Regimentum Mixtum

We can not explain the modern picture of the universe if we do not have definite concepts (or at least hypotheses) about the initial conditions for its evolution [SAKHAROV A.D. 1968, 74].

Like in astronomy, we have several tools for studying written history, the application of which and the complementarity of the results obtained with their help will allow us to draw up a satisfactory picture of the recent past. To answer what happened before the moment of maximum density, physicists are looking for tools to analyze the accumulated observational data. The same applies to the reconstruction of prehistoric processes. Here, the initial data are objects of the material culture of the ancients and a large number of languages, whose roots go back to the prehistoric era. The combined efforts of archaeologists and linguists can provide a reconstruction of the initial stage of the ethnocultural history of mankind, but if archeology has found methods for studying ancient cultures, linguistics cannot yet answer the question about their ethnicity.

In principle, linguistics has a huge amount of facts that can provide an answer to the particularities of prehistoric ethnogenetic responses. However, these facts must be systematized according to a certain law by similar signs and stratified chronologically. Otherwise, their interpretation will be arbitrary, depending on the subjective assumptions of individual scientists. At present, there are theories in historical linguistics based on hypothetical initial premises adopted speculatively. The lack of a generally accepted discussion platform leads to the struggle of conflicting opinions and does not contribute to reconstruction, but only confuses the imagination of diachronic processes in the history of mankind. Without the application of accurate research methods, the situation cannot change. Ukrainian philologist Illarion Svenetsky, who, defending the need for the use of mathematics in the humanities, wrote:

… It is important only that all sorts of human and world relationships are easiest to denote by numbers, volume, and position in space and time, as they can easily fit into the framework of mathematical symbols [SWIENCYCKYI I., 1927, 53]

Such a method, which determines the relative position of related languages in space at a certain time, exists, and it allows you to explore the origin and development of languages in the prehistoric period. This method , called by me graphic-analytical, allows research on the origin and development of languages in prehistoric times by means of available lexical material collected from dictionaries of various types. The idea of the method consists of a geometrical interpretation of interrelations between cognate languages on the basis of quantitative estimation of mutual linguistic units in pairs of languages within one language family or group. The greater kinship of languages is usually connected with the greater amount of mutual linguistic units and these are exactly mutual words that are most suitable for statistical processing. A large number of words allows you to avoid overestimating the significance of the characteristic units of languages for assessing their kinship when the number of such units is small. This method is based on a supposition that the inverse proportionality exists between the number of mutual words in a pair of languages and the distance between natural habitats where these languages were formed. To put it simply, the closer to each other the carriers of two cognate languages lived, the greater amount of mutual words they had in their languages. The use of vocabulary as a material for the estimation of the affinity of languages causes distrust due to the large number of loan-words. However, observations show that the loan-words relate primarily to a more «cultural» layer of words but ancient words, which correspond to the lower cultural level, still remain in the language. These ancient words in the language at the same time are the most commonly used. According to A.V. Desnitsky, native vocabulary includes a significant part of the most common words which reflect the basic concepts and create the largest number of word-producing nests [DESNITSKAJA A.V. 1966: 9]. M.V.Arapov and V.V. Herz say in their work about the dependence of the frequency of using a word and its age so:

There is a relationship between the frequency and the time of occurrence of the word in his language… Most of the words with a high frequency of use are ancient words, and vice versa – the lower the frequency of a word, the more likely that the word is new-created [ARAPOV M.V., HERZ V.V., 1974: 3]

The authors note that for the first time this connection was remarked by George Kingsley Zipf in 1947 and appreciated its significance for the quantitative analysis of the facts relating to the history of a language (Zipf’s law). However, it should be borne in mind that some words with a low frequency may be ancient, and there are many newly created words, which have a greater frequency of use, but they can be very easily removed in lexical and statistical studying according to their meaning. The difference between languages having a common origin, a German linguist associated with their place of residence as follows:

We must admit, strictly speaking, that there are as many separate languages in the world as there are individuals… If the intensity of communication were uniform at all points of a given language territory, then individual languages, where they are closely related, would only produce slight deviations, while at the opposite ends of the territory, sharp differences still occurred. Then it would be impossible to single out any group of individual languages in order to contrast it as a closed integrity with another similar group. The language of each individual could then be regarded as a transitional step to the languages of many other individuals. This situation, however, has never existed anywhere. It would become possible if there were no natural borders, no political and religious associations, if, say, the whole people lived on a single plain, not crossed by any significant river, in separate farms located at the same distance from each other, without common gathering places. However, in this case, too, the process of combining languages would be observed, at least in the languages of individual families [PAUL H. 1960: 58, 61].

If we try to reflect the language situation described by H. Paul in his hypothetical territory graphically, it has the appearance of the line MS in Figure 1.

Fig.1 Distribution of the number of mutual words between the dialects on the space without geographical boundaries

N is the number of mutual words between dialects. L is the distance between the habitats. M is the total number of words in one of the dialects. Q is the number of common words for all dialects. X – the distance on which new mutual words disappear.

Since the relationship between dialects is invariant, that is, the number of new mutual words depends only on the distance between them and does not depend on their location relative to other dialects, the relationship between the number of mutual words in dialects and the distance between habitats of their speakers will be linear and expressed by the function

N = (M – Q) – kL,

where k is the proportionality constant, depending on the population density, the number of dialect groups and other factors.

If the space of the speakers of a native language has geographical barriers which prevent their equable movement and communication and causes the formation of more or less permanent settlement areas of these groups, then not a continuum of dialects, but a certain number of discrete dialects arise within of this space.

In this case, the function N = (M – Q) – kL becomes a discontinuity at the point of intersection of the natural boundary. Simply put, the number of mutual words between different groups within the habitat decreases monotonically in proportion to the distance between their settlements but decreases abruptly at the border. We can assume that a certain more or less constant percentage of the mutual words is being lost at every crossing of the boundary. In this case, the distribution of the number of mutual words, depending on the distance will be like that shown in Figure 2 by the broken line MTUVWXYZ.

Fig. 2. Distribution of the number of mutual lexical items between dialects in areas, separated by ethnical boundaries.

N – the number of mutual lexical items in dialects; L – the distance between the habitats (areas); Q – the number of first-level lexical items, being the same for all dialects; M – the total number of words in an isolated dialect; AB, BC, CD, DE, – areas of distinct dialects.

This distribution has too complex am mathematical expression. But if we agree to consider newly developed distinct dialects within areas AB, BC, CD, and DE as individual language units, we can consider the distance between them to be equal to the distance between their area centres. Thus, connecting the centres of segments MT, UV, WX, and YZ, we obtain the distribution of mutual lexical items (words, for simplicity) in dialects as the line abcd. And if we move the origin of the co-ordinate to point Q, we’ll see that the shape of this line in its central part will be close to the hyperbola; therefore it can be described with the function of inverse proportionality y=k/x. In this case, the correlation between the number of words of the second level in the dialects and the distance between the centres of habitats can be approximately described with the formula:

M – Q = K/L,

where K is the proportionality constant.

Certain inaccessibility of habitats of isolated dialect speakers will eventuate in such difference between these dialects that the parent unitary language will split into new distinct languages which we shall call further the languages of the second level. These languages can be derived again and produce new languages of the third level, if the second level language speakers migrate to a new large territory. The combined complex of words of the first and second levels will remain in the languages of the third level. This process can continue further in producing the family tree of monophyletic languages.

As the result of this process the great deal of the word complex of low levels was conserved in the languages of the higher levels, but only words of the highest level will be subordinate to the law of inverse proportionality, i. e. when the number of mutual words of this level are depended on the distance between the language areas. Thus when we analyze languages of the higher levels, we have to remove all the words of lower levels from the study, as a rule, such words are common for all analyzed languages, and it considerably facilitates their exclusion.

Based on such considerations, the idea arose of representing related languages as a graphical model which can be located in a suitable place on the surface of the Earth. Experience has shown that such a place may be the only one. To build a model, a special type of graph is used that maybe still await its description in mathematics (the author has not found it in graph theory). So far, it can be characterized as a “weighted” graph, in which links exist not between distinct nodes, but necessarily between them all, and not only the link itself is important, but also its intensity, reflected by the distance between each of the nodes. In our case, the length of the edge of the graph corresponds to the number of mutual words in a pair of languages. However, the exact number of such words is unknown to us, since it is impossible to find them all in the dictionaries.

Using the graphic-analytical method, graphic models of the kinship of the following languages were compiled: Sino-Tibetan Tungus-Manchu, Mongolic, Nostratic, Abkhaz-Adyghe, Nakh-Dagestanian, Info-European, Finno-Ugric, Turkic, Germanic, Iranian, Slavic. For all these languages, territories were found on the geographical map where their primary dialects from the common parent language were formedю

In Eastern Europe, the Proto-Indo-European, Proto-Finno-Ugric, and Proto-Turkic languages are divided into distinct languages in the Volga, Dnieper, and Don rivers basins (see the map in the figure 3) [STETSYUK VALENTYN. 1998: 42-53] .

Fig.3. The Resettlement of the Indo-European, Turkic, and Finno-Ugric tribes in Eastern Europe circa the 5th mill. BC.

The Abbreviation for the languages: Alt – Southern Altai (Oirot), Arm – Atmenian, Balt -Baltic, Bulg – Volga-Bulgarish, Celt – Celtic, Est – Estonian, Fin – Finnish, Hung – Hungarian, Ill – Illyrian, Ind – Indo-Aryan, Ir – Iranian, It – Italic Kar – Karluk (Uzbek and New Uighur), Khak – Khakas, Kipch – Kipchak (Kumyk, Karachai, Balkarian, Crimea-Tatar, and Karaim), Kyrg – Kyrgyz, Mord – Mordovian, Phryg – Phrygian, Tat – Tatar and Bashkir, Thrac – Tracian, Tuba – Tuvinian and Karagasian, Yak – Yakut.

During the last decades, interdisciplinary research on the osculation of humanities and natural sciences put under the theoretical base for the application of the study by means of the graphic-analytical method. The impulse for the new approach to such researches was given by the work of B. B. Mandelbrot “The Fractal Geometry of Nature” [MANDELBROT B. B, 1982] where the author has introduced in scientific employment the category of the fractal. This term characterizes a geometrical figure composed of parts that are similar to this figure itself. Using the category of the fractal in synergetic natural systems, Czech scientist Radan Květ substantiates the theory of four joined nets in nature:

- the net of geological fault lines;

- the hydrological net;

- the net of prehistoric paths;

- the information net.

The essence of this theory is such. The faults of Earth’s crust and especially the fault zones with inclination from the highest points to the sea level conditioned the configuration of the hydrological net of water streams. Mainly on the first fluvual terraces, footpaths were put by man absolutely unintentionally, and the net of prehistoric paths was simultaneously the primary information net. This net promoted the widening of technological experience, world-view ideas, artistic tastes, etc [KVĚT R. 1998: 43, KVĚT RADAN. 2000: 294]. It goes without saying that together with the dissemination of experience and ideas, new words were also distributed, corresponding to the newly formed concepts. However, it should be borne in mind that the river network is very discrete and water flows can both contribute to the communication of people and prevent such communication. Small rivers and paths along them form a local area of close human communication, limited by wider rivers, which are a difficult obstacle for the dissemination of new information. Thus, in certain areas, a community of people is organized, and connected by real economic ties, a common language (dialect), and common cultural and ideological ideas. People’s awareness of this community becomes the determining factor for the formation of primary ethnic communities, which is impossible without a common language, another Czech scholar wrote about as early as 1940:

Tribal affiliation is the main and objective feature of the people because it embodies a complete geographical and genetic relationship. And only in this interrelation, a social organization arises leading to a common language and culture…. It is obvious that the national originality cannot be maintained without the peculiar spiritual atmosphere provided by the communicative feature of its own language [KORČAK JAROMÍR. 1940: 6]

Primary ethnic communities were based on blood ties, i.e. consisted of people of common origin and aware of this. A feature of these communities was the absence of social stratification in them, which contributed to the formation of a unified culture in which social and ethnic specificities coincided [CHEBOKSAROV N.N., CHEBOKSAROVA I.A. 1985: 70].

Tribe arises from a consolidation of primary communities with a tendency towards endogamy [BROMLEY Y.V. 1986: 431]. This trend contributes to the fact that some anthropological features are consolidated and spread in individual tribes. In one area there can be one or several tribes that make up one ethnic community. The geographical features of the areas (mainly natural boundaries) determine the unification of individual ethnic centers into a single community with pronounced linguistic, cultural, and social characteristics. As has happened many times in history, ethnic communities increase in number over time and leave their ancestral areas, migrating in search of new places convenient for living. However, usually part of the inhabitants remains in the old place and subsequently merge with the newly arrived population. Newcomers borrow elements of culture and language from indigenous peoples, and this is how a new ethnos is formed in the same natural conditions. With a repeated change in the population of areas, such a process can occur every time, therefore, such areas can be called ethno-producing

However, the primary ethnic groups that arise in the ethno-producing areas do not avoid communication with similar neighbors, although the exchange of information is no longer as intense as inside the area. With the emergence of ethnic identity, due to the feeling of differences in the languages and culture of the primary ethnic groups, the process of their separation is consciously taking place when people on the opposite bank of a large river are perceived as different or alien. At the same time, the river itself becomes not only a natural but also a psychological boundary between ethnic groups. As V. Evsyukov notes, in ancient human notions water space «is thought of as the magical boundary between worlds, the boundary between the transitory and the eternal, life, death and immortality» [YEVSIUKOV V.V. 1988: 47]. Usually, in the ancient worldview, own kin is considered as an embodiment of only positive, the other – of all negative. In addition, a different kin with its own customs and culture is often identified with the other world. Hence the motive of the water barrier separating «this» world from «that» [ibid: 54].

It goes without saying that natural obstacles can be not only big rivers, but also mountain ranges, forests, swamps, and the like. The assumption of the existence of natural boundaries between individual ethnic groups is natural and has long been perceived by scientists. For example, Telegin wrote that “natural frontiers (rivers, mountains, frontiers of landscape zones) often and for a long time served as boundaries for the settlement of certain ethnic groups” [TELEGIN D.Y. 1968: 21]. The importance of the existence of inter-ethnic boundaries was caused by the need to regulate the use of the territory. Referring to J. Balandier, L. Kubbel argues that such a need existed “even in the very early stages of the history of human society” [KUBBEL L.E. 1982: 126]. One can easily agree with this statement if we recall the existence in the biology of the designated boundaries of settlements of individuals and groups of higher mammals (bear, wolf, etc.), as well as of certain species of birds. In the period of the transition of man to a productive economy, the role of these boundaries becomes more and more important. This became especially noticeable when human communities with different types of management were neighbors and representatives of productive and unproductive economies came into contact. And the importance of organizing the territory grew in cases where different communities used the same ecological niche. “Moreover, just in these cases the limiting role of natural frontiers was especially clearly manifested” [ibid: 127].

Rivers are often the boundaries of archaeological cultures, although not always sufficiently clear. Sometimes we meet facts when material items of the same culture can be found along both banks of the river. Obviously, in such cases, we are confronted with the phenomenon of the ethnic membrane. When the formation of dialects has gone so far that their speakers begin to identify themselves as a separate ethnic unit with their own language and spiritual world, then natural obstacles already play the role of boundaries between ethnic groups no longer on their own, but as people-conscious boundaries between settlements. According to S. Arutyunov, such ethnic boundaries cannot be impenetrable, however, like a membrane, such a boundary can be permeable for some bonds and impermeable for others, it can be permeable in one direction and impermeable in the second (osmosis phenomenon). He gives an example of Khanty-Nenets relations. Marriage ties, movement of individuals and entire groups, and mutual assimilation of entire kins are bilateral, while the ethnic boundary remains fairly stable [ARUTYUNOV S.A. 1982: 77].

The fractal category introduced into scientific circulation by Benoit Mandelbrot should be among these principles since it reflects the peculiarities of the construction of many natural systems. This term characterizes a structure consisting of parts similar to the figure itself, that is, in a certain sense, a hierarchical structure. In such a structure, each part functions independently of the others, but in harmony with the whole following the idea adopted for its construction. The fractal principle contains a necessary, but no more than sufficient part of freedom in any construction. In particular, the human body, the river system, and many other things, in particular, to a certain extent, space, are built according to the fractal principle. The fractal principle is comprehensive in the physical world and the spiritual world should be created according to the same principle, that is, it can be applied in any creative work. We will proceed from this, considering the Universe an act of creativity, and observe the facts of similarity in it, as the idea of ​​​​a fractal, in various phenomena of the physical and spiritual world. The development of interhuman relations was influenced by factors absent in the animal world. Under the influence of these factors, man is fundamentally different from the animal. Fukuyama sees this difference in man’s desire to be a being with a certain dignity. He considers dignity as «the first glimmer of freedom» (Fukuyama Francis. 2004, 16). However, as already noted, a certain amount of freedom is present in the fractal.