Introduction. To Verify Harmony by Algebra

Introduction. To Verify Harmony by Algebra
Authors: Grinin, Leonid; Korotayev, Andrey
Almanac: History & Mathematics:Economy, Demography, Culture, and Cosmic Civilizations


The spatial distribution of folklore-mythological motifs is shown to correlate rather tightly with the distribution of mitochondrial DNA (mtDNA) and Y-chromosome (NRY) haplogroups. The analysis of spatial distribution of folklore-mythological motifs confirms earlier findings of geneticists which identified South Siberia as the Old World homeland of the main wave of the peopling of the New World (the diffusion of the respective populations in the New World turns out to be associated with the spread of Clovis and para-Clovis archaeological cultures). Indeed, this is just South Siberia where the highest concentration of the Amerindian folklore-mythological motifs in Eurasia is observed. On the other hand, it turns out to be possible to connect the penetration of mtDNA HG C and NRY HG Q > Q3 to the New World with this migration wave. The spatial distribution of the ‘Circumgobi-Amerindian’ folklore-mythological motifs follows rather closely the distribution of mtDNA HG C in the New World. This makes it possible to re-construct up to a considerable detail the mythology brought to the New World from South Siberia by this migration wave. Another migration wave turns out to be associated with the distribution of mtDNA HG B and motifs of ‘Melazonian’ mythological complex whose highest concentration is observed in Melanesia, on the one hand, and Amazonia, on the other. These motifs form a few connected sets, which suggest certain possibilities for the reconstruction of some features of ‘proto-Melazonian’ mythology brought to the New World by the bearers of mtDNA HG B. MtDNA HG A frequencies in Siberian and American populations display a rather strong and statistically significant correlation with the number of the ‘Raven Cycle’ motifs in respect of folklore-mythological traditions. There are certain grounds to believe that both these motifs and the respective genetic marker (‘Arctic A’) were brought to the extreme American North-West and extreme North-East Asia (‘Transberingia’) later than both maternal lines B+C and Circumgobi-Amerindian, Melazonian and Ural-Amerindian motifs had been brought to the New World. The presence of a relatively homogenous Transberingian ‘genetic-mytho-logical’ zone characterized by high frequencies of both mtDNA HG A and the Transberingian motifs seems to be accounted for, first of all, by the fact that they were brought to this zone relatively later with the migrations apparently corresponding to the movement to this area of Dene, Esko-Aleut and Chukotko-Kamchatkan language speakers and replaced to a considerable extent earlier genetic markers and folklore-mythological motifs. But, on the other hand, the same fact seems to be additionally accounted for by the functioning up to the Modern Age of the Transberingian communicative network, as in the Holocene the communication through the Bering straits does not appear to have ever interrupted, and led to additional homogenization of the zone. And the movement through the Bering straits definitely went in both directions, in the framework of which their way to the Old World appears to have been found by both some New World genetic markers (e.g., NRY HG Q3), and apparently some folklore-mythological motifs which were developed already in the New World (the possibility of the migration of some Transberingian motifs from the New World to the NE Asia [suggested {in a bit exaggerated way} already by the members of the Jesup Expedition] seems to be supported by a higher concentration of these motifs in the New World part of this zone). The analyzed evidence suggests that the Ural-Amerindian mythological complex was brought to the New World by a wave of migration which took place between 10,000 and 13,000, i.e. not long after the main wave of the peopling of Americas.

Keywords: Deep History, mythology, folklore, genetics, mitochondrial DNA, Y-chromosome, peopling of Americas, migration, paleolithic.

The scope of human thought along with its ability to proceed from reconstruction of the most ancient periods to anticipation of the distant future, from small objects to galaxies and the Universe as well as, to embrace different trends and dimensions of reality never cease to amaze us. Generally speaking, such comprehension has always been characteristic for creative and inquiring human mind that tries to perceive the world in its grandeur and diversity.

The present Yearbook (which is the sixth in the series) to some extent reveals the extraordinary potential of scientific research. In particular, it opens with a large co-authored investigation ‘Genes and Myths: Which Genes and Myths did the Different Waves of the Peopling of Americas Bring to the New World?’ by Andrey V. Korotayev, Yuri E. Berezkin, Svetlana A. Borinskaya, Albert I. Davletshin, and Daria A. Khaltourina. This contribution shows the ability of scientific thinking to find correlations between different phenomena. For example, in what way can genes be connected with myths? And still the link does exist and is far from incidental. Myths have been spread by the carriers with peculiar features of genotype. Myths and genes of ancient populations have survived in some way in their offspring and nowadays due to scientific quantitative methods one can study the ancient heritage. The paper studies the spatial distribution of folklore-mythological motifs to show their correlation with the distribution of mitochondrial DNA (mtDNA) and Y-chro-mosome (NRY) haplogroups.

We hope this paper will allow an informed reader to make many interesting discoveries. Among them the most important one will be the significant hypothesis allowing an insight into the period of the utmost importance for the perception of human history, namely, the dispersal of Homo sapiens from Africa which may be considered as a starting point of the humankind's history and social life. The migration of H. Sapiens from Africa can be dated to at least 50,000 thousand years ago (and probably much earlier). The hypothesis presented in the paper may give an idea (at least a supposition) of what the ancient humans may have thought about. For example, it turns out that they thought about death and immortality since the myth about Shed Skins (according to the authors of the paper, one of the most ancient myths) explains the origin of death and loss of immortality for humans.

Furthermore, the Yearbook concludes with the paper (‘Dynamical Generalizations of the Drake Equation: The Linear and Non-linear Theories’) by Alexander D. Panov. Basing on the reinterpretation of the Drake equation, the author of the paper attempts to suppose which is the number of Communicative Civilizations (ССs) and how it changed in the course of time. Communicative civilizations (CCs) are the ones which tend to send messages to other civilizations and are able to receive and analyze messages from other civilizations.

Our Yearbook also covers other relevant issues including, in particular, the technological activity and competition starting from the Middle Ages; the process of urbanization, and problems of modern economy and values.

Since the present issue of the Yearbook covers such a wide range of issues we have given it the subtitle Economy, Demography, Culture, and Cosmic Civilizations.

The common feature for all our Yearbooks, including the present volume, is the usage of formal methods and social studies methods in their synthesis to analyze different phenomena. In other words, if to borrow Alexander Pushkin's words, ‘to verify harmony by algebra’. One should note that publishing in a single collection the articles that apply mathematical methods to the study of various epochs and scales – from deep historical reconstruction to the pressing problems of the modern world – reflects our approach to the selection of contributions for the Yearbook. History and Mathematics, Social Studies and formal methods, as previously noted, can bring nontrivial results in the studies of different spheres and epochs.

The present Yearbook consists of four sections, the first three of which comprise two contributions each.

Section I ‘Historical and Technological Dimensions’ includes the described above article by Andrey V. Korotayev, Yuri E. Berezkin, Svetlana A. Borinskaya, Albert I. Davletshin, and Daria A. Khaltourina (‘Genes and Myths: Which Genes and Myths did the Different Waves of the Peopling of Americas Bring to the New World?’).

The second article of this Section (‘The Technological Activity and Competition in the Middle Ages and Modern History: A Quantitative Analysis’) by Andrey V. Korotayev and Leonid E. Grinin presents a quantitative analysis of innovative activity and competition in technological sphere in the Middle Ages and Modern Period (until the early 20th century). The authors consider the innovative competition in two aspects. In the first part of the paper they show the growing number of innovations over half-century intervals in Europe and Asia. In terms of such historical breakthroughs, it is very important to trace the changes of leadership in Europe. The second and the third sections of the paper are devoted just to this aspect. Here the authors consider the dynamics of technological inventions in Europe from the 15th to the 19th centuries and offer some interesting conclusion.

The contributions of Section II ‘Economic and Cultural Dimensions’ are mostly focused on modern period. The article by Leonid E. Grinin and Andrey V. Korotayev (‘Inflationary and Deflationary Trends in the Global Economy, or Expansion of “the Japanese Disease”’) shows the connections between current economic trends of weak inflation and even deflation and the depressive development of economy in the last decade. The authors attempt to explain why the problems of deflation previously manifested only in Japanese economy have spread to other European countries. Basing on the analysis of available resources and the theory of long cycles, the authors suppose that a new crisis will start in 2018. They also suppose that in the next five or ten years, the global economy will remain in the crisis-depression phase with rather sluggish and weak rises. The paper also offers some forecasts for the forthcoming sixth Kondratieff wave (from 2020 to the 2060/70s) as well as identifies its possible technological basis and discusses possible evolutionary consequences of the forthcoming technological transformations.

The article by Arno Tausch (‘Towards New Maps of Global Human Values, Based on World Values Survey (6) Data’) provides a new approach to the study of the evolution of global values, based on a statistical analysis of the freely available data from the World Values Survey, the 6th wave of global opinion surveys which now has been made public.

Section III ‘Modeling and Theories’ opens with Antony Harper's article (‘An Equation-Based Systems Approach to Modeling Punctuated Equilibria Apparent in the Macropattern of Urbanization over Time’). This paper presents a detailed description and explanation of a model of punctuated growth since that pattern of growth is related to population size, carrying capacity, and level of technology. General limits to modeling are introduced to give context to the results of the model, and the model itself is a set of differential equations representing the relationships between the aforementioned variables. The description of the construction of the model, an intuitive construction, is given, the model is then used to generate results consistent with the occurrence of both punctuation and stasis, and a simple mechanism is proposed to explain the interaction between population size, carrying capacity, and level of technology that would then produce the pattern of punctuation over time. Finally, further modifications of the model to give greater reality to the results are presented.

The section concludes with the article by Alexander D. Panov which we have described above (‘Dynamical Generalizations of the Drake Equation:
The Linear and Non-linear Theories’).

Section IV ‘Reviews and Notes’ contains a review by Antony Harper of a recent book ‘Great Divergence and Great Convergence’ by Leonid E. Grinin and Andrey V. Korotayev (Springer, 2015) which studies the interaction between global economic and demographic evolution.


Goldstone J. A., Grinin L. E., and Korotayev A. V. ( Eds.) 2015. History & Mathematics: Political Demography & Global Ageing. Volgograd: ‘Uchitel’ Publishing House.

Grinin L. E., de Munck V. C., and Korotayev A. V. (Eds.) 2006. History & Mathematics: Analyzing and Modeling Global Development. Moscow: KomKniga/URSS.

Grinin L. E., Herrmann P., Korotayev A. V., and Tausch A. (Eds.) 2010. History & Mathematics: Processes and Models of Global Dynamics. Volgograd: ‘Uchitel’ Publishing House.

Grinin L. E., and Korotayev A. V. (Eds.) 2014. History & Mathematics: Trends and Cycles. Volgograd: ‘Uchitel’ Publishing House.

Grinin L., and Korotayev A. 2015. Great Divergence and Great Convergence. A Glo-bal Perspective. New York, NY: Springer.

Turchin P., Grinin L. E., de Munck V. C., and Korotayev A. V. (Eds.) 2007. History & Mathematics: Historical Dynamics and Development of Complex Societies. Moscow: KomKniga/URSS.

* This research has been supported by the Russian Foundation for Basic Research (Project
№ 17-06-00476).