsirel S (2020) Big History and Singularity as metaphors, hypotheses and prediction. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 119–144. https://doi.org/10.1007/978-3-030-33730-8_6 Vidal C (2008) A cosmic evolutionary worldview: short responses to the big questions. In: Vidal C (ed) Foundations of science (special issue of the conference on the evolution and development of the universe). Ecole Normale Supérieure, Paris, pp 280–305 Weinberg S (1993) The first three minutes: a modern view of the origin of the universe. Basic Books, New York Widdowson M (2020) The 21st century Singularity: the role of perspective and perception. In: Korotayev AV, LePoire D (eds) The 21st century Singularity and global futures. A Big History perspective. Springer, Cham, pp 489–516. https://doi.org/10.1007/978-3-030-33730-8_22

David J. LePoire has a PhD in Computer Science from DePaul University and a BS in Physics from CalTech. He has worked in environmental and energy areas for many governmental agencies over the past 25 years. Topics include uncertainty techniques, pathway analysis, particle detection tools , and physics-based modeling. He has also explored historical trends in energy, science, and environmental transitions. His research interests include complex adaptive systems, logistical transitions, the role of energy and environment in history, and the application of new technologies to solve current energy and environmental issues.

Historical Mega-Trends

Forecasting the Growth of Complexity and Change—An Update Theodore Modis

Review My article (Modis 2002) had shown that “cosmic” milestones have been crowding into clusters from the beginning of the universe. These clusters of milestones have made their appearance more and more frequently and have given rise to an accelerated rate of change and complexity in our lives. I thought at the time that I was the first to have made this observation only to find out later that a whole movement with the increasing number of followers was growing around it. The set of data that I had painstakingly collected for that article was used in one of the central graphs—and served as evidence for forecasting the Singularity—by Ray Kurzweil (2005) in his celebrated book The Singularity Is Near. However, while Kurzweil argued for exponential (and double exponential) rates of growth to just about everything, I argued for logistic growth of change and complexity versus milestone number, which is a more natural approach considering that a logistic function is par excellence the description of natural growth processes. In my article, I had tabulated 28 clusters of milestones of primordial and consequently comparable importance. Because there may be some ambiguity in the definition of “primordial importance” I reproduce here, as examples, the last three clusters of milestones in my dataset (Table 1), and I maintain that they can be reasonably considered to be of primordial and of comparable importance. Figure 4 from Modis (2002) showed how an exponential fit compared to a logistic fit on the same set of data. My conclusion was (and still is) that the logistic fit was not only somewhat better in quality but also more appropriate.

T. Modis (&) Growth Dynamics, Lugano, Switzerland e-mail: [email protected] © Springer Nature Switzerland AG 2020 A. V. Korotayev and D. J. LePoire (eds.), The 21st Century Singularity and Global Futures, World-Systems Evolution and Global Futures, https://doi.org/10.1007/978-3-030-33730-8_4

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Table 1 The Last three clusters of milestones (Modis 2002) Milestone-cluster number

Years before 2000

26

100

Events in the cluster

Modern physics/radio/electricity/automobile/ airplane/capitalism and colonialism 27 50 DNA/WWII/Cold War/Sputnik/transistor/nuclear energy 28 5 Internet/human genome sequenced Words in bold represent the main feature of each milestone

The fitted logistic curve turned out to be half-way completed around our times implying that we have been experiencing the highest rate of change and that such clusters of milestones will appear less and less frequently in the future, in sharp contrast to the accelerated rate advocated by the Singularitarians. Table 2 from Modis (2002)—partially reproduced here (Table 2)—lists the forecasted timing of the next three milestone clusters according to the two fits, namely exponential and logistic.

The Facts From the above table we can conclude that according to the exponential forecast we should have already seen three more “cosmic” events by now, one in late 2008 (1995 + 13.4), another one around the end of 2015 (1995 + 13.4 + 6.3), and a third one around the end of 2018 (1995 + 13.4 + 6.3 + 3). But we have seen none! Granted there have been numerous scientific achievements but none of the importance comparable to such developments as electricity, nuclear energy, the transistor, DNA, or the Internet, the onslaught of which impacted society dramatically and immediately. Conceivably, a cluster of achievements in AI, robotics, nanotechnology, and bioengineering could qualify as one cosmic milestone in the same way modern physics, radio, electricity, automobile, airplane, capitalism, and colonialism had done at the turn of the twentieth century (milestone-cluster number 26). But these new processes are ongoing and are making continuous progress every day. They are all in the very early stages of their development, and their impact on society is hardly felt yet. The timing of their primordial importance could be better positioned

Table 2 Forecasting the timing of future milestone clusters (in years after the previous one) Milestone-cluster number

Logistic fit (years)

Exponential fit (years)

29 30 31

38 45 69

13.4 6.3 3.0

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around 2033 (the next milestone forecasted by the logistic fit—namely 38 years after 1995) instead of years 2008, 2015, and 2018 forecasted by the exponential fit.

A Very Simple Argument Kurzweil and many of the Singularitarians agree that all exponentially growing processes will eventually turn into logistics (S-shaped curves), but they argue that this will happen very long time from now and that the ceilings of these S-curves may be unfathomably high, something impossible to estimate today. But I have a very simple rule of thumb to estimate an upper limit for the ceiling of any natural growth process from very early data. The logistic S-curve describing natural growth is preceded and followed by states of chaos (Modis and Debecker 1992). During this chaotic state, large fluctuations prevent an overall trend from unambiguously developing. It is during this period that infant mortality takes place. In living organisms—such as plants—infant mortality typically occurs during the development of the first 5–10% of the organism’s final height. Therefore, at the end of infant mortality the process can be expected to grow another 10–20 times its present size. We can use this rule by analogy for all logistic fits on variables describing processes of natural growth, be it in technology, economy, or other social endeavor. This does not mean that all growth will cease at the end of a logistic curve determined. S-curves are known to cascade (Modis 1994). There can always be further growth, which will follow a new logistic, triggered by unknown-yet technologies, discoveries, breakthroughs, or other events. But the approach does put an upper limit (a cap) on the ceiling of all well-established processes (i.e., those that have proceeded beyond infant mortality) as at most 20 times the present level. On the other hand, if the growth process has not proceeded beyond infant mortality yet, no forecasts can be reliably made because during this chaotic state turbulence may distort the trend, and moreover, because the whole process may not survive it. One way or another, unfathomably high forecasts cannot be justified if we are dealing with natural growth processes; forecasting a Singularity amounts to pure speculation.

References Kurzweil R (2005) The singularity is near: when humans transcend biology. Viking Penguin, New York, NY Modis T (1994) Fractal aspects of natural growth. Technol Forecast Soc Chang 47(1):63–73. https://doi.org/10.1016/0040-1625(94)90040-X

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Modis T (2002) Forecasting the growth of complexity and change. Technol Forecast Soc Chang 69(4):377–404. https://doi.org/10.1016/S0040-1625(01)00172-X Modis T, Debecker A (1992) Chaoslike states can be expected before and after logistic growth. Technol Forecast Soc Chang 41(2):111–120. https://doi.org/10.1016/0040-1625(92)90058-2

Theodore Modis is a strategic business analyst, futurist, physicist, and international consultant. He specializes in applying fundamental scientific concepts to predicting social phenomena. In particular, he uses the logistic function or S-curve to forecast markets, product sales, primary-energy substitutions, the diffusion of technologies, and generally any process that grows in competition. He is a vehement critic of the concept of the Technological Singularity. Modis carried out research in particle physics at Brookhaven National Laboratories and at CERN before moving to work at Digital Equipment Corporation (DEC) for more than a decade as the head of a management-science consultants group. He has on occasion taught at Columbia University, the University of Geneva, Webster University, the European business schools INSEAD and IMD and was a professor at DUXX Graduate School of Business Leadership in Monterrey, Mexico between 1998 and 2001. He has been on the advisory board of the international journal Technological Forecasting & Social Change since 1991. He is also the founder of Growth Dynamics, a Swiss-based organization specializing in business strategy, strategic forecasting, and management consulting.

Hyperbolic Evolution from Biosphere to Technosphere Alexey Fomin

Introduction This chapter further elaborates the findings of Chapter “The Twenty First Century Singularity in the Big History Perspective. A Re-analysis” above (Korotayev 2020; see also Korotayev 2018) that demonstrates that the pattern of the hyperbolic growth is not a phenomenon of human population growth only. In the present chapter, three quantitative regularities are considered which provide evidence for much earlier hyperbolic growth patterns before the well-established hyperbolic growth pattern in the population of our planet (see, e.g., von Foerster et al. 1960; Kremer 1993; Kapitza 1996, 2003; Korotayev and Malkov 2016; Podlazov 2017; Fomin 2018, as well as Chapter “The Twenty First Century Singularity in the Big History Perspective. A Re-analysis” (Korotayev 2020) above): (1) The regularity discovered by Alexander Panov (see Fig. 1) of major evolutionary events (see Chapter “Singularity of Evolution and Post-singular Development” (Panov 2020) below for detail). We will provide an explanation based on a generalization of the population measure to the case of biological evolution. (2) The dynamics of sedimentary rocks accumulation (thickness) where the something pattern of accumulation acceleration is similar to the population hyperbola including a consistent projected singularity time. (3) The dynamics of the density of marine animal species which shows a similar hyperbolic growth.

A. Fomin (&) International Center for Education and Social and Humanitarian Studies, Moscow, Russia e-mail: [email protected] © Springer Nature Switzerland AG 2020 A. V. Korotayev and D. J. LePoire (eds.), The 21st Century Singularity and Global Futures, World-Systems Evolution and Global Futures, https://doi.org/10.1007/978-3-030-33730-8_5

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Fig. 1 Reducing the time intervals between planetary revolutions: t* − tn = T/an, by minimizing the variance, t* turned out to be equal to 2004 (Panov 2004). But if we calculate this value by the points of human evolution only, then t* is equal to 2027 (Panov 2007), which gives an idea of the error of this parameter. Data source Panov (2004); see also Chapter “Singularity of Evolution and Post-singular Development” below (Panov 2020) for more detail

A conclusion is drawn that a single hyperbolic pattern (with the same singularity point) is associated with both human population and the biosphere growth. In the case of biological evolution, the growth is in the number of biological species, and in the case of the more rapid technological evolution, it is in the technological species (and the corresponding types of products). And since technological activity is related to human population, the population also grows according to the same hyperbolic law. The change from biological evolution to technological evolution was due to the increasing rate of the new ecological niches that could only be explored with human technological innovation. But it preserved and continued the hyperbolic trend of biological evolution. Earlier, a similar conclusion was drawn by us (see Fomin 2010) on the basis of a rough reconstruction of the dynamics of the number of marine species (without dividing their number by the area they occupy). In this chapter, this conclusion has been produced in a more rigorous way.

Panov’s Pattern Alexander Panov detects a hyperbolic pattern of evolutionary development (Fig. 1) from the first known life on the Earth to the present in the sequence of revolutionary events (see Chapter “Singularity of Evolution and Post-singular Development” (Panov 2020) below for detail). The hyperbolic trend means that the frequency of these events tends to infinity as time approaches the singularity point, t*.

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This moment is similar to that found in the hyperbolic human population growth trend. For example, in my previous work (Fomin 2018), the singularity time was identified as about 2037 CE. This suggests that such a similarity is not an accident, but instead a manifestation of a general evolutionary pattern embracing both the biological and socioeconomic evolution (hyperbolic growth of the Earth’s human population). An issue with this latter hypothesis is a great subjectivity in the choice of revolutions. Nevertheless, objectivity is indicated by the fact that the list of revolutions in Fig. 1 was composed by Panov on the basis of two independent periodizations that were simply joined together. There are many similar lists (“timelines”) found on the Internet, but they often cover the narrower time interval of human history. But their trends indicate a singularity similar to the hyperbolic trend in population growth. In Chapter “The Twenty First Century Singularity in the Big History Perspective. A Re-analysis” above, Korotayev (2020) analyze the Modis–Kurzweil event series and arrive at strikingly similar results to the Panov series (note also that Korotayev applies a bit different technique of mathematical analysis (see also Korotayev 2018)). That the two independent results are so similar suggests the objective nature of the above-described trend (Korotayev 2018, 2020).

Derivation of Formula for the Panov Pattern Panov’s analysis suggests that some evolutionary units grew much earlier with the same hyperbolic trend (with the same singularity point) as the planet’s population. Indeed, it is possible that every similar increase (by a multiplicative factor) in the population leads to some characteristic socioeconomic change. That is, if the population follows: 2037
t ¼ N0 =N

ð1Þ

where N0 is some empirical constant, then the numerical regularity illustrated in Fig. 1 would look as: 2037
t ¼ T=an :

ð2Þ

which resembles Eq. (1), if we assume that N  an :

ð3Þ

Equation (3) means that whenever the population of the planet increases by the same factor, a, then n increases by 1 as some typical sociotechnological breakthrough (phase transition) occurs.

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One can also derive the relationship that the increase of the world population by a factor of a is accompanied by the reduction of duration between phase transitions by the same factor of a.1 That is, in a hyperbolic growth the product of the number of evolutionary units (the generalized name of the population for the case of both biological and social evolution) and the time to the singularity is constant, so a factor increase in the number of units leads to the same factor decrease in time until the singularity. Therefore, from the hyperbolic growth of the Earth’s population and the assumption that an increase in the population in the same number of times should lead to some characteristic evolutionary changes, the pattern in Fig. 1 So, let t1 < t2 < t3—be the moments at which the hyperbolically growing population N = A/(t* − t) increases consecutively by the same number of times, equal to a in comparison with the previous one. It can be shown that the shortening of the time intervals k = {t2 − t1}/ {t2 − t3} will also be the same each time. We write down the formula for hyperbolic population growth in the form: t = t* − A/N. Now write it in the above 3 points: t1 = t* − A/N1; t2 = t* − A/ N2; t3 = = t* − A/N3; substitute these values in the formula for k: k = {t* − A/N2 − (t* − A/N1)}/ {t* − A/N2 − (t* − A/N3)} = {(1 − N1/N2)/{(N2/N3 − 1)}. By definition, over the considered time intervals, population growth occurred in the same number of times: N2/N1 = N3/N2 = a. Substituting this in the previous formula, we get: K ¼ fð1
1=aÞ=fða
1Þg ¼ a (4) We can also use another derivation. The regularity presented in Fig. 1 can be obtained from hyperbolic population growth/evolutionary units on the basis of the following intuitive considerations. These considerations indirectly indicate the existence of a biological analogue of the population (evolutionary units), which evolutionally smoothly develops into the human population. Indeed, the regularity of Fig. 1 means that the number of biospheric revolutions per unit of time increases in proportion to the population hyperbola: It follows from (2) that n = ln{T/(2027 − t)}/ln(a) and if we differentiate this expression with respect to time, then the number of biospheric revolutions per unit of time is dn/dt = {1/ln(a)}/(2027 − t); if we neglect the difference between 2027 and the singularity point of the population hyperbola t*, then it turns out that the intensity of biospheric revolutions is proportional to the population hyperbola: dn=dt  N ¼ N0 =ðt
tÞ (5) But, on the other hand, it seems intuitively plausible that the number of social and economic revolutions in the world per unit time should grow in proportion to the number of people. Because the more people—the proportionally more (if other conditions are the same) biospheric revolutions/major technological breakthroughs here and there (see Chapter “The Twenty First Century Singularity in the Big History Perspective. A Re-analysis” (Korotayev 2020) above for more detail about this). That is, the number of biospheric revolutions/major technological breakthroughs per unit of time should grow in proportion to the population hyperbole. Hence, a similar conclusion is drawn for the number of biospheric revolutions per unit of time: The number of biospheric revolutions per unit of time should grow in proportion to the number of evolutionary units (the generalized name of population for the case of biological evolution). But this is none other than the relation expressed in Eq. (5). And from Eq. (5), in turn, we can obtain Eq. (2). Indeed, integrating Eq. (5), we obtain: n − n0 = F ln(t* − t), where n0 and F are some constants. The right-hand side of this expression coincides with the left-hand side of Eq. (2), and the left-hand side for some choice of the corresponding constants {a = exp(1/А), T = exp(n0/F)} is equivalent to the right-hand side of the same Eq. (2). That is, Eq. (2) actually follows from Eq. (5) for the mentioned choice of constants. Thus, for the case of human evolution, the banal, intuitive idea that the more people, the more proportionally biospheric revolutions/major technological breakthroughs occur, leads to the regularity in Fig. 2. This suggests a generalization to the case of biological evolution with the generalization of people by certain biological, evolutionary units. Only now we should assume that already the intensity of biotic revolutions is proportional to a certain number of evolutionary units within the process of biological evolution. 1

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emerges from the hyperbolic growth of the Earth’s population and the assumption that an increase in the population in the same number of times should lead to some characteristic evolutionary changes, the pattern in Fig. 1 emerges. That is, the hyperbolic growth of the Earth’s population seems to be a particular continuation of some more general law for the hyperbolic growth of some characteristic of sociobiological diversity. If this is so, then this can prove to be a valuable tool for macroevolutionary research, since it gives the key to understanding a number of biological processes on the basis of social processes and vice versa.

Comparison with Actual Data The fact that between the neighboring points of the graph in Fig. 1 each time there is an increase in the population to some approximately the same factor is illustrated by Table 1. Moreover, as can be seen from the table, it is indeed approximately equivalent to the reduction in the corresponding intervals of time between revolutions.

Subjectivity Problem Other lists/periodizations are also possible, which are similar to those used in the construction of the graph in Fig. 1. The analyses of these lists give slightly different results, but the singularity point remains approximately the same. However, all such lists do not offer clear criteria on which they are built; that is, they have a great deal of subjectivity. Indeed, the table shows that a relatively subjective choice can demonstrate both significant differences among themselves and a mismatch with the corresponding population growth. The situation is even more complicated when searching for a common criterion for periodization in conjunction with biotic evolution, which would allow building a periodization of both on a single basis. Therefore, we need some objective criteria that would indicate a hyperbolic growth during biological evolution with a singularity point similar to the one of the population hyperbola.

The Growth Rate of Sedimentary Rocks’ Thickness On the Possibility of Global Influence of the Biosphere on Sedimentation The dynamics of the sedimentation rate also demonstrates a pattern related to the population hyperbola. But before proceeding directly to this issue, the question of the global biotic influence on sedimentation should be discussed.

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Table 1 Comparison of the period reduction factors in Fig. 1 (their dating was taken from Panov 2007) with a corresponding increase in the world population Biospheric revolution/major global technological breakthrough

Appr. dates of revolutions, CE

World population, millions

Population growth since the previous revolution, times

Time interval since the previous revolution (years)

Reduction of periods in relation to the previous period, times

Upper paleolithic −40,000 2.0 75,000 revolution Neolithic revolution −10,500 5.25 2.6 29,500 2.6 Urban revolution −3500 38.7 7.3 7000 4.2 Imperial antiquity, −759 98.2 2.2 2740 2.5 iron age, axial age revolution The destruction of the 500 199.5 2.0 1260 2.2 ancient world, the beginning of the middle ages Beginning of the early 1500 435.3 2.2 1000 1.3 modern period, the first industrial revolution The second industrial 1835 1128.8 2.6 335 3.0 revolution. steam, electricity, mechanized production Information 1950 2536.4 2.2 115 2.9 revolution, beginning of the post-industrial era Crisis and 1991 5398.3 2.1 41 2.8 disintegration of the world-system of totalitarian planned economy, information globalization Average 2.9 2.7 Note The population estimates have been obtained by averaging (for the same time point) from a larger number of different authors who reconstructed the dynamics of population, the list of which is cited in Tsirel 2008

The possibility of a biogenic origin of sedimentary rocks was demonstrated by Balandin (1979). He points out that the growth of sedimentation (Fig. 2) is too accelerated to have an abiogenic nature. In support of this, an investigation of the influence of ants on the formation of calcium and magnesium carbonate from minerals reveals a global impact of the biosphere on geological processes (Dorn 2014). The ants’ activity accelerated this soil process by a factor of 50–300. It was suggested

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that ants could possibly be responsible for the global cold snap in the Cenozoic, about 145 million years ago (ICC 2013) since the described soil process binds atmospheric carbon dioxide (Dorn 2014), thereby increasing the rate of sedimentation. Indeed, the biomass of ants in the tropics is not less than the biomass of large ungulates, whereas ants account for about half of the vegetation eaten in the savannahs. Examples like this led Koronovskii and Yakushova (1991: Chapter “Dynamics of Technological Growth Rate and the Forthcoming Singularity”), to state that “more than 50% of the ocean’s sediments are of biogenic origin.” Recent numerical modeling of the influence of the biosphere on the rate of sedimentation has shown that the biosphere can in many ways be responsible for the existence of continents (Höning et al. 2014). The biosphere facilitates the sequence of events including the intensive destruction of terrestrial rocks; the formation of sedimentary rocks; the resulting volcanic activity; and, finally, the increased formation of the continents. Geophysicist Norm Norman of Stanford University believes that such a picture fits perfectly into what is now known about the evolution of the Earth’s crust. In particular, the discovered alumina in ancient sedimentary rocks with a high probability indicates their biogenic origin (Slezak 2013). Recently, German geophysicists have constructed a model of planetary evolution, taking into account the “lubrication” effect that water gives, penetrating deep into the Earth due to the erosion that life creates. Life on Earth is influential in eroding material that facilitates this water lubrication which accelerates geological processes such as continental formation. And, as the model showed, if life on Earth had never existed at all, then the continents would occupy an area of about a quarter of the current one (Lenta.ru 2015; Reed 2015). Therefore, there is every reason to believe that the rate of sedimentation can be a global evolutionary indicator of the biosphere.

Logarithmic Growth Rate of Sedimentary Rocks Thickness Now, let us consider the dynamics of the sedimentation rate shown in Fig. 2 covering the time from 472 to 72 million years ago. This linear trend is seen with a logarithmic time scale based on the time before the singularity of 2037 CE. This dynamic is similar to the trend of the logarithm of the previously discussed population trend. That is, a hyperbolic trend began long before hominids evolved. The logarithmic increase in the rate of increase in the thickness of sedimentary rocks means that with each new revolution, the growth rate of thickness of sedimentary rocks grew by approximately the same amount.2 2

Indeed, it follows from (2) that the ordinal number of the n points of Fig. 1 satisfies the relation n = ln(T)/ln(a) − {1/ln(a)} ln(2027 − t)  ln(T)/ln(a) − {1/ln(a)} ln(t* − t). Using logarithmic dependence for the growth rate of the sedimentary rocks thickness P = 421.08 − 21.18 ln(t* − t), together with this ratio, it can be determined from the expression Eq. (2) that the increase in sedimentation rate P2 − P1 between two t2 and t1, respectively, is equal to = P2 − P1 = 21.18 ln (a) (n2 − n1). Hence, taking into account that n2 − n1 = 1 for the instants of time between each adjacent revolutions in Fig. 2, it turns out that the increase in the rate of growth of sedimentary rocks between them each time will be equal to 21,18 ln(a).

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Fig. 2 Dynamics of the growth rate of the sedimentary rocks thickness (relative units) and its logarithmic parameterization 421.08 − 21.18 ln (2037 − t), obtained by minimizing the dispersion, but with a constant 2037, taken from the log-hyperbolic parameterization of the Earth population (see Fomin 2018)

Dynamics of Marine Species Density Hyperbolic Growth—Like the Population of the Earth The previous two analyses (that is, the rates of milestone events and sedimentation) suggest that before the emergence of people on the Earth, something (e.g., evolutionary biological units) increased quantitatively according to the same hyperbolic law, according to which population growth then continued. Now, a third pattern with units of marine species density will be analyzed (since currently there is not a measure for the number of all species). For species, a reconstruction of the global dynamics of the number of marine animal species was carried out by Alexander Markov and Andrey Korotayev3. However, before looking for hyperbolic growth in this data, we should consider the additional factor of the changing marine area. This area is the territory of marine environments on the continents (Fig. 3). Since the number of species is correlated with large-scale changes in marine areas, it is more appropriate to divide the reconstructed number of species by this concurrent marine area (i.e., the density of marine animal species). 3

It is based on an approximate pattern of paleontological data on the relationship of neighboring marine taxa (i.e., neighbors in the line “type, class, family, order, genus”). The regularity is that a taxon of any rank (from the said line), for example an order, contains the same number of taxons of the next lower rank (Markov 2003). The mentioned regularity (which made it possible to calculate the number of species by the number of genera) means the presence of a fractal in the taxonomic structure: The smaller taxa are similar to the larger ones in terms of the relationship with their “neighbors.” This is in good agreement with the fact that larger taxa (for example, families) once emerged from smaller (genera). Therefore, it is logical that they could inherit their structure. It is logical to assume that species density (or alpha diversity) is proportional to the total number of species (see Markov and Korotayev 2007a, b, 2008, 2009; Grinin et al. 2013; Korotayev, and Markov 2014, 2015).

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Fig. 3 Dynamics of water areas in the territory of the current continents in million km2. Xaxis = calendar million years. Data source Monin (1977), Fig. 35

Fig. 4 Hyperbolic parameterization of the marine density of animals species. The X-axis is the calendar time t in million years (540–1.4 million years). Broken line denotes the reconstructed number of species (corresponding to the known paleontology number of marine genera), divided by the water areas in million km2, on the territory of the present continents (that is  the area of their habitat). The direct line is the hyperbola of the Earth’s population (see: Fomin 2018), multiplied by the constant obtained by minimizing the dispersion: 14382.9/(0.002037 − t). Reconstruction of species was carried out in: Markov (2003), data on the dynamics of the water areas are from Fig. 3(An overview of the data on the dynamics of the sea surface in the territory of the present continents is given in Miller et al. 2005. But at such a wide interval, as in Fig. 4, there are data only for two authors (see: Sloss 1963, Ronov 1994). The remaining data are presented in an incommensurably smaller interval. If instead of the data used in Fig. 4, we use this data, then the approximate linear dependence in Fig. 4 remains true. Data on the dynamics of the water areas in the territory of the present continents, used in Fig. 4, were chosen simply because the author found them first. But, later, it turned out that they make the cycles much more visible, which is discussed in Fig. 5)

The dynamics obtained after such a division develops approximately according to the hyperbolic law of the population of the planet, as shown in Fig. 4. However, without such a division, the reconstruction of the dynamics of the number of paleontological species can also roughly resemble the hyperbola of the Earth’s population (Fomin 2010). Also, since the marine environment on the continental

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shelves (presently 5 million km2 from Verpoorter et al. 2014.) is much larger than fresh water lakes (