The concepts of the subconscious and the unconscious, in particular of the collective unconscious, seem to be well known for everybody, along with interpretations of many phenomena of culture, social and political life that make use of them. Dreams, myths, fairytales, alchemy treatises, organisation of primitive tribes, other irrational displays have become the instruments for cognition of human behaviour, patterns of culture, including the modern ones. In contrast to such approaches, in the present book the concept of the rational unconscious is formulated. What can stand behind these words? - Practically, very ordinary and obvious things.

Firstly, we, people, being proud of our reasonability, do not know real issues of rationality. For example, what kind of forces are responsible for the ability to perform trivial logical actions such as counting, elementary combinatorial manipulations (incl. classifications), for the sense of measure and proportionality, and the like? We use such rational aptitudes constantly - in everyday life, in sciences. But obviously, we could never give them an appropriate explanation, because any investigation uses the mentioned operations and the resulting explanation becomes a tautology, a vicious circle. But we do know that the primordial people, even some classes of animals have rudiments of flair for counting. The simplest logic has pre-human roots and is based on the ground of the unconscious.

Secondly, more interesting for us is the development of the rational abilities. The modern societies can be characterised by the generality of school education. Which subjects are studied in the school first of all? - Arithmetic and writing. The former is the one we are about to discuss, but in writing, as well, occur operations of decomposition into basic elements (letters, words, sentences), following the joining-up tasks and observation of the obligatory rules. At the senior school grades the specific weight of mathematics and similar disciplines (physics, chemistry) is by no means reduced. This is a picture with some tinge of grandeur: from generation to generation in different countries, regardless of the language, the ideology, the religion, the social status, we have been learning basically the same subjects in the course of years, adding to this at the most receptive age, what accounts for our sustainable habit to the elementary logical operations. But this is only a half-deal.

What happens later to the abundance of theorems, axioms, methods and formulas, which were studied at school? - Most of them have become forgotten as time goes, being displaced into the semi- or completely unconscious sphere. But should we conclude that the school years go away without a trace? The negative answer, I assume, should not give rise to any censures. Regardless of our profession, inclinations, we are not able to get rid of the stereotypes, the standards of thinking which were imprinted when we were children. In general, we all are like this, and the elementary mathematics has become what makes us interrelated - besides, on top, or, vice versa, "from below" the real variety. The concept of the new unconscious, rational and collective by its nature, is proposed particularly on that ground. The assumed peculiarity of social psychology, according to here admitted hypothesis, is responsible for many features of human culture (especially the mass and the popular one), as well as for social and political life. The same reasons hand over the right to study a number of cultural invariants, forms of social organisation, etc. by means of elementary mathematical methods, that, in fact, is the main topic of the present book.

Chapter 1 is dedicated to the research of the premises of widely known concepts in which integers are involved. We mean such numbers that have internally obligatory nature, rather than random one, without which we could hardly understand the sense of mentioned concepts, thus which might be called immanent, culture-formative ones. Why, for example, do we prefer in language and grammar to hold on to the model of three persons: I - You - (He, She, It), - three genders (masculine - feminine - neuter), three tenses (past - present - future)? Why does the same figure appear in other concepts, which are no less integral and internally indispensable: three-dimensional space in classical physics, three classes of the modern Western societies (rich - middle - poor), three branches of the state power (legislative - executive - judicial)? In other cases the similar creative role is performed by the number "four": e.g., four-dimensional space-time in the theory of relativity. The list of the examples pls. see in the Content. A characteristic cultural role refers, of course, not only to two named numbers, and in the present chapter their logical origin is analysed.

In chapter 2, the author turns his attention to patterns of political conditions of mass societies as a result of political revolutions (or upheavals) linked to corresponding numbers. What in common have the countries that have gone through one revolution on the one side, through two on the other, through three in the third case, through four, etc.? What kind of political achievements do they have? It is obvious, that every serious revolution is supposed to have ended sooner or later, and it must be succeeded by a more or less stable state. Therefore, we can research any society from the point of view as if its revolutions were in the past (until the next one). In the interval between the revolutions, the behaviour of the society, its self-consciousness are subordinated to certain stable, self-consistent patterns and laws. Insofar as society is a mass one, the mentioned laws could not be other, but the simplest (usually, mass consciousness serves as a sample of banality). The same society, being modern by its type, is relatively educated one, so that the elementary mathematical stereotypes play one of the title-roles. The realm of the past appears as certain strikingly lit spots, a pop-knowledge about previous revolutions, and this common knowledge seems to be very powerful form-creative factor.

For example, the USA has had up to now two major revolutions: the War for Independence (at the same time the antifeudal revolution) and the Civil War (in the course of which the crucial question of political future was being decided). In Britain there has been the same number of revolutions: Great English and Glorious revolutions. Both the USA and Great Britain are traditional samples of the liberal regimes. The February revolution of 1917 in Russia (which was the second one by its number, after the revolution of 1905), by the analogy, brought about social and political liberation, but shortly afterwards the third one happened, the Great October revolution, which established the totalitarianism. "The National Revolution" of 1932-33 in Germany was also the third one by its number (after the revolutions of 1848 and November 1918). The result was, in principle, the same: the totalitarianism. On the contrary, after November 1918 (#2) in Germany the Weimar republic came to existence, with fairly liberal features. Whereas consistent patterns found in historical material of many countries have proven to be considerably distinctive, and their explanations are quite simple, it is possible to use the developed conclusions for prediction, also: what we should expect from one or another country having gone through the next revolution.

In chapter 3 various social and political proportions and reasons of their appearance are considered. The main attention is paid to electoral processes. Why shall one particular political party (one candidate for president, governor) get such percentage of votes and the other a different one? What kind of forces are responsible for actual achievements? - On the current stage of research, the author avoid any help from previous electoral theories and suggests his own theory, which is much simpler. Calculations are produced without references to the results of public opinion polls, without figures representing social, national, religious structure of society, but based on characteristic signs of social consciousness during the election campaign. A comparison with the empirical data shows a highly satisfactory efficiency of the offered model. Besides, the model is proved to be suitable for the description of the outcome of the elections in a number of different countries, both the democratic and the post-totalitarian. A common feature of the two types of countries is that their population is educated and therefore subject to the laws of the rational unconscious.



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