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Tetrasociology: Science about Social and Individual Harmony

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Tetrasociology Textbook

First edition - July 2008

Approved by the GHA Board, November 14, 2009


The following stage of development of the textbook o­n Tetrasociology is the chapter published below which unfolds a logic structure and the basic content of this textbook.

Tetraphilosophy and Tetrasociology: a Science of Social Harmony


Dr. Leo Semashko


A discussion about the Harmonious Civilization Declaration philosophy took place in July 2009 with Reimon Bachika, Noor Gillani, Laj Utreja, Martha Dewitt and other GHA members that pushed and inspired the author to write this outline of Tetraphilosophy and Tetrasociology, putting them together to make Tetrism.


1. Philosophical Basics of Tetrasociology

2. Tetrasociology: a Science of Social and Individual Harmony

2.1. Tetrasociological Axiom

2.2. Fundamental Elements (Spheres) of Social Harmony

2.3. Laws of Tetrasociology

2.4. Structure of Tetrasociology

3. Pragmatics of Tetrasociology

3.1. Statistics of Tetrasociology: Matrixes of Sphere Indices

3.2. Mathematics of Tetrasociology: Tetra-mathematics

3.3. Tetrasociological Technologies

3.4. Projects of Tetrasociology and Empirical Tetrasociology

4. Conclusion. Tetrism: Global Ideology for a Global Harmonious Civilization


Quaternion is an inexhaustible source of life.

A measure is the basis for all. Pythagoras, 6 BC


Quaternion is a depository of eternal universal order;

it is the same thing as God-Creator. Hierocles, 5 AD


The higher the hammer is lifted in Heaven, the more deeply it cuts into Earth,

Creating either a sculpture or a palace. Michelangelo


Religiosity of the scientist consists in enthusiastic

relation to the laws of harmony. Albert Einstein


We must design the good future for children

To quest our new civilization for the true wealth and peace

To create our new life wisdom

To listen the harmony of this world. Kae Morii, Poet, Japan


Tetrasociology is a new social science that provides its rationale

and framework. Martha Ross DeWitt, Sociology Dr., USA



1. The Philosophical Basics of Tetrasociology


Any science originates from a certain philosophical basis. Tetrasociology as a pluralistic four-dimensional science of social and individual harmony of a harmonious civilization also has its philosophical base under the following name: Tetraphilosophy (or Tetrism). The author developed it parallel with Tetrasociology since 1976 (in dialectics and logics since 1967). Different variants of this philosophy are presented in his works of different years [1]. However, these philosophical basics of Tetrasociology are, itself, a major topic, worthy a special book. We introduce a general picture of Tetraphilosophy sufficient for the purposes of this book: understanding of a harmonious civilization and its thinking. Tetraphilosophy may be reduced to any of the below-mentioned models or to any block of models that gives the corresponding level of its understanding. At each stage, this philosophy, as well as any another, incorporates new, corresponding expression.

Tetraphilosophy is a pluralistic four-dimensional dialectic philosophy of harmony of nature, society and personality. It includes four tetra-theories: Tetra-ontology, Tetra-dialectics, Tetra-gnoseology and Tetra-logics. We limit ourselves to their summary. They are presented in Model-1: Structure of Tetraphilosophy of Harmony:





Tetra-ontology unfolds, develops, and emphasizes knowledge and understanding in regard tothe spheres of the world harmony as its fundamental elements, sources or foundations. Tetra-ontology recognizes four universal spheres of world harmony:

1. Existence (as in Jaspers and Heidegger, or separate as in Aristotle),

2. Information(or consciousness/spirit along with knowledge as in Kant and Hegel),

3. Organization (as in Comte and Spenser, or will as in Schopenhauer), and

4. Matter (as in Marx and Lenin).

Universal spheres allow interpretation of traditional Being/Existence as world harmony, transforming traditional ontology into ontology of harmony or harmonious ontology.

Model-2: Universal Spheres of World Harmony:



The universal attributes of world harmony spheres are:

1. They cannot exist separately; therefore they are inseparable, always single in diversity, diverse in unity and existing o­nly as mutually inclusive (nesting).

2. They are equally essential (necessary, required); each cannot exist without the others.

3. They inevitably confine or restrict each other up to certain limits in regard to their indivisibility and equal necessity.

4. The limits of mutual restriction of spheres serve as their equilibrium or balance and a proportion of these limits make HARMONY as a border of existence of spheres, i.e. a border of Being.

Model-3: Universal Attributes of World Harmony Spheres:


(Indivisibility or mutual inclusiveness/nesting, equal necessity, mutual restriction, = equilibrium = balance = proportion = harmony)


The notion of harmony in Tetraphilosophy integrates key attributes of Being at any level. In Tetra-ontology, the balance of mutual restriction of four inseparable and equally essential spheres is a final source of world harmony. Therefore, world harmony is treated as a balance of four inseparable and equally essential (necessary) spheres of existence that mutually restrict each other up to certain limits, making a measure of their harmony as a measure of their being. World harmony is a final source of the Universe existence.

Mutual restriction of inseparable spheres in their balance is a deep, maximum structure of the world harmony that is reproduced at all levels from micro-particles up to mega-Galaxies, including in individual human and a society. Tetrasociology deals with the reproduction of the deep structure of harmony at a level of society and personality.

Harmony is equally inherent in its four elements/spheres in their unbreakable unity. They possess equal opportunities to create and support harmony as a way of keeping their coexistence in balance. Each of these four elements is capable of advancing harmony as a unity of diversity. None of them (as well as not any other) has the monopoly for harmony.

Tetra-ontology may be expressed most briefly in the following o­ntological basic notions and laws of the world harmony of spheres, which are summed up and synthesized from the previous history of philosophy and culture:

1. Basis: There are four inseparable and mutually restricting, equally necessary(essential, required) and sufficient, universal and opposite spheres (realms) of Being: existence (or any individual phenomenon as unity of spheres), information, organization and matter. These make a deep, limiting structure of the world harmony at all levels of the Universe. Their unity is provided by their mutual inclusiveness: o­ne includes all; o­ne does not exist without the other. The principle All are in everything was formulated by Anaxagoras 2500 years ago.

A Law: The absence of at least o­ne of the spheres of Being makes existence of other spheres impossible, therefore they can exist o­nly in a mutual inclusion and restriction that determines harmonious unity of their diversity. This is the eternal objective law of the world sphere harmony. It is the law of existence of spheres and any phenomena of harmony. It is the law of all laws.

2. Basis: World harmony is a mutual restriction in mutual inclusiveness of the four inseparable spheres of Being that determines their equilibrium or balance, proportion, limit and measure. World harmony is a way of existence and cosmic order of the Universe at all levels.

A Law: Each phenomenon of Being has a special form and measure (a proportion and limits) of sphere harmony as an internal limit of existence.

3. Basis: Each phenomenon is a unity and mutual inclusiveness of all spheres, therefore the phenomena are identical and inseparable in a united deep four-dimensional structure, differing o­nly in priorities and measure of development of each sphere.

A Law: In each phenomenon the spheres are mutually inclusive, forming unbreakable harmonious unity of their diversity, differing in priorities and measure of development of spheres.(It is the differentiation of priorities of the world harmony spheres.)

4. Basis: Ontology of the priorities of the world harmony spheres and of each phenomenon determines the history of their development. Each sphere and its phenomenon is a unity of four spheres similar to a four-layer pie in which the top layer determines constant quality of the sphere (an absolute internal priority of spheres), and the priorities of other layers are variable (a relative external priority of spheres) depending o­n place, time and relations.

A Law: Constancy and change of sphere priorities determines the history of the world harmony at all levels.

Model-4: o­ntological Laws of the World Harmony Spheres:



Tetra-dialectics unfolds, develops, and emphasizes knowledge and understanding in regard to the relations and structural connections of the world harmony spheres. We formulate herein the following bases and laws of Tetra-dialectics.

1. Basis: Spheres of Being, as universal opposites of the world harmony, are subordinated to the laws of the dialectics of harmony.

The law of unity and harmony of sphere opposites as a source of development of the world harmony: Any world phenomenon is a unity and harmony of the universal sphere opposites (spheres) in which the struggle of particular elements is a demonstration of its (harmony) limit case in the form of abnegation of disharmonious particularunity and transition to a new harmonious particular unity.

2. Basis: quantitative changes of the sphere elements of harmony in any phenomenon lead to a qualitative change of their priorities.

The law of transition of quantitative changes of spheres of harmony into qualitative change of their priorities: Quantitative changes of spheres in any phenomenon lead to qualitative change of their priorities, which determine qualitative changes of the phenomenon.

3. Basis: Dialectics of the world harmony is realized through mutual negation of the two forms of sphere priorities: absolute and relative. Each sphere and any of its manifestations possess an absolute internal priority (primacy), which provides their qualitative constancy, and also a relative external priority in a different place, time and attitude, which provides their infinite variety and excludes external primacy of any sphere. No sphere possesses absolute primacy (absoluteness). Such kind of primacy of any sphere excludes harmony, hence, Being. Therefore, absolute primacy (in every respect) is impossible by definition. It is o­nly harmony of all four spheres that creates primacy in every respect (absolute). Differentiation between absolute and relative priorities is a slight, but basic, difference that divides monism from pluralism.

The law of mutual negation of two forms of priorities of the world harmony spheres: Spheres of the world harmony and any of its manifestations possess opposite forms of priority: absolute or qualitative and relative or quantitative, both of which constantly mutually deny and limit each other this determines and facilitates an infinite and continuous process of change and development of world harmony at any of its levels.

4. Basis: Double negation (negation of negation) of priorities of spheres defines concrete aspects of harmony, its repeatability and cyclicity (spiral-shaping), and its structural measure in historically varying place, time and relations.

The law of repeatability of priorities of the world harmony spheres: Double negationof the sphere priorities defines repeatability of structural measures of world harmony.

Dialectic laws (or laws of dialectics) of world harmony reveal different aspects of its development: the source (the first law), the way (the second and third laws), and the form (the fourth law). These laws transform laws of traditional industrial dialectics into the laws of harmonious dialectics and philosophy of a harmonious civilization; they also create and establish essentially new o­ntological, gnoseological, social and individual sense.

Model-5: Dialectic Laws of the World Harmony Spheres:



Tetra-gnoseology unfolds, develops, and emphasizes concepts and understanding in regard to the specific character of the knowledge of the four spheres of the world harmony and the laws of their dialectics. We formulate herein the following bases and laws of Tetra-gnoseology.

1. Basis. The idea of unity and dialectics of the four spheres of the world harmony has a long history in world philosophy: four basic monistic philosophic schools existentialism, idealism, organizism and materialism tried to describe it in terms of separation and absolutism. Those philosophies completely absolutize the priority of o­ne sphere, which has caused them to be irreconcilable in the long run of history. Full absolutization of o­ne sphere creates a monism that is o­ne-dimensional, disharmonious, aggressive, monopolistic, totalitarian and completely false. A monism philosophy can be true for no more than 25 percent of the society because it recognizes the superiority of o­nly one sphere of harmony, placing it above the other three. Monistic philosophies have found favorable social ground in history and were often personified as ideological colors of the corresponding empires: brown, white, green and red and numerous other hues. (This is a special question, which I shall not touch o­n here, but it is considered in [1].)

A Law: Cognitive absolutization of o­ne of the spheres of the world harmony creates four monistic directions in the world philosophy, which often serve as ideologies of private antagonistic classes and parties in their irreconcilable enmity in the most different societies and civilizations up to a harmonious civilization. Monism is a philosophy of enmity and a precondition of Tetrism.

2. Basis. The knowledge of the unity and dialectics of the spheres of the world harmony through the different number of its spheres starts from a pluralistic philosophy direction. This has been true since the most ancient times as found in the teachings of Pythagoras, Confucius, Empedocles, Lao-Tszy, and others. It developed parallel to monism but remained as a marginal philosophical concept up until the end of the 20th century, until the emergence of the information society and the first signs and preconditions of a harmonious civilization.

A Law: A long period of development of pluralistic multidimensional philosophies from two-dimensional to infinitely multi-dimensional preceded the holistic knowledge of the world harmony spheres in their dialectic unity. Unlimited multidimensional pluralism is a forerunner of Tetrism.

3. Basis. Knowledge of the unity and dialectics of the world harmony four spheres, and in their indivisibility, starts in a four-dimensional pluralistic philosophy (Tetrism). It begins the moment of conscious refusal of a total (absolute) priority of any spheres, recognition of the spheres equal necessity (essentiality), and their mutual inclusion and mutual restriction as an absolute condition of harmony. Such understanding came o­nly at the end of the 20th century as a part of the process of globalization, i.e. general interdependence of people, societies and nature.

A Law: The integral knowledge of the world harmony and the four spheres in their dialectic unity finds its way in the corresponding (four-dimensional) pluralistic philosophy of Tetrism as a philosophy of the world harmony at all levels. Tetrism is a philosophy of the world harmony.

4. Basis. Knowledge of the unity and dialectics of the world harmony and the four spheres in their indivisibility continuously develops in the four-dimensional pluralistic philosophy of Tetrism. This occurs through a conscious synthesis that saves all rational heritage for a harmonious society and its people, a monistic (one-dimensional) and pluralistic (multidimensional) knowledge from any branch, any society and civilization of any historical epoch. Such four-dimensional pluralistic knowledge, being the most adequate to natural and social harmony, finds favorable circumstances within the origin of a society and becomes integral to a conscious harmonious civilization. This civilization can arise o­nly o­n the basis of corresponding scientific knowledge and corresponding philosophy as its ideology and worldview. Cultivation of harmony by people and societies up to a harmonious civilization is carried out spontaneously and intuitively, contrary to and steadily overcoming dominating tendencies of enmity, violence and disharmony. Conscious cultivation of harmony starts with the advent of Tetrism philosophy and a social science of harmony, which become the possession of all people through the global harmonious education, which provides conscious formation of a harmonious civilization in each society and at each level.

A Law: The integral knowledge of the world harmony of the four spheres in their dialectic unity continuously develops in Tetrism through the synthesis of the required knowledge from all sources. Tetrism is a worldview and ideology of a harmonious civilization that provides all-round conscious cultivation of harmony by each society and each person according to their individuality.

Model-6: Laws of Knowledge of the World Harmony Spheres:



We should remember that the gnoseological peculiarity of any philosophy represents a hypothesis of universal Being that never finds complete empirical proof but exists as a necessary precondition of any special theory or science, the quality of which is predetermined by quality of its philosophical preconditions. This may be fully attached to Tetraphilosophy or Tetrism as to the basis of Tetrasociology, the quality of which depends o­n the quality of Tetrism. In a view of hypothetical character of philosophical preconditions, these are constantly transformed and reformulated for the purpose of their continuous adjustment to practical applications in definite conditions or rejected by practice as inadequate to the new requirements.

Tetra-logics unfolds, develops, and emphasizes knowledge and understanding in regard to the ways of thinking and structures of conceptual expression of the universal spheres and laws of the world harmony. Tetra-logics incorporate all the laws of traditional formal and mathematical logics and use them as a foundation for its own logic laws and tools. Tetra structure of the world harmony and knowledge of it supports its own corresponding tetra logic structure of thinking. In our exposition, this logic is expressed in four forms: Tetra-logic structures, Dialectic modeling, Structural tetra-abbreviations, and Tetra-net harmonious thinking.

1. Tetra-logic structures. Tetra-logic structures are the measure of the logic formulations of Tetraphilosophy. Such a rigid requirement cannot be reached either immediately or completely. Rather, it is an unachievable ideal to which the four-dimensional knowledge of the four-dimensional spheres of the world harmony constantly aspires.

2. Dialectic modeling represents the dialectic models of the four-dimensional tetra structures. Dialectic model (in abbreviated form: d-model or tetramodel) is a unity (also called a complex or a block), that consists of four concepts that express various aspects of the four-dimensional world harmony and several (bunch) of their twelve direct and return dialectic connections. These also express different attitudes of their mutual inclusion to the whole and the parts, as a unity of diversity and a diversity within unity. The d-model is a model of harmony and a logical skeleton of dialectic thinking of harmony. It is an elementary logic cell/segment of harmonious thinking of the four-dimensional world harmony in any of its representations and forms of knowledge: philosophy, science, religion, ethics, arts, politics, law, and so o­n. These d-models create a special form of harmonious thinking that can be named dialectic-modeling thinking of harmony. They become an evident support of abstract harmonious thinking. The dialectic modeling, raised up from the dialectics of the whole and its parts, was developed by the author beginning in 1967 and is presented in detail in many of his works [1].

3. Structural tetra-abbreviations, as well as the dialectic models, represent o­ne more cell/segment of harmonious thinking. Structural tetra-abbreviations also create a special form of harmonious thinking that can be called the thinking of harmony. Both forms of harmonious thinking demonstrate compactness, word economy, meaningfulness and efficiency that are not accessible to traditional forms of industrial thinking of world harmony. Abbreviations and d-models facilitate expression of the complexity of world harmony as well as its spheres and dialectic beyond all limitations in a sufficiently simple, evident, effective and quantitatively countable statistical form of matrixes of the sphere indices (see below).

4. Tetra-net harmonious thinking. Tetra-net harmonious thinking is the most adequate logical way of thinking of tetra-net world harmony, especially at the social and individual levels. In this network, as in the Mendeleyev Table of Chemical elements, the empty cells can potentially be filled in the future. This network is similar to the Internet. The tetra-net of d-models and abbreviations expresses a deep structure of Internet harmony, which is a spontaneous information cultivation of harmony. The GHAs 19 projects, in particular the Harmonious Civilization Universal Declaration, are also examples of tetra-net harmonious thinking,. Each GHA project is an open conceptual net of harmonious thinking.

Model-7: Logic Forms of Harmonious Thinking of Spheres:



The initial integrated section and the center of network harmonious thinking is a Universal Worldview Model of Harmony (UWMH), which are detailed in [2]. We shall repeat it here.




This model is capable of being infinitely deep because each element may be expressed by a new model, which can also be extended infinitely when each element joins new models, thuscreating an infinite network of models similar to an infinite network of world harmony. For example, some of the o­ntological models (and abbreviations) created above have network connections with the WORLD block. Sociological models, created below, join the SOCIETY block, and so o­n. The fragment of this logic network of four-dimensional harmonious thinking, constructed of some d-models, is presented o­n the separate Scheme-1 in the appendix of this book.

In conclusion of our brief presentation of Tetraphilosophy, we shall compare its harmonious thinking and philosophy with industrial thinking and philosophy according to a number of criteria.

1. Instead of a priority of ideological antagonism, enmity, separation and alienation of the o­ne-dimensional monistic philosophies Tetraphilosophy propose a priority of ideological harmony, multidimensionality, association and synthesis of previous rationalities for a harmonious civilization and a harmonious person.

2. Instead of the multivolume expressions accessible solely to the old age spiritual aristocrats Tetraphilosophy appear simple with capacious dialectic models and abbreviations that are clear to any young person; in other words, we have democracy instead of aristocratism.

3. Instead of rigid binary opposition of truth and lies Tetraphilosophy offer an infinite continuum and constant movement from deceit to true knowledge. From this point of view, Tetraphilosophy is more truthful than the traditional industrial philosophy, but its truth is also relative.

4. Instead of the orientation o­n the past and its extrapolation into the future Tetraphilosophy create a future orientation that selects from the past everything that is valuable for the present and creation of a sustainable and harmonious future.

Let us now compare segments/cells of industrial and harmonious thinking. The industrial (monistic) thinking cell includes three objects: two elements and defining determination/causation of o­ne of them. The philosophical and sociological theories of industrialism are created on this cell of thinking. Especially Marxism, in which all interactions are reduced to defining the determination of the Matter or Economy in a society: social being and social consciousness, productive forces and relations of production, basis and a superstructure, working class and dictatorship of the proletariat, and so o­n. History has discredited this o­nE-DIMENSIONAL determinism and corresponding o­nE-DIMENSIONAL thinking. The cell of harmonious thinking includes 16 objects: 4 elements and 12 straightforward and feedback determinations (or "cumulative causation") between them that are presented in each d-model.This MULTIDIMENSIONAL, pluralistic and probabilistic determination as a cell of MULTIDIMENSIONAL harmonious thinking replaces the obsolete o­ne-dimensional (monistic) determination and a cell. Therefore, determinism/causation in philosophy and social sciences has not died, as some philosophers and sociologists believe, but o­nly changes form from monistic into pluralistic. It has died o­nly for those who are limited by the monistic (industrial) form of determinism and thinking and those who do not see its pluralistic (harmonious) perspective. Therefore harmonious thinking is much more adequate, true and, hence, more effective, than industrial thinking.

To paraphrase Albert Einstein: Problems cannot be solved by the same level of thinking that created them. It is possible to approve that tetra-net harmonious thinking is that new level of thinking that can resolve industrial problems of war, violence, poverty, ecology, instability, and so o­n, which are insoluble through the methods of industrial thinking.

As a conclusion of our brief description of Tetraphilosophy, we have to emphasize that we do not pretend to introduce a theory the completeness or finality of which are basically unachievable. This philosophy is open for infinite development.


2. Tetrasociology: a Science of Social and Individual Harmony


Tetraphilosophy is an o­ntological and methodological platform for theoretical Tetrasociology.

Definition: Tetrasociology is a pluralistic four-dimensional science of social and individual harmony.

Tetrasociology Subject: elements (spheres) and laws of their harmony in social space-time.

Tetrasociology Social Function: global scientific worldview and ideology of a harmonious civilization.

Tetrasociology Basis: 1. Initial axiom; 2. Twenty fundamental elements/spheres of social and individual harmony; 3. Laws of harmony; 4. Pragmatics.


2.1. Tetrasociological Axiom


Tetrasociological initial axiom or an axiom of sphere social resources similar to the spheres of the world harmony sounds like that: The existence of a society and an individual or social harmony in any place and at any time are provided with four necessary and sufficient resources: People (P), Information (I), Organizations (O) and Things (T). (Things include material benefits and services). These resources are designated with the acronym PIOT. These resources represent the colossal social complexes that provide social harmony within all history. They are referred to as the sphere resources that form social statics and they are a subject of the theory of social statics in Tetrasociology. They compose universal resources of humankind at all levels: global, national, regional and local. Twenty fundamental elements/spheres of social and individual harmony are deduced from the Tetrasociological axiom.


2.2. Fundamental Elements (Spheres) of Social Harmony


Tetrasociology, as a science, starts with the definition of fundamental elements (spheres) of social and individual harmony. In this analytical fragment, we limit ourselves to the elements of social harmony.

The history of philosophical and sociological thinking allocated 20 necessary and sufficient spheres of social harmony. We call them the elements of social harmony because the balance of their mutual restriction provides harmony. Elements of harmony are extremely large spheres; therefore these elements refer to as sphere elements.

There are four groups of fundamental elements (spheres) of social harmony: RESOURCES, PROCESSES, STRUCTURES and CLASSES of population. They are necessary and sufficient for the existence and harmony of any society in any place and at any time.

The main frame of fundamental elements of social harmony consists of four sphere PIOT resources People (P), Information (I), Organizations (O) and Things (T) that are defined by a tetrasociological axiom. Each resource sphere is empirically evident but demands theoretical definition.

PEOPLE are a priority social resource because they possess the unique quality (ability) to make all other resources, including themselves. People include all human beings from conception, irrespective of other qualities: gender, race, age, nationality, culture, religion, and so o­n. People, from the moment of birth, are actualized as population. Further, we will limit the people resource by the population o­nly. Zero population, or zero people, mean a zero society.

INFORMATION comprises the whole of human knowledge and ideas, both individual and collective, whether from those who are alive or who have died, and is substantiated in any its carriers irrespective of the quality of this knowledge and its representations: in regard to location, time, subject, form, aim, duration, way of expression, and so o­n. Information of a society and a person is social information. Zero social information is a zero society.

ORGANIZATION/S is any public and individual relationship in a limiting and normalizing institution. Organizations/institutions of a society and its individuals are a social organization. Zero social organization means a complete social and individual chaos, i.e. a zero society.

THINGS are the sum of all the material benefits of society and individual, without exception. Things of a society and its individuals are social things. They differ from natural things, which, however, become social as soon as they are used by people. Zero social things are a zero society.

Thus, it is possible to demonstrate that, without PIOT resources, societies and individuals never existed and cannot exist. This shows the necessity and sufficiency of the PIOT resourcesfor any society and individual. A more detailed description of these resources and their dialectics are presented in [3].

It is also important to note that PIOT resources do not exist ready-made in Nature. Therefore, a society and individuals are compelled to reproduce them continuously throughout their entire life from birth to death. This is known as reproductive employment [4.] Reproductive employment of a society and people, first of all their labour, is a unique source of the PIOT social resources.

As Adam Smith and Karl Marx showed, each PIOT resource passes four necessary and sufficient processes of reproduction: Production (P), Distribution (D), Exchange (E) and Consumption (C), which are designated by the abbreviation PDEC [5]. These processes represent extremely large functional social complexes or spheres that we refer to as sphere processes (functions) and which form social dynamics. These settle the dynamics of any society. They compile the subject of the theory of social dynamics in Tetrasociology.

PIOT resources are inseparably connected with PDEC processes, forming a fundamental social structure of four spheres of social reproduction. The PIOT resources are the subject and the product of the four necessary and sufficient structures of social reproduction:

1. Social sphere, or Sociosphere (S), the subject and the product of which are P;

2. Information sphere, or Infosphere (I), the subject and the product of which is I;

3. Organizational sphere, or Orgsphere (O), the subject and the product of which are O;

4. Technical (economic) sphere, or Technosphere (T), the subject and the product of which are T.

These structures, designated by the abbreviations SIOT, represent extremely large social complexes that we refer to as spheres of reproduction and they form social structuratics. The SIOT spheres unite the PIOT resources and the PDEC processes for the reproduction of PIOT. They are inseparable because production of any product demands a certain complex of all the PIOT resources; therefore no o­ne production sphere can exist separately from other spheres. Thus, they are equally necessary, which excludes the constant primacy of any of them. They are made similar by means of the others, that is, each PIOT product is made from a corresponding resource by means of and with the help of other resources. SIOT defines the structure of social needs, abilities, employment, work, property, money, distribution, exchange/markets, and so o­n. The SIOT spheres are the subject of the social structuratics theory in Tetrasociology [6]. Harmonious development of a society is a harmonious development of its SIOT spheres in their unity and balance of mutual restriction.

A society and a human being coexist and coincide in their fundamental, deep sphere structure. The four spheres of society correspond to the four fundamental spheres of reproduction/life of each individual:

  • CHARACTER (including orientation, values and morals),
  • CONSCIOUSNESS (including information and spiritual culture),
  • WILL (including individual order and self-organizing) and
  • BODY (including temperament, subconsciousness and physiology).

The four spheres of an individual, designated by the abbreviations CCWB [7], also correspond to the four kinds of the individuals needs, abilities, work, employment, property, distribution and exchange. The spheres of the individual are interconnected by system sphere needs, abilities, communications and exchanges. Therefore, harmonious development of an individual is a harmonious development of these spheres in their unity and balance of mutual restriction and relationships. Individual spheres represent the extremely large psycho- socio- physio-complexes that form individual structuratics and become the subject of the humanism theory in Tetrasociology, i.e. a complex of the humanitarian studies of a person.

The SIOT spheres of social harmony are impossible without CCWB spheres of individual harmony and vice versa, therefore the CCWB spheres are included into the structure of elements of social harmony. However, we shall remind, that, in the given analysis, we are limited to social harmony; therefore, we do not consider here all the elements of individual harmony, but o­nly its basis and beginnings.

SIOT spheres cover the entire population. They include each person from birth to death. All personal life activities are represented as reproductive employment in these spheres, and change (replacement) of this sphere employment in time. It is a universal employment for each person from birth to death.

Therefore, SIOT spheres divide the entire population, without exception, into four eternal classes.

Classes of the population occupied (employed) in the SIOT spheres of reproduction are:

SOCIOCLASS, who are employed in the sociosphere;

INFOCLASS, who are employed in the infosphere;

ORGCLASS, who are employed in the orgsphere;

Technoclass, who are employed in the technosphere (it is material or economic sphere).

These classes differ not in particular or time attributes of property or stratification but in general spheres of the SIOT employment (activities); therefore they are referred to as SPHERE classes. In abbreviated form, they are designated as SIOT-CLASSES. An individual simultaneously belongs to all classes in that he or she is occupied every day in each sphere even for a minimum of time. However, at each life stage, the sphere that takes the most of an individuals time has a priority. Each stage of the individuals class identification is determined by this criterion. Therefore, sphere classes are soft o­n the surface, being both locally limited and temporary as class and group structures are formed. However, this does not prevent them from being deep, eternal and fundamental.

Together with the SIOT spheres, the SIOT-CLASSES make a deep social structure or deep structure of social harmony. Sphere classes cover the entire population and are actors within the theatre of social harmony. During the pre-harmonious history of humankind, they acted as spontaneous, intuitive and unconscious actors of harmony. They have since become conscious actors of a harmonious civilization, seizing and embracing scientific knowledge of social and individual harmony. Therefore, there is a differentiated spontaneous and conscious cultivation of harmony by a society and the individual. SIOT-CLASSES and their universal occupation/employment are the subject of the theory of social occupatics in Tetrasociology. The term occupatics is made from an English word occupation, which means any employment or any kind of activity.

Each of the listed tetrads is expressed not o­nly by abbreviations, but also through d-models (we omit them here) that, in aggregate, make a tetra-net kernel of the harmonious social thinking. Each reader can construct missing d-models independently and join in the innovative process of tetranet harmonious thinking and thus contribute to a harmonious civilization.

Each of 20 fundamental elements of social harmony united by a deep SIOT sphere structure passes four necessary and sufficient evolutionary states in history: Blossoming (the top harmony) (B), Misbalance (M), Decline (D) and DYING (D). These conditions, designated by the abbreviation BMDD, represent extremely large historical stages of evolution of any society and form social genetics, which is the subject of the corresponding social theory of Tetrasociology. They are not elements of social harmony, but they express its measure from the top: the Blossoming of spheres, through its critical decrease through Misbalance (delay) of spheres, through Decline of spheres when measures of their harmony and disharmony are leveled, to Dying (destruction) of spheres and society when the measure of their disharmony essentially exceeds the measure of their harmony. The states of misbalance (delay), decline and destruction make disharmony. The state of misbalance (delay) makes weak disharmony. The states of decline and destruction make strong disharmony. The scientific knowledge of elements and laws of harmony allows a society and an individual to be constantly within the borders of harmony, to avoid the states of strong disharmony and to minimize states of weak disharmony.

The PIOT resources, PDEC processes, and SIOT spheres and classes make spatial coordinates of social harmony. The BMDD adds the coordinate of time. Together, they form a united four-dimensional space-time of social harmony, a detailed analysis of which is found in [8].

All elements of social harmony are presented (exist) in all social objects: family, enterprise (firm, corporation, etc.), branch, region, country, humankind (social world, global society, etc.). However, in each object and at each level, they are presented specifically, i.e. in a qualitatively unique image and in an infinite variety [1].


2.3. Tetrasociological Laws


The laws of social harmony in Tetrasociology express the basic qualities and relations of 20 fundamental elements. The basic qualities of these elements are universality, necessity, sufficiency and priority. All elements have universal character and are necessary for a society because the absence of at least o­ne excludes existence of a society. All of them are sufficient because no other universal social elements for a society and its harmony exist. This equal necessity of elements is supplemented by a different priority at a different historical time and in a different social space. The basic forms of element dependence are: disharmonious and harmonious. A disharmonious relationship is a spontaneous uncontrollable interrelation of elements, characteristic for all types of disharmonious societies. Harmonious relations are based o­n the most balanced and optimal proportion (distribution) of all fundamental elements within a society. The harmonious proportions of elements are quantitative measures that demand corresponding statistics and mathematics, which are created in Tetrasociology. The harmonious proportions of the listed elements are consequences of the laws of social harmony, the most important of which are the following.


Tetrasociological Laws of a Deep (Sphere) Structure of Social Harmony:

1.There is a deep similarity between the spheres of world harmony and its universal qualities, structures and laws and the fundamental spheres/elements of harmony in humanity, any society and any individual.

2.All social spheres/elements of harmony are necessary and sufficient (natural and universal), of different priority levels, and mutually limiting to each other in harmony.

3.Social harmony is a balance (proportion, equilibrium) of social spheres through their mutual limitation.

4.Individual harmony is a balance (a proportion, a balance) of individual spheres of an individual person through their mutual restriction.

5.Among all elements (spheres) of social harmony, the most significant (priority) are the PIOT resources.

6.The primary resource is People; they earn this maximum status because people produce all resources, including themselves. o­nly people are capable of consciously cultivating harmony, which means that harmonious proportion/distribution of all elements depends o­nly o­n human beings.

7.Children deserve maximum priority among all humans, which means the quality of children defines the quality of the entire humans and society.

8.The spheres and sphere classes of harmony have corresponding sphere needs, abilities, labor, employment, property, money and markets. Their measure of harmony is defined by the harmony measure of PIOT resources.

9.Society and individuals coincide in the most fundamental, harmonious and deep sphere structure.

10.Only the harmonious society/civilization provides a conscious cultivation of social harmony through universal scientific knowledge and global harmonious education.

11.The conscious harmonization of spheres and their branches demands a legislative organizational establishment: 1, Children as a priority in a society; 2, A step-by-step harmonious education of people beginning with early childhood; 3, Sphere democracy as an equitable distribution of state power between the four population sphere classes and four-party harmonious political system, parliament and government; 4, Harmonious limits/proportions of economic growth, profits and interdependence of poverty and wealth.

12.Social harmony actors, that is, harmonically educated sphere classes of population, provide a conscious harmonization of spheres and their branches.

13.Global harmonious education is the best way for humankind to survive, overcome social pathologies, and generate world peace, justice, prosperity and nonviolent solutions to all global problems.

14.Harmonious education is a balanced and coordinated informing, learning, training, thinking and development of humans in accordance with the spheres of the world and social and individual harmony.

Laws of a survival, sustainable development and harmonious peace for the 21st century:

15.Survival Law: Humankind will either survive in conscious harmony or destroy itself.

16.Efficiency Law: The most effective method of functionality for humans and society is the concerted development of the four spheres while, at the same time, exercising a conscious self-restriction of spheres and their branches o­n the basis of corresponding scientific knowledge of harmony laws. Any o­ne-dimensional development is inefficient and ultimately destroys individual humans as well as the global human society.

17.Sustainable Development Law:Sustainable development comes from the conscious concerted development of the four social spheres as o­ne whole unit and the self-restriction of each sphere within the whole.

18.Freedom Law: In the past, freedom was the knowledge of a general necessity o­nly. In the early 21st century, harmony has become a social necessity and freedom becomes harmony that results from the conscious concerted self-restriction of spheres and their branches. Freedom exists within harmony of spheres and comes from that harmony. Any o­ne-dimensionality that remains unlimited and whose uncontrolled actions are not realized and not restrained by society creates a state of non-freedom or a negative destruction of freedom, both of which are disharmonious.

19.Equality Law: All people are equal in harmony and in the conscious concerted self-restriction of individual and social spheres. People remain unequal o­nly when they remain unconscious of unlimited, unrestrained o­ne-dimensionality.

20.Justice Law: For all people and nations, justice is the conscious concerted self-restriction of spheres of social and individual harmony. Injustice, inequity, and disharmony occur when the population remains unconscious of any unlimited, unrestrained and o­ne-dimensionality.

21.Happiness and Health Law: Happiness and health of all people and nations exists in harmony as the conscious, concerted self-restriction of the spheres and their branches. Misfortunes and pathologies root in society when the population is unconscious of any o­ne-dimensionality that remains unlimited and unrestrained.

22.World Harmonious Democracy Law: A source of the worlds democratic power in a harmonious civilization is the population that operates as a unified body of four harmonious and equal sphere classes that share rights and political powers equitably at all levels: global, regional, national and local. This law is a basis for the Global Constitution of a Harmonious Civilization.

23.Global Four-party Political Organisation Law: The political tool for achieving and maintaining global harmonious democracy is the four-party political organization that operates and functions as a unified, harmonious body of four global parties, each expressing interests of the four sphere (harmonious) classes of the population at all levels: global, regional, national and local o­n the basis of the o­ne Global Constitution of a Harmonious Civilization.

24.Harmonious Peace Law: Humanitys harmonious peace is an inevitable consequence that comes from fulfillment of the previous global harmony laws, which, if followed, preclude and exclude the deep sources and key root causes of violence, poverty, enmity and war of any kind and at any level.

Although many of these laws were presented in previous works [1], they are very far from perfection and require further theoretical and empirical research.


2.4. Structure of Tetrasociology


The structure of Tetrasociology includes scientific theories of four dimensions of social space (spheres = morphology) and four dimensions of social time (stages of development), united by social genetics with corresponding integral theories of individual dimensions. The structure also includes the theory of future, i.e. the theory of harmonious civilization and pragmatics of social and individual harmony. The general structure of Tetrasociology may be presented asthe following scheme.




1. Social Morphology: Theories of harmony spheres in social space:

Social Statics: the scientific theory of PIOT sphere resources;

Social Dynamics: the scientific theory of PDEC sphere processes;

Social Structuratics: the scientific theory of spheres of SIOT reproduction;

Social Occupatics: the scientific theory of sphere SIOT -CLASSES; and

Humanism: the scientific theory of deep structure of individual harmony.


2. Social Genetics: Theories of harmony stages in social time

The theory of harmony Blossoming as equilibrium, balance, proportion and the spheres prosperity;

The theory of Misbalanceas the spheres delay;

The theory of Decline as the spheres degradation;

The theory of Dying as the spheres destruction; and

The theory of individual harmony through its developmental stages.


3. The Theory of a Harmonious Civilization (Futurology of Harmony)

This theory is similar to the morphology and genetics theories, limited by frameworks and purposes of a harmonious

civilization. In a complex and in practical application, these are presented in the GHAs Harmonious Civilization

Universal Declaration.


4.Pragmatics of harmony (Tetrasociological Toolkit)

Tetra-statistics of social and individual harmony;

Tetra-mathematics of social and individual harmony;

Technologies of social and individual harmony o­n the basis of Tetrasociology; and

Tetrasociology Projects and empirical Tetrasociology.


The Structures of Tetrasociology can be presented in the corresponding d-models. We invite readers to construct them and to join in the process of tetranet harmonious thinking.

All of the listed theoretical sections of Tetrasociology are presented here in their initial formulations. They require improvement thorough scientific study and extensive empirical and mathematical research.


3. Tetrasociological Pragmatics

Tetrasociological pragmatics includes a toolkit necessary for realization of this social and individual harmony theory in social and individual life. It is pragmatics that provides conscious cultivation of social and individual harmony. But this is possible o­nly through theoretical Tetrasociology. The Pure and Practical reason of Kant, known for its criticism, is a good analogy here. Practical reasoning for Kant conveys moral laws that conduct pure reason in life. In much the same way, Tetrasociological pragmatics serve to embody its pure theory and put that theory into practice.

Tetrasociological pragmatics has four tool blocks:

1. Statistics (Tetrastatistics),

2. Mathematics (Tetra-mathematics),

3. Technologies, and

4. Projects and empirical researches.

The practical scale of Tetrasociology within the past 35 years is outlined in the Appendix, which contains 200 entries regarding Tetrasociology applications in different spheres and branches.


3.1. Tetrasociological Statistics: Matrixes of Sphere Indices


Qualitative elements (spheres) of social and individual harmony demand adequate statistical (quantitative) equivalents. PIOT resources are the basic elements of harmony that create all of its other elements, and PIOT statics determines all other dimensions (coordinates) of social harmony in space and time. PIOT quantitative formulae/indices are necessary and sufficient for quantitative measurement of all other elements and laws of social and individual harmony in the corresponding statistics. Such statistics is Tetrasociological or sphere statistics and it is based o­n the alphanumeric indices of PIOT resource spheres.

We shall not repeat here a detailed description of this statistics and its indices, which are already presented in a number of previous works [9.] Sphere indices (and statistics) exist in the matrix form, and they make systems and rows of sphere matrixes, i.e. matrixes of the sphere indices.

Sphere indices and their matrixes for statistical and mathematical calculation have numerical representation (because they are numbers) that contain two kinds of measure units. All sphere indices, without exception, measure unit costs in any currency: rubles, dollars, euro, harmon and so o­n. P-indices (people, population) have an additional natural unit of measurement. This unit of measurement is used for various instances and tasks such as expenditure, distribution, consumption, production of the resources by o­ne person, and/or by groups of population of 10, 100, 1000, 10000, 100000 and so o­n. This unit of measurement is also used for calculation of the quantity of the population and its dynamics. We do not mention here the operationally complex but principally resolved problem of the measurement units for sphere indices and their origination from the traditional statistical indices. Instead, we represent here o­nly the logic of the basic and derived matrixes of sphere statistics.

In the limits of modern humankind, the global society (GS) represents in statics the sum of sphere (necessary and sufficient) resources:

GS = P+ I ++T (1), where

P is a current number of humankind (the population of a planet),

I is a set of the information (any human knowledge),

is a set of all organizations/institutions (legal, political, financial, an so o­n), and

T is a set of all things (humankinds material benefits and services).

With reference to any society, not o­nly the global society, the generalized formula (1) looks like:

S = P+ I + + T (2), where S = Society.

According to an axiom for continuous reproduction (that is, life and existence), each o­ne of PIOT resources requires a corresponding complex cluster of PIOT parts. Hence, each o­ne of PIOT resources will be divided into four parts that are necessary and sufficient as PIOT reproduction resources. This regularity system will be expressed by the following 4-by-4 matrix, which refers to the basic matrix of sphere indices or sphere statistics:

P = P1 + P2 + P3 + P4, where P is the population, and P1, P2, P3, and P4 are the sphere classes necessary and

sufficient for reproduction of corresponding PIOT resources:

P 1 - for reproduction of P (people);

P 2 - for reproduction of I (information);

P 3 - for reproduction of (organization);

P 4 - for reproduction of T (things);

I = I1 + I2 + I3 + I4, where I is the information, and I1, I2, I3, and I4 are its clusters necessary and sufficient for reproduction of corresponding PIOT resources.

= 1 + 2 + 3 + 4, where is the organizations, and 1, 2, 3, and 4 are their clusters necessary and sufficient for reproduction of corresponding PIOT resources.

T = T 1 + T 2 + T 3 + T 4, where T is the things, or material benefits, and T1, T2, T3, and T4 are their clusters necessary and sufficient for reproduction of corresponding PIOT resources.

In the pure state, the 4-by-4 sphere matrix of PIOT resources looks like:

P1 + P2 + P3 + P4

I1 + I2 + I3 + I4

1 + 2 + 3 + 4

T1 + T2 + T3 + T4 (3)

All matrixes that derive from a basic sphere resources matrix are referred to as sphere matrixes. All sphere matrixes elements are referred to as sphere indices, which form sphere statistics and which are essentially different but connected to the traditional (branch or industrial) statistics. In this way, all indices are integrated in sphere indices, where they are regulated and systematized in harmonious (sphere) logic. However, it is important to note that sphere matrixes, sphere indices, and sphere statistics do not appear in industrial statistics, which is illogical and disharmonious.

The sphere matrix columns represent inputs of the corresponding production spheres, using PIOT as a resource, and the sphere matrix lines (rows) represent outputs of the corresponding manufacturing spheres that produce PIOT as a product.

In Tetrasociology, we remind, four necessary and sufficient spheres of (re)producing PIOT resources are noted:

1. Social sphere, or sociosphere, the object and product of which is P (people).

2. The information sphere, or infosphere, the object and product of which is I (information).

3. Organizational sphere, or orgsphere, the object and product of which is O (organization).

4. The technical (economic) sphere, or a technosphere, the object and product of which is T (things).

Complex spheres of reproduction are designated as SIOT.

The dual nature of sphere resources (and the sphere index) as input/resource and output/product of the SIOT spheres is expressed in double letter/numerical (alphanumeric) representation of these resources and corresponding indices.

Note. Indices of the line/row P in the basic sphere matrix represent reproduction of the population in the first sphere, which is the social sphere; in contrast, serial numbers of P indices designate sphere classes of population reproduced for corresponding spheres: P1 is the social class, which reproduces for the social sphere; P2 is the infoclass, which reproduces for the information sphere, P3 is the orgclass, which reproduces for the organizational sphere, and P4 is the technoclass, which reproduces for the technical sphere.

Indices of line I express reproduction of information in the second sphere, that is, the information sphere, and serial numbers of indices I designate the clusters of information reproduced for corresponding spheres from the first to the fourth. This same rule applies to the indices of other rows.

On the basis of the 4-by-4 basic matrix, the infinite hierarchical system of sphere matrixes may be created in exponential 4-by-16, 4-by-64, 4-by-256, etc. dimensions. Their continuum is possible not o­nly in the positive, but also in the negative, in fractional and in other infinities. However, at the first stage, we are bound by sphere matrixes o­nly in a positive infinity, that is, 44n, where n is the number of natural numbers from +1 to infinity. The following matrix is the matrix of the 4-by-16 dimension:


P1 = P11 + P12 + P13 + P14

P2 = P21 + P22 + P23 + P24

P3 = P31 + P32 + P33 + P34

P4 = P41 + P42 + P43 + P44


I1 = I11 + I12 + I13 + I14

I2 = I21 + I22 + I23 + I24

I3 = I31 + I32 + I33 + I34

I4 = I41 + I42 + I43 + I44


1 = 11 + 12 + 13 + 14

2 = 21 + 22 + 23 + 24

3 = 31 + 32 + 33 + 34

4 = 41 + 42 + 43 + 44


T1 = T11 + T12 + T13 + T14

T2 = T21 + T22 + T23 + T24

T3 = T31 + T32 + T33 + T34

T4 = T41 + T42 + T43 + T44


A subsequent infinity of sphere matrixes is constructed according to the same algorithm: each line/row of any matrix turns into a column of the underlying matrix, and each index in the underlying matrix line appears as the sum of four indices that express a cluster of resources, necessary and sufficient for its reproduction. This principle expresses sphere matrixes self-similarity, which is why their constellation simultaneously represents a fractal of social resources.

The sphere matrixes characteristic of fractal similarity, that is, mutual inclusion (nesting), is the foundation for the corresponding four-dimensional fractal mathematics of social harmony, which we have named Tetra-mathematics.


3.2. Mathematics of Tetrasociology: Tetra-mathematics


Tetra-mathematics is mathematics of the sphere matrixes of social and individual harmony o­n the basis of their fractal similarity in Tetrasociology. Fractal similarity was already recognized in 1975. Fractals, as infinitely nested hierarchical recursive and self-similar structures, were brought to world attention by Benoit Mandelbrot, father of the mathematical theory of fractals. His The Fractal Geometry of Nature gave birth to the fractal theory in 1977 [10].

One of the basic properties of fractals is self-similarity, which states that any part of a fractal contains information of the whole. Mandelbrot defines fractal as a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.[11] The theory of fractals manifests the initial mathematical expression of ancient philosopher Anaxagoras who presented the concept of all in everything, which was the first quantitative representation of a qualitative idea of self-similarity or structural mutual inclusion (or nested structures) that has been further developed by many philosophers and scientists within last 2500 years. The theory of fractals has found intensive development in the theory of infinite hierarchical nesting of matter or the discrete fractal paradigm, the main conclusions of which appeared within first five years of the 21st century [12].

The fractal theory deals with natural, biological, mathematical, spatial [13] and similar fractals, but it has not been applied to social fractals. However, Tetrasociology offers several social fractals, with the first being the fractal of the sphere resources. Following the concept of fractals, Tetrasociology unfolds in a hierarchical structure of self-similar matrixes of the sphere indices of resources, processes, structures and populations the fractal nature of a society and the person at a qualitative level. In this way, matrixes of sphere indices are social fractals of Tetrasociology.

By applying algorithms of production, distribution, exchange (markets), consumption, rate (speed, pace), proportions, balances, productivity, efficiency, stability, rotation, and so o­n to a resource fractal form, we get social multifractals, which are at the first fractal level.

Social multifractals of harmony (or multifractals of social harmony), are at second, or higher fractal level. These are formed after imposing harmonious proportions (algorithms) o­n the first level of fractals. Formation of social multifractals of the higher levels is possible also. Thus, we see that the beauty of fractals [14] as they express their harmonious nature, is inherent in social fractals too.

Social fractals are restricted to a certain area globe, continent, region, country or nation, state or province, city or municipality, precinct or neighborhood, corporation or firm or businesses district that degenerate into social pseudo-fractals or social forefractals. Nevertheless, they are also of scientific and practical value along with the ideally determined fractals.

Among social fractals, multifractals, pseudo-fractals and forefractals, four groups can be differentiated o­n the basis of four spheres of reproduction: humanitarian, which is social in the narrow sense of the word, corresponding to the social sphere, informational, organizational and economic. o­ne of the examples of the latter is presented in [15].

All the considered fractals, multifractals and pseudo-fractals make an inter-related class of Tetrasociology social fractals.

Fractals of social harmony are derived from an axiom of the sphere harmonious proportions: each established numerical index of any element of any sphere matrixes has a harmonious (golden) proportion of numerical values of all other elements of this matrix. This means that any change of numerical value of any element of sphere matrixes will result in a corresponding change of the whole harmonious proportion of this matrix.

Fractals of social harmony require generalized matrix gold proportions that are still unknown to any branches of the mathematics of harmony: the major problem of mathematics of harmony is to discover them.

Professor Stakhovs theory of the generalized harmonious (golden) proportions, which is being developed as a part of his mathematics of harmony [16], is the o­nly instance of theories we need. However, golden proportions are limited to two elements (numbers, pieces or others elements). This raises the question as to whether such bi-dimensional theory can find application in the four-dimensional Tetrasociological fractals of social harmony? Is it possible to reduce four-dimensional harmonious fractals to bi-dimensional golden proportions? If so, such a mathematical device could provide adequate measurement of a total four-sphere society in a four-dimensional social time and space. This would then be the Tetrasociological mathematics of harmony (Tetra-mathematics), or, as Prof. Stakhov has suggested, Golden Tetrasociology.

This variant of the mathematics of harmony has specific features. It should express golden proportions not of numerical sequences, but of numerical n-dimension sphere matrixes. Yet, sphere matrixes consist of two sequences: lines/rows and columns. And the number of columns in every matrix is equal to four. So the problem of generalized sphere matrixes golden proportions can be reduced to interdependence of generalized golden proportions of lines and columns of these matrixes. It is necessary to emphasize that the author of golden proportions in bi-dimensional mathematics of harmony has not yet found an opportunity to overcome this bi-dimensional limitation and expand it to a four-dimensional mathematics of harmony ( see review of his public replies).

An essentially different approach for construction of tetra-mathematics was offered in 2008 by talented mathematician P.J. Sergienko. Its foundation lies not in bi-dimensional golden proportions developed by 13th century Italian mathematician Fibonacci but in the harmony of a three-dimensional geometrical triangle. A special article, From Fractal Mathematics of Trialectics Harmony to Fractal Mathematics of Harmony in Tetrasociology, by P.J. Sergienko is devoted to this approach. In this work, Sergienko defines the harmonious triangle as a spatial measure device of fractal and scale harmony. [17]

A definition of a Sphere Harmony Index (SHI) based o­n Sergienkos three-dimensional mathematical theory of harmony appears in the frame of Gold Tetrasociology [17] or Tetra-mathematics.

This Index is the number that expresses the interdependence of generalized harmonious proportions of all lines and all columns of any sphere matrix. This number, for example, 0 or 1, is a fluctuation area (border) of the Harmony Index, which includes + and - vectors. The index is also the extent of its approach to the maximal ideal level at which it always aims but never reaches.

The Index of sphere harmony (or harmonious development) would be capable of expressing a degree of harmonization of any regional, national or global society or any their branch. It would also measure the deviation of their spheres from the ideal exponent at any moment in their evolution. Generally, this Index would express the rate not o­nly of a full sphere matrix or matrixes, but also the value of any sphere parameter in any sphere matrix as well as their positive or negative deviation from the ideal or the norm as measured in absolute or relative figures.

One more approach to mathematics of Tetrasociological harmony is called Invariant Statistics of Social Harmony. This approach has been developed by a mathematician V. Y. Trifanov but, unfortunately, is not yet published

In addition to these other great thinker, the name and the ideas of Belarus philosopher E. Soroko should be mentioned. Twenty-five years ago, Soroko has formulated the great idea of the infinite structural harmony of systems. His theory has much in common with the ideas of fractals and sphere matrixes [18].

It is quite clear from this great body of work that other approaches to harmony mathematics may also exist that will give hope to the transformation of fractal Tetra-mathematics from the status of hypotheses to that of high-grade mathematical theory practiced in and applied to the field of information technologies (IT).


3.3. Tetrasociological Technologies


Two classes of innovative technologies are created in Tetrasociology: these are informational and socio-cultural.

Prof. Castells has shown that today information technologies (IT) have become the most effective way to develop our modern social world. IT is the o­nly practical device to put the sociological theory into social practice. Sociology traditionally looks for its own algorithmic-mathematical instrument necessary and sufficient to make it part of IT. However, Comtes problem of mathematical models in sociology has not solved until now. The question of whether sociology can speak the language of mathematics remains unresolved. And that situation is not accidental. If the indices to be put under consideration are not clear, no mathematical formulae can be of help. Therefore, until sociology has its own indices, it has no chance to become a technology.

The most perspective illustrations of sociology as a technology are those in which the sociological information quantumta are classified and operated as indices. And Tetrasociology is o­ne such illustration. A system of sphere indices makes a base for Tetrasociological IT. This technology stands o­n four tenets.

The first is sociological. It is represented by 20 fundamental elements of social harmony, as described above.

The second is statistical. It is represented by a system of sphere/sociological statistics and their matrixes, as described above.

The third is algorithmic/mathematical. It is represented by blocks of numerical algorithms consisting of transformed sphere indices as well as Tetramathematics, as described above. Technological information software products (software) or applied programs packages (APP) are created o­n that basis.

The fourth is programming. It is represented by a set of program blocks and software, which create a new information technology called a Sphere/sociological Information Statistical Technology (SIST). SIST is a statistical technology that creates, transforms and uses the system of sphere/sociological indices. SIST represents a completed program level of Tetrasociology. It is expressed in the programs written in computer languages that are then decoded by computers. Software products are physically presented o­n any of several magnetic accessories: disks, diskettes, and so o­n. The SIST software family has different members. Its basic groups include:

Individual SIST, which is intended for harmonization of individual development and the individuals occupation in general, including the indices of time with predetermined levels in regard to resources and age.

Family SIST, which is intended for harmonization of family development, occupation of the family in general, family attitudes, and a way and standard of family living that includes the indices of time and cost.

Expert SIST, which is intended for experts in different specialties dealing with various types of social information.

Other possible SIST variants are: Office (State, Corporate, International), Country or Nation, World society, Environment, and others. It is necessary to pay attention to special opportunities to use SIST in the development of essentially new Internet search systems based o­n qualitatively new Internet resources. In 1980 through 1988, SIST was adopted into St.-Petersburgs municipal Programmed Economic Planning with such subsystems as: City Population Standard of Living, Public Health Services, Culture, City Paid Services, Consumer Goods Manufacturing, and others (see Appendix). A more detailed presentation of SIST is presented in [19].

The socio-cultural technology of Tetrasociology includes a number of technologies: harmonious education, sphere political democracy, harmonization versus militarization, nuclear disarmament o­n the basis of global harmony, financial harmonization through global harmony currency, harmonious sphere-like marketing, harmonization of the global market economy, harmonic games (similar to Olympic games), organizational harmonization and others presented in the Appendix. A more detailed description of these technologies is presented in [19] and in the numerous other GHA projects. Practically any information or socio-cultural technology within the last 35 years is reflected in the corresponding projects, ideas or created specifications (Technical Tasks).


3.4 Tetrasociology Projects & Empirical Tetrasociology


Projects fulfilled o­n the basis of Tetrasociology are the best representation of its pragmatic aspect. A partial list appears in the Appendix. The GHA 19 projects, which have been created over the last five years, collectively have special practical value. Presentation of these projects is the primary goal of this book.

Another important level of pragmatic Tetrasociology is empiric research. The most important item in that regard is the ten-year dynamic study of Russian population sphere classes from 1991 through 2000 [20]. Other extensive empirical studies of the dynamics of tetrasociological sphere classes have occurred over the past 50 years, from 1960 through 2010, in the worlds leading countries, including China, USA, European Union, India, Russia. However, lack of financial support for such studies has placed an obstacle in their way. Certainly, such studies would dismiss all doubts in regard to the scientific and practical efficiency of Tetrasociology.


4. Conclusion. Tetrism: Global Ideology for a Global Harmonious Civilization


To complete this outline of Tetraphilosophy and Tetrasociology (they both are Tetrism), I wish to underline two significant events:

1. The first significant event is the leading role of the GHA discussions within last five years that intensified the development of different aspects of Tetraphilosophy and Tetrasociology (Tetrism). This book shows the difference in their level of development in 1970s, 1980s, 1990s, 2000, and 2005. Because of this great history, it is not possible to announce All rights reserved for me as the o­nly author. Frankly speaking, the real author of these texts is the entire Global Harmony Association (GHA).

However, I do claim personal responsibility for the words and word formulations found in this text. I also credit numerous others who contributed their ideas, points of view and remarks, which have influenced and improved the presentation of my words. I am sincerely grateful to the GHA participants for their theoretical discussions, most often presented through the connectivity of the Internet. I especially acknowledge the co-authors of our eight-year poly-log (tetra-log) who have been working and contributing to this concept since 2002: Prof. Reimon Bachika of Japan, Marta DeWitt, D.S., of the USA, and Bernard Scott, D.S., of England. To this group, we add the new theorists who joined the discussion in 2003 and many GHA members from all world who became involved since 2005.

Collective development of the Tetraphilosophyand Tetrasociology (Tetrism) during the last five years by representatives of the basic world cultures and religions, united in and through the GHA, has made a unique historical and ideological feature of Tetrism. Tetrism, through its universal harmonious essence, has avoided any conflict that has occurred in the past when ideological unification encounters resistance from entrenched ideological antagonism, intellectual alienation, spiritual aristocratism, theoretical isolation and fighting that is characteristic of monisms, especially Marxism, the theorists of which proudly called themselves militants. Tetrism is a direct opposite to Marxism, which, although it unified its adherents within did not withstand the test of interpretation among its different national groups: French, Chinese, Yugoslavian, Cuban etc. Tetrism is a direct opposite to Marxism, which is aggressive in its relations with ALL other ideologies. Therefore, the countries of the Marxist camp were in a condition of constant military animosity with the entire world. Therefore, Marxism failed to bring about internal unification but rather created a split and external antagonism that led to the collapse of the USSR and the world socialist system. Therefore, Marxism can not and did not become an ideology of global peace, the first necessary precondition of which is ideological peace, i.e. harmonious unity of the ideological diversity, the general core of which is social harmony.

Tetrism, unlike Marxism and others monisms, presents ideological peace as the unity of an ideological diversity in universal world harmony. And global peace is impossible without ideological peace, which was rejected by all industrial ideologies. Industrialism creates an ocean of ideological enmity and totalitarianistic violence through its milliard of replicated, duplicated messages and advertisements in the mass media. Then, humankind bathes in this ocean of negative violence every day, each hour, in the afternoon and at night, forming a global public consciousness of violence. Within this culture of violence, industrialism has created a long-standing ideological antagonism in various dualistic forms: science and religion, science and arts (Charles Snows two cultures), morals and policy, policy and law, world religions and local indigenous civilizations. This totally negative and destructive ideological antagonism is reproduced continuously through mass media messages of violence and fear. It is even taught, through discussion, in the education system. Tetrism is capable of opposing total ideological, educational and information violence as well as its inherent antagonism toward ideological harmony and peace. Tetrism attains ideological peace because it opens within the hearts of humans a deep spiritual essence and the general denominator of all forms of public consciousness in world harmony: philosophy, science, religion, arts, morals, policy and right-thinking combined with right actions. Tetrism proves that humankind can survive not in an ocean of ideological antagonism but in the global space of ideological harmony by totally duplicating within public consciousness, mass-media and education systems, not violence, but world harmony in all its infinite, joyous and precious diversity.

Therefore, Tetrism is the necessary ideological precondition of the global harmonious peace that will exclude wars, enmity and violence between nations. Tetrism is the ideological condition that will, instead, unite cultural nationalism and ideological diversity into universal global harmony. GHA and its five years of ideological experience with Tetrism is the social experiment for humanity who is searching for and seeking approbation a global ideology that will provide harmonious spiritual unity to the glorious human diversity. An inevitable consequence of harmonious spiritual unity is global peace without wars, enmity and violence.

Final definition: Tetrism is a global peace ideology that manifests within the global harmonious (sphere) classes of humankind of a harmonious civilization.

Shortest definition: Tetrism is the ideology of a harmonious civilization or harmonism.

This ideology is expressed first and most completely, for now, in the GHA collective project: Harmonious Civilization Universal Declaration.

2. The second significant event is the four-dimensional network harmonious thinking (further in abbreviated form it is: tetranet thinking) and the four-dimensional scale of deep structure of world harmony in Tetrism at all levels of nature, society and individual. Harmony is the uniting centre of its any parts.The GHA projects, presented, first of all, in this book, illustrate how, by means of new harmonious thinking, different global problems have been created by o­ne-dimensional industrial thinking, which is, likewise, incapable of solving the problems it has created. Therefore these projects pave a conscious path to a harmonious civilization through the solution of the global societys basic current problems: nuclear disarmament, reserve currency, global (harmonious) education and others. Therefore, the tetranet thinking and Tetrism is the culture of thought and ideology of a harmonious civilization. The tetranet thinking is a positive alternative to the ideological crash of industrial society, i.e. to the crash of all of its o­ne-dimensional ideologies: imperialism of all colours, colonialism, Nazism, Marxism, liberalism, and so o­n, which are responsible for the whole spectrum of modern crises and social pathologies.

The harmonious civilization finds in its thinking a most important spiritual foundation. Tetrism is the ideology of a new civilization that is simultaneously an alternative and a synthesis of industrial ideologies, primarily Marxism. Tetrism is the alternative to Marxism all ways: philosophy, sociology, futurology and pragmatics. But Tetrism, at the same time, synthesizes within itself all the advantages of Marxism as well as the positive components of other industrial monisms. Tetrisms primary synthesis consists of its deep integration of Western monistic structural ideas and the Easts value of harmony. Tetrism is the original global worldview, thought and ideology of the global harmonious civilization, which is opening a new era humanity that will for many thousands of years.

02/11/2009.Edited by Robert Weir, writer, USA, October 30, 2009



1.Leo Semashkos books and websites: Integrated evident schemes in a philosophy course. Co-authors: D.V.Pivovarov, V.F.Setkov, Sverdlovsk, 1981; Sphere Approach: Philosophy, Democracy, Market and Human. St.-Petersburg, 1992, p.30-41 and etc; Sociology for Pragmatists. St.-Petersburg, 1999; Tetrasociology as the Revolution of Social Thinking, the Way of Harmony and Prosperity. St.-Petersburg, 2000; Tetrasociology: Responses to Challenges. St.-Petersburg, 2002; Tetrasociology: from Sociological Imagination through Dialogue to Universal Values and Harmony, with 14 co-authors, St.-Petersburg, 2003; Childrens Suffrage, St.-Petersburg, 2004; Harmonious Era Calendar, with 26 coauthors, St.-Petersburg, 2006; Magna Carta of Harmony, with 42 coauthors, St.-Petersburg, 2007; World Harmony/Peace Academy, with 80 coauthors. St-Petersburg, 2008; Encyclopedic Fund of Russia: www.russika.ru; GHA Website Peace from Harmony: www.peacefromharmony.org.

Reviews: Dr. Martha Ross DeWitt, USA. The Scope of Sociology. Review of Leo Semashkos three books o­n Tetrasociology in Journal: International Sociology. Reviews of Books. Volume 22, # 2, March 2007, http://www.peacefromharmony.org/?cat=en_c&key=15;

Dr. Bernard Phillips, USA. Review of Leo Semashkos book: Tetrasociology: Responses to Challenges (2002, 158 p.). The Canadian Review of Sociology and Anthropology o­n line: http://alcor.concordia.ca/~csaa1/BookReviews.htm; http://www.peacefromharmony.org/?cat=en_c&key=15;

Dr. Bernard Scott, UK, and Dr. Bernd R. Hornung, Germany. Reviews of Leo Semashkos book: Tetrasociology: Responses to Challenges (2002, 158 p.), Journal of Sociocybernetics, V4, N2, Fall/Winter 2003-2004, p.40-46, www.unizar.es/sociocybernetics/;

2.Sociology for Pragmatists, p.36-40;

3.Idem, p.186-198;

4.Idem, p.211-225; Tetrasociology: Responses to Challenges, p.39-57, etc;

5.Sociology for Pragmatists, p.201-225, etc;

6.Idem, p.226-251, etc;

7.Tetrasociology: Responses to Challenges, p.65-72; Magna Carta of Harmony, p.15-16, etc;

8.Tetrasociology: Responses to Challenges, p.37-57;

9.Idem, p.58-61; Sphere Approach, p.223-242; Sociology for Pragmatists, p.278-326, etc;

10.Mandelbrot, B.B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Company;

11.Feder, J. (1988). Fractals. Plenum Press, New York;

12.Theory of infinite hierarchical nesting of matter: http://en.wikiversity.org/wiki/Infinite_Hierarchical_Nesting_of_Matter; Fractal: http://en.wikipedia.org/wiki/Fractal;

13.Teerikorpi P., Baryshev Y., Discovery of Cosmic Fractals, 2002;

14.Peitgen, Heinz-Otto, and Dietmar Saupe, eds. The Science of Fractal Images. New York: Springer-Verlag, 1988;

15.Benoît Mandelbrot and Richard L. Hudson. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, Basic Books, 2004;

16.Alexey Stakhov (2008), The Mathematics of Harmony. From Euclid to Contemporary Mathematics and Computer Science. The broad abstract in "Visual Mathematics": http://www.mi.sanu.ac.yu/vismath/sg/stakhov2008/index.htm; http://peacefromharmony.org/?cat=en_c&key=330;

17.Peter Sergienko. From Fractal Mathematics of Trialectics Harmony to Fractal Mathematics of Harmony in Tetrasociology, 2009, http://www.peacefromharmony.org/?cat=ru_c&key=373;

18.Eduard Soroko. Gold Section, Self-organizing Processes and Systems Evolution: Introduction in the General Theory of Harmony of Systems, 2006, http://www.peacefromharmony.org/?cat=ru_c&key=351;

19.Sphere Approach, p.214-241; Sociology for Pragmatists, p.316-326; Tetrasociology: Responses to Challenges, p.51-53, 80-88; etc;

20.Tetrasociology: Responses to Challenges, p.69-77; etc;

Global Harmony Association (GHA)

July 31, 2008 - July 31, 2009




Science about Social and Individual Harmony

Base Textbook for Academies and Schools of General Harmonious/Peace Education




Dr Leo Semashko

with the 57 GHA collaborators from 20 countries:


Main editor and author of the textbook basic text is Dr Leo Semashko


Co-authors from Russia and other countries:






Was approved by the Board, the Honorary Advisory Committee and General Directorate of the Global Harmony Association


Project publications:

In Russian: http://peacefromharmony.org/?cat=ru_c&key=371

In English: http://peacefromharmony.org/?cat=en_c&key=345


Copyright 2009 Global Harmony Association

Copyright 2009 Leo Semashko


Religiosity of the scientist consists in enthusiastic

relation to the laws of harmony

Albert Einstein


We must design the good future for children

To quest our new civilization for the true wealth and peace

To create our new life wisdom

To listen the harmony of this world

Kae Morii, Japan


Tetrasociology is a new social science provides its rationale

and framework

Martha Ross DeWitt, Dr of Sociology, USA




The textbook "Tetrasociology: Science about Social and Individual Harmony" is 70 percent complete as it includes a previous textbook written in 1999: Leo Semashko. Sociology for Pragmatists. Textbook for the university students. Part 1, St.-Petersburg, 376 p. (in Russian)

Therefore main task is the editing and translation of the textbook with Russian o­n the English language up to July 31, 2009. The beginning of a new edition of the textbook in Russian is here: http://peacefromharmony.org/?cat=ru_c&key=371



Leo Semashkos books:


2008. World Harmony/Peace Academy and General Harmonious Education in an Information

Society, with 64 coauthors from 20 countries, in 2 languages. St-Petersburg, Russia,"LITA ", pages 104. http://peacefromharmony.org/?cat=en_c&key=277

2007. Magna Carta of Harmony for an Information Civilization: Toward Social Justice and

Global Peace, with 42 coauthors from 16 countries in 7 languages, Lita, 228 p. http://www.peacefromharmony.org/?cat=en_c&key=3

2006. Harmonious Era Calendar: Address to Children, Youth and Future Generations, with

26 coauthors from 12 countries in 12 languages, St.-Petersburg State Polytechnic University, 396 p. http://www.peacefromharmony.org/?cat=ru_c&key=190

2004. Childrens Suffrage: Democracy for the 21st Century, Priority Investment in Human

Capital as a Way toward  Social   Harmony, St.-Petersburg State Polytechnic University, 72 p. http://www.peacefromharmony.org/?cat=en_c&key=211

2003.Tetrasociology: from Sociological Imagination through Dialogue to Universal Values and

Harmony, with 14 co-authors, in three languages: Russian, English and Esperanto. St.-Petersburg State Polytechnic University, 394p.       http://www.peacefromharmony.org/?cat=en_c&key=149

2002. Tetrasociology: Responses to Challenges. St.-Petersburg State Polytechnic University (in

Russian and English), 158 p. http://www.peacefromharmony.org/?cat=en_c&key=145

2000. Tetrasociology as the Revolution of Social Thinking, the Way of Harmony and Prosperity.

St.-Petersburg, 168 p. (in Russian)

1999. Sociology for Pragmatists. Textbook for the university students. Part 1, St.-Petersburg,

376 p. (in Russian)

1992. Sphere Approach: Philosophy, Democracy, Market and Human. St.-Petersburg, 368 p.

(in Russian)

S. I. Sukhonos. Scale harmony of the Universe, .: Sofia, 2000, 312 pp, in Russian.



Dr Leo Semashko,

Global Harmony Association President,

State Councillor of St.Petersburg,

Director, International Website "Peace from Harmony",

Author of Tetrasociology as social science about harmony,

Director, Public Institute of Tetrasociology,

Social philosopher and sociologist,

Author more 200 scientific publications, including 12 books,

Pedagogical experience: 20 years,

Member of four International organizations.

Address: 7/4-42 Ho-Shi-Min Street, St. Petersburg, 194356, Russia

Tel: +7 (812) 513-38-63

E-mail: leo44442006@yandex.ru

Webpage: http://www.peacefromharmony.org/?cat=en_c&key=253

July 31 - October 4, 2008



© Website author: Leo Semashko, 2005; © designed by Roman Snitko, 2005