Macroevolution of Technology

Among all major technological breakthroughs in history the most important are the three production revolutions: 1) the Agrarian Revolution; 2) the Industrial Revolution and 3) the Scientific-Information Revolution which will transform into the Cybernetic one. From our point of view, each revolution initiates a new phase of development of the world productive forces as well as a transition to a new stage of historical process. In the age of globalization one observes a growing interest in the global technological transformations as well as in other global processes.

The present article introduces a new explanatory paradigm – the theory of production principles and revolutions – relevant for the analysis of the causes and trends of major technological breakthroughs as well as of the global shifts in historical process.

1. On Historical Process

One should make a few remarks to clarify our understanding of the ‘historical process’ notion (for more details see Grinin 2007a, 2012). The first point to note is that this concept is in no way synonymous with ‘world history’.^[1] Of course, the notion of historical process is based on world history facts. However, firstly, there have been chosen only those facts that are the most important from the point of view of process and changes; secondly, this set of facts has been ordered and interpreted in accordance with the analyzed spatial and temporal scales, trends and logics of historical development of humankind (or at least the World-System) as a whole, as well as the present-day results of this development. In other words, historical process is in no way a mechanical sum of histories of numerous peoples and societies, it is not even just the process resulting from movement and development of these people and societies. The historical process is a growing and even cumulative process of societal integration that has a certain direction and result. The notion of the historical process of humankind does not imply that humankind has always been a real system. It implies the following: (a) we select a respective scale for our analysis; (b) we take into account the fact that during all periods of historical process the societies, civilizations and its other actors have been developing unevenly, that is at a different rates of social progress; (c) from the methodological point of view it indicates that for the analysis of historical process the most important is the model of the influence produced by the more developed regions on the less developed ones; (d) the interaction scale expands from one period to another until it reaches the scale of the whole planet (in this situation it becomes equal to the notion of the World-System); (e) thus, the historical process of humankind is, first of all, the process of movement from autonomous and isolated social minisystems towards the formation of the present extremely complex system of actively interacting societies; (f) when (and if) humankind transforms into a subject whose development as a whole is determined (at least partially) by a common and explicitly expressed collective will, the historical process in its current meaning will come to its end, and this will lead to a transition to a new generation of processes.

Thus, historical process is a notion that generalizes an intricate complex of internal transformations and actions of various historical subjects, as a result of which some important societal changes and integration, continuous enlargement of intersocietal systems take place, a transition to new levels of development is going on, and (taking into account the present results and future prospective), the humankind in general transforms from a potential unity into an actual one.

2. The Production Principles and Production Revolutions

According to the theory that we develop, the historical process can be divided most effectively into four major stages or four formations of historical process. The transition of any of these formations into another is tantamount to the change of all basic characteristics of the respective formation. However, in addition to this principal basis of periodization (that determines the number of distinguished periods and their characteristics), we need an additional basis to work out the chronology in detail.

As such an additional basis we propose the production principle (e.g., Grinin 2007a; 2007b; 2012: ch. 1; 2013) that describes major qualitative stages of development of the world productive forces. One may regard three production revolutions (the Agrarian, the Industrial, and the Cybernetic ones) as the borders between production principles.

We single out four production principles:

1. Hunter-Gatherer.
2. Craft-Agrarian.
3. Industrial.
4. Scientific-Cybernetic.

Though the qualitative transformations in some spheres of life are closely connected with changes in other ones (and, thus, no factors can be considered as absolutely dominant), some spheres (with respect to their influence) can be considered as more significant; that is, changes within them are more likely to produce changes in other spheres than the other way round.[2] The production principle belongs to such spheres due to the following reasons:

1. Significant changes in the production basis lead to the production of more surpluses and to a rapid population growth. And both these processes lead to changes in all other spheres of life. Still a transition to new social relations, new religious forms, etc. is not so directly connected with demographic changes as are the transformations of the production principle.

2. Though a significant surplus can be the result of some other causes (natural abundance, successful trade or war), such exceptional conditions cannot be borrowed, whereas new productive forces can be borrowed and diffused, and thus, they appear in many societies.

3. Production technologies are applied by all members of a society (and what is especially important, by the lower social strata), whereas culture, politics, law, and even religion are systems developed by their participants (usually the elites).

The change in production principles is connected with production revolutions. The starting point of such revolutions can be regarded as a convenient and natural point from which the chronology of formation change can be established.

The production revolutions are the following: 1) the Agrarian Revolution (the ‘Neolithic Revolution’); 2) the Industrial Revolution; 3) the Cybernetic Revolution. The production revolutions as technological breakthroughs have been discussed for quite a long time. The Industrial Revolution became an object of extensive research already in the 19^th century.[3] The first ideas on the Neolithic (Agrarian) Revolution appeared in Gordon Childe's works in the 1920s and 1930s, and he developed the theory of this revolution in the 1940s and 1950s (Childe 1948, 1949, 1952). In connection with the Cybernetic Revolution (which started in the 1950s as the Information-Scientific one) the interest in the study of production revolutions significantly increased. Much has been written about each of the three production revolutions (see, e.g., Reed 1977; Harris and Hillman 1989; Cohen 1977; Rindos 1984; Smith 1976; Cowan and Watson 1992; Ingold 1980; Cauvin 2000; Knowles 1937; Dietz 1927; Henderson 1961; Phyllys 1965; Cipolla 1976; Stearns 1993, 1998; Lieberman 1972; Mokyr 1985, 1993, 1999; More 2000; Bernal 1965; Philipson 1962; Benson and Lloyd 1983; Sylvester and Klotz 1983); however, there is a surprisingly small number of studies concerning these revolutions as recurrent phenomena, each representing an extremely important landmark in the history of humankind. We have developed a theory of production revolutions (Grinin 2007a, 2007b, 2012) within the framework of general theory of a world historical process.

The production revolution can be defined as a radical turn in the world productive forces connected with the transition to the new principle of management not only in technologies but in the interrelations of society and nature. The difference of a production revolution from various technical overturns is that it touches not only some separate essential branches but the economy on the whole. And finally, the new trends of management become dominant. Such an overturn involves in the economical circulation some fundamentally new renewable or long inexhaustible resources, and these resources must be widespread enough within most territories; it increases labor productivity and/or land carrying capacity (the yield of useful product per unit of area) by orders of magnitude; this is also expressed in the creation of several orders greater volume of production and the demographic revolution (or the change of the demographic reproduction type).

As a result, the most powerful impetus for qualitative reorganization of the whole social structure is generated. Although the production revolution begins in one or a few places but as it signifies the turn of the world productive forces, it represents a long lasting process gradually involving more and more societies and territories. As a result a) the societies where it took place become progressive in the technological, economical, demographical, cultural and often military aspects; b) joining new production system becomes a rule.

Each production revolution has its own cycle. We can speak about three phases, including two innovative phases and between them – a modernization phase of expansion of new production principle, that is a long period of distribution and diffusion of innovations.

Thus, a cycle of each production revolution looks as follows: the initial innovative phase (the emergence of a new revolutionizing productive sector) – the modernization phase (distribution, synthesis and improvement of new technologies) – the final innovative phase (improving the potentials of new technologies up to the mature characteristics). See also Fig. 1.

Each innovative phase of a production revolution represents a major breakthrough in production. During the first innovative phase the new production principle hotbeds are formed; those sectors that concentrate the principally new production elements grow in strength. Then the qualitatively new elements diffuse to more societies and territories during the modernization phase. In those places where the most promising production version has got formed and adequate social conditions have appeared, the transition to the second innovative phase of production revolution occurs, which marks the flourishing of the new production principle. Now the underdeveloped societies catch up with the production revolution and become more actively engaged in it. Thus, we confront a certain rhythm of the interchange of qualitative and quantitative aspects. A general scheme of two innovative phases of production revolution within our theory looks as follows:

Agrarian Revolution: the initial innovative phase – transition to primitive hoe agriculture and animal husbandry (12,000–9,000 BP); the final phase – transition to intensive agriculture (especially to irrigation [5300–3700 BP] or non-irrigation plough one).

Industrial Revolution: the initial phase starts in the 15^th and 16^th centuries with the vigorous development of seafaring and trade, mechanization on the basis of water engine, the deepening division of labor and other processes. The final phase is the industrial breakthrough of the 18^th century and the first third of the 19^th century which is connected with the introduction of various machines and steam energy.

Cybernetic Revolution: its initial phase, which we call the scientific-information epoch, dates to the 1950–1990s. Breakthroughs occurred in automation, power engineering, synthetic materials production, space technologies and in particular in the development of electronic means of control, communication and information. The final phase will begin in the 2030–2040s and it will last until the 2060–2070s. This forthcoming phase can be called the epoch of controllable systems because the main point lies in the ability to create systems that could be self-controlled or indirectly controlled either through other systems or by means of point impact and corrections. As a result there will be much more opportunities to influence without direct human interference upon various natural, social and production processes whose control at present is impossible or quite limited. We suppose the final phase of Cybernetic revolution will originate in a narrow sphere at the crossing of medicine and biotechnology, it may start with a drastic increase of opportunities to influence human biological nature. In the last section of the article we present preliminary ideas and prognoses about the main features and dimensions of the forthcoming phase of Cybernetic revolution, otherwise called the epoch of controllable systems. There is a number of various suppositions concerning changes of that kind, they are dealt with by intellectuals in different fields starting from philosophers to fantasists (see, e.g., Fukuyama 2002; Sterling 2005). However, our prognoses have an advantage over many of them because we base on the scientific theory.

We believe that the production revolution can be regarded as an integral part (the first ‘half’) of the production principle, after which the development of mature relations takes place. Such an approach demonstrates in a rather explicit way the main ‘intrigue’ of the cyclical pattern of historical formations. In their first half we observe mostly the radical production changes, whereas in the second half we deal with especially profound changes of political and social relations, public consciousness and other spheres. Within these periods, on the one hand, political-judicial and sociocultural relations catch up with more developed production forces, and, on the other hand, they create a new level, from which an impulse toward the formation of a new production principle starts.

However, a production principle cycle can be also represented in a classical three-phase fashion: formation, maturity, and decline. Yet, in some sense it appears more convenient to represent it in six phases, each pair of which demonstrates an additional rhythm of change of qualitative and quantitative characteristics. Such a cycle looks as follows:

1. The first phase – the beginning of production revolution and the formation of a new production principle. The latter emerged in one or a few places, however, in rather undeveloped, incomplete and imperfect forms.

2. The second phase – the stage of initial modernization. It is connected with a wider diffusion of new production forms, with reinforcement and vigorous expansion of a new production principle.

3. The third phase – the final stage of a production revolution. The production principle obtains mature characteristics.

4. The fourth phase – the stage of maturity and expansion of production principle. It is connected with the diffusion of new technologies to most regions and production branches. The production principle acquires its mature forms and that leads to important changes in social-economic sphere.

5. The fifth phase – the stage of an absolute dominance of a production principle. It leads to the intensification of production, the realization of its potential almost to the limit.

6. The sixth phase – the stage of non-system phenomena or a preparatory phase (for a transition to a new production principle). Intensification leads to the appearance of non-system elements (for the given production principle) that prepare the formation of a new production principle (when under favorable conditions these elements can form a system, and in some societies a transition to a new production principle can take place, and a new cycle begins).

[4] Note that this date is not identical with the modern dating of the emergence of Homo sapiens sapiens (100,000–200,000 years ago). Though discoveries of the recent decades have shifted the date of the Homo sapiens sapiens formation back in time to 100–200 thousand years ago (see, e.g., Stringer 1990; Bar-Yosef 2002; Bar-Yosef and Vandermeersch 1993; Marks 1993; Pääbo 1995; Gibbons 1997; Holden 1998; Culotta 1999; Kaufman 1999; Lambert 1991; Zhdanko 1999; Klima 2003: 206; White et al. 2003; Shea 2007), the landmark of 40,000–50,000 years ago still retains its major significance. This is that time, since which we can definitely speak about the humans of modern cultural type, in particular, about the presence of developed languages and ‘distinctly human’ culture (Bar-Yosef and Vandermeersch 1993: 94). And though there are suggestions that developed languages appeared well before 40–50 thousand years ago, these suggestions remain rather hypothetical. Most researchers suppose that the dependence on language appeared not earlier than 40,000 years ago (see Holden 1998: 1455), whereas, as Richard Klein maintains, ‘everybody would accept that 40,000 years ago language is everywhere’ (see Holden 1998: 1455). Klein, a paleoanthropologist at Stanford University, has offered a theory which could explain such a gap between the origin of anatomically modern Homo sapiens and much later emergence of language and cultural artifacts: the modern mind is the result of a rapid genetic change. He puts the date of change at around 50,000 years ago, pointing out that the rise of cultural artifacts comes after that date, as does the spread of modern humans from Africa (see Zimmer 2003: 41 ff.). So the period 50,000–40,000 years ago was the time of the beginning of social evolution in the narrow sense (see below).

The third phase may begin approximately in the 2030s–2040s. It will mean the beginning of the final phase of the Cybernetic Revolution that in our view may become the epoch of ‘controllable system’, that is, the vast expansion of opportunities to purposefully influence and direct various natural and production processes (see Grinin 2007a, 2012).

For the expected lengths of the fourth, fifth, and sixth phases of the Scientific-Cybernetic production principle see Table 1 in Appendix. In general, it may end by the end of this century, or by the beginning of the next one.

Instead of a Conclusion. Some Ideas about the Cybernetic Revolution

Now let us make a predictive analysis of major changes that the Cybernetic Revolution has already yielded and will bring about. Our forecast is based on the revealed developmental patterns at the final and initial stages of the previous production revolutions and already visible trends of the Cybernetic Revo- lution.

We suppose that the leading trends of the epoch of controllable systems will be: biotechnologies, human medicine and to a lesser extent nanotechno-logies.

The most important characteristics of the Cybernetic Revolution are the following:

1. A qualitative growth of control over systems and processes of various kinds, scales, complexity, and levels. It means an ability to create sustained systems, which can self-regulate without human interference; as well as such systems' capacity to autonomous functioning and adaptation to changes.

Within this leading trend there exist and will appear numerous variants of providing such control and self-regulation, including the influence on the key elements of systems and process steps; a controllable maintenance of the weakest elements of the system by means of resources of the system itself or with minimal interference; a prognosis and prevention of possible failures, probable regeneration of particular, most vulnerable elements, etc.

2. The determination of optimal operations within particular objectives and tasks (as a logic consequence of the first characteristics).

3. The creation of complex synthesized systems (which can be termed the transcybernetic ones) resulting from the development of self-regulation. One can speak about a large diversity of synthesis of principles and materials of different levels, as well as of an active development of systems comprising principles and materials of different levels of systems: inanimate, animate and technical, etc.

In particular, there will start a process of creation of biotic (biotechnical) systems (including human organism) which will involve to a different degree principles and materials of animate and inanimate nature functioning on the basis of both biological and technological principles, as well as on the more complex biosocial and technological ones.

The group of attributes of task-aware adaptation of materials and system:

4. Individualization as a guideline in the development of technologies and business strategies. Individualization manifests in the development of technologies of mass short-run or individually-tailored production with account of a consumer's particular demands as well as in the creation of goods that adapt to the consumer's desire (given him or her an opportunity to adjust them rather significantly to one's own demands). In the future, the opportunities will grow to choose an individual strategy as the most optimal (here one can also trace the connection with Item 2), in particular to solve certain tasks, to meet the individual's goals, for particular farming lands, etc. With development of medicine, the orientation to individual peculiarities of human organisms and people's desires will become much more important than in modern economy.

Miniaturization trend; that is a constant decreasing of the size of particles, mechanisms, electronic devices, etc.

6. The resource and energy saving in any sphere of activity also through the miniaturization of systems, localization of domain of impact, etc. (here the nanotechnologies come to the fore).

7. The development of the predetermined but previously non-existent properties in chemical, biological and bionic (techno-biological) systems.

We will shortly discuss some of these criteria.

We suppose that all trends of the Cybernetic Revolution will be tightly interconnected and support each other.

Biotechnology

Biotechnology is one of the most rapidly developing branches of industry. By the 2020s, the global market of biotechnological industries is expected to reach 700 billion dollars. Biotechnology is tightly connected with food, pharmaceutical[9] and biochemical industries.

In biotechnology production we can see the trends that lead to the formation of self-regulatory systems. This will affect the production processes, which will become more efficient and cost effective. Nowadays, the self-regulation is well traced at the genome level. In gene construction the scientists insert, alongside with a useful gene, special controlling genes-promoters that launch a necessary gene only under certain conditions. In future this technology will develop. A number of gene constructions will be inserted in an organism at once. This will provide flexible response to different changing factors, such as weeds, vermin, drought and others. The genetic engineering allows manipulating genes and expanding an organism's biological properties for specified purposes. Due to huge internet databases and automatization of manipulations with DNA, even today one can select a necessary gene for a plant or an animal and insert it in the organism. Genetic modification can already change a whole population, for example, the mosquitoes carrying the gene of infertility are being introduced into the wild population, spreading the gene, when crossed, and thus reducing the number of insects (Tkachuk et al. 2011).

The number of genetically modified organisms grows every year. As a result of completed cybernetic revolution the genetic engineering will be individualized for the sake of the slightest peculiarities. In other words, producers will be able to create a plant or a domestic animal variety in small home laboratories according to their requirements for particular climate and regions. Cloning is an important part of individualization. Nowadays it is well worked-out and employed for plants. With respect to the animal organisms cloning is not that efficient. It is highly improbable that human cloning will develop. One can find much more opportunities for therapeutic cloning when an organism's development is stopped in order to get the stem cells and use them for growing the necessary organs and tissues. In the future this can become an important source of tissues and organs in human medicine.

The biotechnological industry provides a significant production cost saving.

Very promising are biofuels, which today accounts for 10 % of the total energy output. Its use may increase by more than 10 times by 2035 (Kopetz 2013). Biotechnology allows producing new eco-friendly materials (e.g., bioplastic). The range of products made from bioplastics is already very wide. In the period from 2000 to 2008, global consumption of biodegradable plastics based on starch, sugar and cellulose increased by 600 % (Ceresana Research 2011).

We will see a very broad invasion of biotechnology in our lives: a power supply system, a variety of materials, medicine, etc. We think that in the future it is the biotechnologies that can help developing countries to make a qualitative breakthrough, get cheaper energy, establish low-cost production of pharmaceuticals and nutritional supplements, develop agriculture and increase the standard of life.

Medicine

In the second half of the 20^th century, the significance of health care as an economic sector has sharply increased. We suppose that during the Cybernetic Revolution its role will radically grow. The most actively developing branches of medicine are: pharmaceuticals; aesthetic medicine; fight against cureless diseases; implantation; reproductive medicine and gene therapy.

Medicine becomes more and more individualized. This is especially obvious in the selection of an individual treatment program for every person by computers and in the field of aesthetic medicine. The wealthier is a society, the larger part of the income people spend on health and beauty. In the nearest decades one can suppose an explosive growth of all types of aesthetic medicine. Individualization will also manifest at the level of gene therapy by means of which some serious genetic diseases are already treated. In the future every patient will be treated according to his genetic record and the defected genes will be repaired. Bionics will allow expanding human individual properties. The equipment has already been worked out that helps paralyzed people speak, write and even work with computers. One of the criteria for assessing the development of medicine is the production of medicines, their number is steadily increasing. The developed countries invest heavily in the development of drugs (Baker 2013). Pharmaceuticals will become more individualized. Drug production has been steadily increasing. In the future, patients will be prescribed drugs according to the individual characteristics of their organism and transportation of drugs in the body will become so accurate that will require miniscule doses. An important direction of the individual treatment is creation of the artificial immune system (Woollett 2012; Dickert, Hayden, and Halikias 2001). One of the promising trends in medicine is the slowing aging at the molecular level (Slagboom, Droog, and Boomsma 1994). Medicine has a direct impact on life expectancy, which in the future may achieve 90–100 years.

Self-regulation in medicine is expressed at different levels. For example, many processes of self-regulation are provided by special biochips implanted in the organs which make it possible to control vital processes. Thus, the treatment can proceed even without human interference. In 2011, the first pancreas transplantation was fully performed by the surgical robot Da Vinci. The surgery required only a seven centimeter incision and three small holes in the abdominal wall. In future such surgeries will become common. Thus, the job of a doctor in its present sense can disappear at all.

The struggle with incurable diseases is the most important branch of medicine. According to the World Health Organization in the developed countries the most frequent diseases that lead to death are heart diseases (12.8 % mortality), strokes, and other cerebrovascular diseases (10.8 %), AIDS (3.1 %), cancer (2.4 %), diabetes (2.2 %) and others (WHO 2011). In the future many incurable diseases will respond to treatment. Cancer control progress is associated with early diagnosis and increasing recovery rates. There appear some ideas how to outwit cancer (Marx 2013). However, it is very likely that by the 2030s cancer still will not be defeated. Surely this victory itself can be a powerful impetus for a general breakthrough in medicine.

Energy and resource saving. The most precise diagnostic methods will give an opportunity to define the required concentrations and forms of medicines, thus reducing the patient's expenses and cheapening the treatment. And nanotechnologies will allow transporting the necessary active substances to the sick cells thus minimizing side effects.

Nanotechnology

Nanotechnology is the manipulation with matter on an atomic and molecular scale. Nanotechnology works with materials, devices, and other structures with at least one dimension sized from 1 to 100 nanometres.

Since ancient times the humankind has used nanomaterials, for example, to produce paints, iron and steel.

Nanotechnologies are among the most actively developing economic sectors. Today nanotechnology is a multi-million dollar industry. The sales achieve nearly 20 billion dollars and by 2017 they will probably grow to 49 billion (BCC Research 2012). Current nanotechnologies are used practically everywhere: in medicine, heavy industry, electronics, and chemical industry, etc. The fastest economically developing sectors are biomedical, optoelelectronics and alternative energy. Despite the substantial progress of nanotechnology in electronics and other industries, a real breakthrough of nanotechnology is likely to happen first in medicine, which will give impetus to the development in other areas. One lays great hopes on nanotechnologies in the sphere of defeating cancer.

Self-regulation in nanotechnologies. A close connection between nanotechnologies and increasing self-regulation of systems is due to the fact that nanotechnology itself is based on the aspiration to make molecules and atoms become ordered in a certain spatial and structural pattern, that is the idea to harness the self-regulatory processes of matter. Many nanotechnological systems are capable to autonomous control. One can mention as an example the self-cleaning mechanism of the car glass treated with special polish. The self-cleaning mechanism is based on the so-called lotus effect. The surface is modified in such a way that a water drop slips down taking dirt with itself. So for this car glass even some rain water is enough to make it clean.

Individualization in nanotechnologies can be traced in the connection with medicine at the level of biochips created on the biotechnological basis. For example, biosensors will be able to monitor the spread of a virus in blood in an online mode (Cavalcanti et al. 2008). It is supposed that nanotechnologies can help to change the tilling land technique by means of nanosensors, nanopesticides and a system of centralized water purification. Individualization will be connected with technical devices. Future models of mobile phones can be able to change the form, size or color according to the individual preferences.

The resource and energy saving. Many nanotechnologies aim at reducing energy consumption as well as at creating alternative energy sources. For example, ‘clever glass’ for buildings that can react to the changing temperature and light with the respective change in transparency and thermal conductance. This is tightly connected with self-regulation in nanotechnologies. A wide usage of electronic paper can save forests on the Earth.

Finally, one should note that the forthcoming changes may bring about serious ethic issues. The radical changes in human organism may seriously damage such vital aspects as family, gender, and outlook on life. That is why the forecasts of the development of the Cybernetic revolution are important. They can help to create beforehand some optimal social, legal and other means so that those changes will not surprise and their negative consequences could be minimized. On the whole, the revolution of controllable systems will also involve social systems, so we should work out certain mechanisms of social forecasts and prevention, which will be introduced at least before the mass diffusion of dangerous innovations or forestall their influence.

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With regard to social disciplines, a question continually arises: are mathematical methods suitable for analyzing historical and social processes? Obviously, we should not absolutize the differences between fields of knowledge, but the division of sciences into two opposite types, made by W. Windelband and H. Rickert, is still valid. As is known, they singled out sciences involving nomothetic methods, that is, looking for general laws and generalizing phenomena, and those applying idiographic methods, that is, describing individual and unique events and objects. Rickert attributed history to the second type. In his opinion, history always aims at picturing an isolated and more or less wide course of development in all its uniqueness and individuality (Rickert 1911: 219).

However, since the number of objects and problems investigated and solved by precise methods is growing rapidly, we may assume that, with time, historical knowledge will also be analyzed by some branches of mathematics.

Thus, the problem remains debatable. Nevertheless, rational attempts to use mathematical methods in theoretical or applied trends of the humanities are on the whole positive. Yet, they ‘dry up’ the soul of history to some extent, but at the same time, they promote self-discipline and self-testing of thoughts, ideas, and concepts of many specialists in the humanities, who, unfortunately, often do not bother to find any methods of testing their conclusions. In addition, this could somewhat reduce the polysemy of the scientific language of the humanities. R. Carnap in his Philosophical Foundations of Physics (carnap 1966) wrote that, even in physics, the use of terms from ordinary language (as the notion of law) for an accurate and unambiguous expression of ideas complicates proper understanding. However, physicists, as well as other representatives of natural sciences, long ago agreed on fundamentals (such as units of measurement and symbols). As for the humanities, which analyze social phenomena, the same objects sometimes have up to ten meanings and hundreds of definitions. Perhaps, the very necessity to formalize the humanities will lead at last to certain conventions and the ordering of terminology. Nevertheless, even today the use of mathematics may help in searching for a common field of research.

Can we after all construct any mathematical models for such a complex subject of inquiry as the historical process? The answer to this question is obvious: yes, it is quite possible when examining countable objects.

However, when we speak about some global general theories, like macroperiodization of the world historical process, any figures, cycles, diagrams and coefficients, of course, cannot prove too much by themselves. Especially, if the respective analysis includes ancient periods for which all the figures are likely to be too much approximate and unreliable. Thus, for general theories covering immense time spans and space, the main proves are a good empirical basis, logics, internal consistency and productivity of theoretical constructions; that is, a theory's ability to explain the facts better than other theories do. On the other hand, any theory is better when it is supported by more arguments. Mathematical proofs can be rather convincing (when they are relevant, of course). This is especially relevant with respect to those aspects that are more liable to mathematical analysis, for example, those connected with demography.

In this paper we have chosen such an aspect that is liable to mathematical analysis and quite suitable for it. This is the temporal aspect of history. Its suitability for mathematical analysis is connected with the following: though it is quite possible to speak about the tendency of historical time toward acceleration, the astronomic time remains the same. Thus, within this study we have a sort of common denominator that helps to understand how the ‘numerator’ changes. Hence, we believe that for the analysis of periodization of history the application of mathematical methods is not only possible, but it is also rather productive.

Now we can start our mathematical analysis of the proposed periodization. Mathematical methods are quite widely used in historical research, but, unfortunately, mathematical studies of historical periodization are very few indeed.[10] However, it is worth mentioning that there have been published several issues of the almanac with a telling title – History and Mathematics (Grinin, de Munck, and Korotayev 2006; Turchin et al. 2006; Grinin, Herrmann, Korоtayev, and Tausch 2010). In the meantime the discovery of mathematical regularities within an existing periodization may serve as a confirmation of its productivity and as a basis for tentative forecasts. Time as a parameter of historical development is quite suitable for mathematical analysis, for example, economic and demographic historians study actively temporal cycles of various lengths (about Juglar and Kondratieff cycles see Korotayev and Grinin 2012; Grinin, Korotayev, and Malkov 2010). Cycles used as a basis for this periodization are not different in any principal way from the other temporal cycles with regard to the possibility of being subject to mathematical analysis.

Table 1 (‘Chronology of Production Principle Phases’) presents dates for all the phases of all the production principles. However, it should be taken into account that in order to make chronology tractable all the dates are approximated even more than the ones used in the text above. Table 2 (‘Production Principles and Their Phase Lengths’) presents the absolute lengths of the phases in thousands of years.

Production principle	1st phase	2nd phase	3rd phase	4th phase	5th phase	6th phase	Overall for production principle
1	2	3	4	5	6	7	8
1. Hunter-Gatherer	40 000–30 000 (38 000– 28 000 BCE) 10	30 000–22 000 (28 000– 20 000 BCE) 8	22 000–17 000 (20 000– 15 000 BCE) 5	17 000–14 000 (15 000– 12 000 BCE) 3	14 000–11 500 (12 000– 9500 BCE) 2.5	11 500–10 000 (9500– 8000 BCE) 1.5	40 000–10 000 (38 000– 8000 BCE) 30
2. Craft-Agrarian	10 000–7300 (8000– 5300 BCE) 2.7	7300–5000 (5300– 3000 BCE) 2.3	5000–3500 (3000– 1500 BCE) 1.5	35000–2200 (1500– 200 BCE) 1.3	2200–1200 (200 BCE– 800 CE) 1.0	800– 1430 CE 0.6	10 000–570 (8000 BCE – 1430 CE) 9.4
3. Industrial	1430– 1600 0.17	1600– 1730 0.13	1730– 1830 0.1	1830– 1890 0.06	1890– 1929 0.04	1929– 1955 0.025	1430– 1955 0.525
4. Scientific-Cybernetic	1955–2000 (1955–1995)* 0.04–0.045	2000–2040 (1995–2030) 0.035–0.04	2040–2070 (2030–2055) 0.025–0.03	2070–2090 (2055–2070) 0.015–0.02	2090–2105 (2070–2080) 0.01–0.015	2105–2115 (2080–2090) 0.01	1955–2115 (2090) [forecast] 0.135–0.160

Note: In this line figures in brackets indicate the shorter estimates of phases of the Scientific-Cybernetic production principle (the fourth formation). Starting from the second column of this row we give our estimates of the expected lengths of the Information-Scientific production principle phases.

Table 2. Production principles and their phase lengths (in thousands of years)

Note: * This line indicates our estimates of the expected lengths of the scientific-cybernetic production principle phases.

Table 3 (‘Ratio of Each Phase [and Phase Combination] Length to the Total Length of Respective Production Principle [%%]’) presents results of our calculations of the ratio of each phase's length to the length of the respective production principle using a rather simple methodology.[11] Table 4 (‘Comparison of Phase Length Ratios for Each Production Principle [%%]’) employs an analogous methodology to compare lengths of phases (and combinations of phases) within one production principle. For example, for the Hunter-Gatherer production principle the ratio of the first phase length (10,000 years) to the second (8,000 years) equals 125 %; whereas the ratio of the second phase to the third (5,000 years) is 160 %. In the meantime the ratio of the sum of the first and the second phases' lengths to the sum of the third and the fourth (3,000 years) phases equals 225 %. Tables 3 and 4 also present the average rates for all the production principles.

Table 3. Ratio of each phase (and phase combination) length
to the total length of respective production principle (%%)

Production principle	1	2	3	4	5	6	1–2	3–4	5–6	1–3	4–6
1. Hunter-Gatherer	33.3	26.7	16.7	10	8.3	5	60	26.7	13.3	76.7	23.3
2. Craft-Agrarian	28.7	24.5	16.0	13.8	10.6	6.4	53.2	29.8	17	69.1	30.9
3. Industrial	32.4	24.8	19	11.4	7.6	4.8	57.1	30.5	12.4	76.2	23.8
4. Scientific-Cybernetic	28.1 (29.6)*	25 (25.9)	18.8 (18.5)	12.5 (11.1)	9.4 (7.4)	6.3 (7.4)	53.1 (55.6)	31.3 (29.6)	15.6 (14.8)	71.9 (74.1)	28.1 (25.9)
Mean	30.6**	25.3	17.6	11.9	9	5.6	55.9	29.6	14.6	73.5	26.5

Note: * In this line figures in brackets indicate the shorter estimates of phases of the Scientific-Cybernetic production principle (the fourth formation).

** The calculation of mean took into account only one version of the Information-Scientific production principle evolution (that is figures before brackets).

Table 4. Соmparison of phase length ratios for each production principle (%%)

Note: * The calculation of mean took into account only one version of the scientific-Cybernetic production principle evolution (that is figures before brackets).

Thus, the proposed periodization is based on the idea of recurrent developmental cycles (each of them includes six phases); however, each subsequent cycle is shorter than the previous one due to the acceleration of historical development. No doubt that these are recurrent cycles, because within each cycle in some respect development follows the same pattern: every phase within every cycle plays a functionally similar role; what is more, the proportions of the lengths of the phases and their combinations remain approximately the same (see Tables 3 and 4). All this is convincingly supported by the above mentioned calculations, according to which with the change of production principles stable proportions of the lengths of phases and their combinations remain intact.

In general, our mathematical analysis represented in diagrams and tables indicates the following points: a) evolution of each production principle in time has recurrent features, as is seen in Diagrams 1–4; b) there are stable mathematical proportions between lengths of phases and phase combinations within each production principle (Tables 3 and 4); c) the cycle analysis clearly indicates that the development speed increases sharply just as a result of production revolutions (see Diagram 5); d) if we calibrate the Y-axis of the diagram,[12] the curve of historical process acquires a hyperbolic (Diagram 6) rather than exponential shape (as in Diagrams 1–4), which indicates that we are dealing here with a blow-up regime (Kapitza et al. 1997).

[1] However, even the very notion of ‘world history’ and ‘universal history’, although a number of scholars recognize it as an important concept (e.g., Ghosh 1964; Pomper 1995; Geyer and Bright 1995; Manning 1996), had been considered rather useless for a long time by historians and social scientists. But the most important is that ‘while historians increasingly recognize the importance of world history, they remain relatively ignorant about it as a developing field’ (Pomper 1995: 1).

[2] Of course, we do not mean continuous and regular influence; we rather mean the moments of qualitative breakthrough. If after a breakthrough within a more fundamental sphere the other spheres do not catch up with it, the development within the former slows down.

[3] For example, by Arnold Toynbee (1852−1883). See Toynbee 1927 [1884]; 1956 [1884].

[5] Yet in some certain important points the biological adaptation and anthropological transformation lasted for quite a long time even after this threshold. Yet in certain significant respects the biological adaptation and anthropological transformation continued for quite a long time after this threshold (see, e.g., Alexeev 1984: 345–346; 1986: 137–145; Yaryghin et al. 1999, vol. 2: 165).

[6] Or using the title of Paul Mellars and Chris Stringer's book such a radical turn can be called ‘The Human Revolution’ (see Mellars and Stringer 1989).

[7] During the last glacial epoch, Würm III. The glacial maximum was observed about 20,000–17,000 BP when temperatures dropped by 5 degrees (Velichko 1989: 13–15).

[8] The point of view that, besides the 18^th century industrial revolution, there was also an earlier industrial revolution (or even industrial revolutions) is widely accepted in Western science (Bernal 1965; Braudel 1973, 1982, 1985; Hill 1947; Johnson 1955, etc.), but until now within Russian academic community it has quite a few advocates. Still it appears that in the last two decades the idea of marking out Early Modern Period (the end of the 15^th – 18^th centuries) has attracted a number of supporters. However, these scholars do not associate Early Modern Period with earlier industrial revolution.

[9] For example, the biotechnological way of medicine production gives a huge number of innovate drugs every year (Woollett 2012).

[10] It appears reasonable to mention here the works by Chuchin-Rusov (2002) and Kapitza (2004, 2006). Some ideas about the detection of mathematical regularities were expressed by Igor Dyakonov. In particular, he wrote the following: ‘There is no doubt that the historical process shows symptoms of exponential acceleration. From the emergence of Homo Sapiens to the end of Phase I, no less than 30,000 years passed; Phase II lasted about 7,000 years; Phase III – about 2,000, Phase IV – 1,500, Phase V– about 1,000, Phase VI – about 300 years, Phase VII – just over 100 years; the duration of Phase VIII cannot yet be ascertained. If we draw up a graph, these Phases show a curve of negative exponential development’ (Dyakonov 1999: 348). However, Dyakonov did not publish the graph itself. Snooks suggests a diagram called ‘The Great Steps of Human Progress’ (Snooks 1996: 403; 1998: 208; 2002: 53), which in some sense can be considered as a sort of historical periodization, but this is rather an illustrative scheme for teaching purposes without any explicit mathematical apparatus behind it.

[11] The absolute length of a phase (or a sum of the lengths of two or three phases) is divided by the full length of the respective production principle. For example, if the length of the hunter-gatherer production principle is 30,000 years, the length of its first phase is 10,000, the one of the second is 8,000, the duration of the third is 5,000, then the ratio of the first phase length to the total production principle length will be 33,3 %; the ratio of the sum of the first and the second phases' lengths to the total production principle length will be 60 %; and the ratio of the sum of the first, the second, and the third phases' lengths to the total production principle length will be 76,7 %.

[12] Within the calibrated scale the changes from one principle of production to another are considered as changes by an order of magnitude, whereas changes within a principle of production are regarded as changes by units within the respective order of magnitude. Such a calibration appears highly justified, as it does not appear reasonable to lay off the same value at the same scale both for the transition from one principle of production to another (e.g., for the Agrarian Revolution), and for a change within one principle of production (e.g., for the development of specialized intensive gathering). Indeed, for example, the former shift increased the carrying capacity of the Earth by one-two orders of magnitude, whereas the letter led to the increase of carrying capacity by two-three times at best.