Is there a connection between various events. What gives stability and predictability to the development of society

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Message about the topic and purpose of the lesson.

Activation of educational activities.

Is there a connection between various events and phenomena in the life of society? What gives stability and predictability to the development of society?

Presentation of the program material.

Storytelling with elements of conversation

Features of the social system

In other words, society is a complex system of systems, a kind of supersystem.

Secondly, feature society as a system is the presence in its composition of elements of different quality, both material (various technical devices, institutions, etc.) and ideal (values, ideas, traditions, etc.). For example, the economic sphere includes enterprises, vehicles, raw materials and materials, industrial goods and at the same time economic knowledge, rules, values, patterns of economic behavior and much more.

Thirdly, main element society as a system is a person who has the ability to set goals and choose the means of carrying out their activities. This makes social systems more changeable and mobile than natural ones.

Public life is constant change. The pace and extent of these changes may vary; there are periods in the history of mankind when the established order of life did not change in its foundations for centuries, but over time the pace of change began to increase.

Hence, Human - it is a universal element of all social systems, since it is necessarily included in each of them.

Like any system, society is an ordered integrity. This means that the components of the system are not in a chaotic disorder, but, on the contrary, occupy a certain position within the system and are connected in a certain way with other components. Therefore, the system has integrative quality that is inherent in it as a whole. None of the components of the system, considered separately, has this quality. It, this quality, is the result of the integration and interconnection of all components of the system. Just as individual human organs (heart, stomach, liver, etc.) do not have the properties of a person, so the economy, the healthcare system, the state and other elements of society do not have the qualities that are inherent in society as a whole. And only thanks to the diverse connections that exist between the components of the social system, it turns into a single whole, that is, into society (just as thanks to the interaction of various human organs there is a single human body).

Integral, i.e., general, inherent in the whole system, qualities of any system are not a simple sum of the qualities of its components, but represent new quality, arising as a result of the relationship, the interaction of its components. In its most general form, this is the quality of society as a social system - ability create all the necessary conditions for its existence, to produce everything necessary for the collective life of people. In philosophy self-sufficiency regarded as main difference society from its constituent parts. Just as human organs cannot exist outside of an integral organism, so none of the subsystems of society can exist outside the whole - society as a system.

Another feature of society as a system is that this system is one of the self-managed. The administrative function is performed by the political subsystem, which gives consistency to all components that form social integrity.

Any system, be it a technical one (a unit with an automatic control system), or a biological one (an animal), or a social one (society), is in a certain environment with which it interacts. Wednesday The social system of any country is both nature and the world community. Changes in the state of the natural environment, events in the world community, in the international arena are a kind of "signals" to which society must respond. Usually it seeks to either adapt to changes in the environment, or to adapt the environment to its needs. In other words, the system responds to "signals" in one way or another. At the same time, it implements its main functions: adaptation; goal achievement, i.e. the ability to maintain its integrity, ensuring the implementation of its tasks, influencing the natural and social environment; maintaining the sample the ability to maintain its internal structure; integration- the ability to integrate, that is, to include new parts, new social formations (phenomena, processes, etc.) into a single whole.

Social institutions

The word "institution" in Latin instituto means "establishment". In Russian, it is often used to refer to higher educational institutions. In addition, as you know from the basic school course, in the field of law the word "institution" means a set of legal norms that regulate one social relationship or several relationships related to each other (for example, the institution of marriage).

In sociology social institutions are called historically established stable forms of organization of joint activities, regulated by norms, traditions, customs and aimed at meeting the fundamental needs of society.

This definition, to which it is expedient to return after reading the educational material on this issue to the end, we will consider based on the concept of “activity” (see § 1). In the history of society, sustainable activities aimed at satisfying the most important vital needs have developed. Sociologists identify five such public needs:

the need for the reproduction of the genus;

the need for security and social order;

need for means of subsistence;

the need for knowledge, socialization of the younger generation, training;

the need to solve spiritual problems of the meaning of life.

institution of family and marriage;

political institutions, especially the state;

economic institutions, primarily production;

institutes of education, science and culture;

institute of religion.

Each of these institutions brings together large masses of people to satisfy a particular need and achieve a specific goal of a personal, group or public nature.

The emergence of social institutions led to consolidation specific types of interaction, made them permanent and obligatory for all members of a given society.

Thus, a social institution is, first of all, set of persons engaged in a certain type of activity and ensuring in the process of this activity the satisfaction of a certain significant need for society (for example, all employees of the education system).

Further, the Institute fixed by a system of legal and moral norms, traditions and customs, regulating the corresponding types of behavior. (Remember, for example, what social norms regulate the behavior of people in the family).

Another characteristic feature of a social institution is the presence of institutions equipped with certain material resources necessary for any type of activity. (Think about which social institutions school, factory, police belong to. Give your examples of institutions and organizations related to each of the most important social institutions.)

Since new needs and conditions arise in the course of the historical process, new types of activity and corresponding connections appear. Society is interested in giving them an orderly, normative character, i.e. in their institutionalization.

Practical conclusions.

Society is a highly complex system, and in order to live in harmony with it, it is necessary to adapt (adapt) to it. Otherwise, you cannot avoid conflicts, failures in your life and work. The condition for adaptation to modern society is knowledge about it, which gives the course of social science.

Society can be understood only if its quality as an integral system is revealed. To do this, it is necessary to consider various sections of the structure of society (the main areas of human activity, a set of social institutions, social groups), systematizing, integrating the links between them, the features of the management process in a self-governing social system.

In real life, you will have to interact with various social institutions. To make this interaction successful, it is necessary to know the goals and nature of the activity that has taken shape in the social institution of interest to you. This will help you to study the legal norms governing this type of activity.

In the subsequent sections of the course, which characterize individual areas of human activity, it is useful to revisit the content of this paragraph in order, based on it, to consider each area as part of an integral system. This will help to understand the role and place of each sphere, each social institution in the development of society.

From the work of a contemporary American sociologist E. Shilza"Society and Societies: A Macrosociological Approach".

…So, we have seen that society is not just a collection of united people, original and cultural groups interacting and exchanging services with each other. All these collectives form a society by virtue of their existence under general authority, which exercise control over the territory marked by the borders, supports and enforces more or less general culture. It is these factors that make a set of relatively specialized original corporate and cultural collectives into a society.

Questions and tasks for the document

What components, according to E. Shils, are included in society? Indicate to which spheres of life of society each of them belongs.

Select from the listed components those that are social institutions.

What does the term "system" mean?

How do social (public) systems differ from natural ones?

What is the main quality of society as an integral system?

What are the connections and relations of society as a system with the environment?

What is a social institution?

Describe the main social institutions.

What are the main features of a social institution?

What is the meaning of institutionalization?

Using a systematic approach, analyze Russian society at the beginning of the 20th century.

Describe all the main features of a social institution using the example of the institution of education. Use the material and recommendations of the practical conclusions of this paragraph.

The collective work of Russian sociologists says: “…society exists and functions in diverse forms… The really important issue is to ensure that society itself is not lost behind special forms, and forests behind trees.” How is this statement related to the understanding of society as a system? Justify your answer.

V. S. Solovyov (1853-1900), Russian philosopher

Evaluation of student responses.

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Lesson in social science on the topic "Society as a complex dynamic system"

Purpose: 1. to get acquainted with the main components of society as a social system

2. characterize the main social institutions

3. to identify the main features of a social institution.

I. Communication of the topic and purpose of the lesson.

II. Activation of educational activities.

Is there a connection between various events and phenomena in the life of society? What gives stability and predictability to the development of society?

III. Presentation of the program material.

Storytelling with elements of conversation

In the second part of the definition of "society", given in § 1, the idea of the relationship of people and the interaction of various spheres of social life is emphasized. In philosophical literature, society is defined as a "dynamic system". The new concept of "system" may seem complicated, but it makes sense to understand it, since there are many objects in the world that are covered by this concept. Systems are our Universe, and the culture of an individual people, and the activity of man himself. The word "system" of Greek origin, means "a whole made up of parts", "a set". Thus, each system includes interacting parts: subsystems and elements. The connections and relationships between its parts are of primary importance. Dynamic systems allow various changes, development, the emergence of new and the withering away of old parts and the connections between them.

Features of the social system

What are the characteristic features of society as a system? How does this system differ from natural systems? A number of such differences have been identified in the social sciences.

First, society as a system is complex, since it includes many levels, subsystems, and elements. So, we can talk about human society on a global scale, about society within one country, about various social groups in which each person is included (nation, class, family, etc.).

The macrostructure of society as a system consists of four subsystems, which are the main areas of human activity - material production, social, political, spiritual. Each of these spheres known to you has its own complex structure and is itself a complex system. Thus, the political sphere acts as a system that includes a large number of components - the state, parties, etc. But the state, for example, is also a system with many components.

Thus, any of the existing spheres of society, being a subsystem in relation to society, at the same time itself acts as a rather complex system. Therefore, we can speak of a hierarchy of systems consisting of a number of different levels.

In other words, society is a complex system of systems, a kind of supersystem.

Secondly, a characteristic feature of society as a system is the presence in its composition of elements of different quality, both material (various technical devices, institutions, etc.) and ideal (values, ideas, traditions, etc.). For example, the economic sphere includes enterprises, vehicles, raw materials and materials, industrial goods and at the same time economic knowledge, rules, values, patterns of economic behavior and much more.

Thirdly, the main element of society as a system is a person who has the ability to set goals and choose the means of carrying out their activities. This makes social systems more changeable and mobile than natural ones.

Social life is in constant change. The pace and extent of these changes may vary; there are periods in the history of mankind when the established order of life did not change in its foundations for centuries, but over time the pace of change began to increase.

From the course of history, you know that certain qualitative changes took place in societies that existed in different eras, while the natural systems of those periods did not undergo significant changes. This fact indicates that society is a dynamic system that has a property that is expressed in science by the concepts of “change”, “development”, “progress”, “regression”, “evolution”, “revolution”, etc.

Consequently, a person is a universal element of all social systems, since he is necessarily included in each of them.

Like any system, society is an ordered integrity. This means that the components of the system are not in a chaotic disorder, but, on the contrary, occupy a certain position within the system and are connected in a certain way with other components. Consequently, the system has an integrative quality, which is inherent in it as a whole. None of the components of the system, considered separately, has this quality. It, this quality, is the result of the integration and interconnection of all components of the system. Just as individual human organs (heart, stomach, liver, etc.) do not have the properties of a person, so the economy, the healthcare system, the state and other elements of society do not have the qualities that are inherent in society as a whole. And only thanks to the diverse connections that exist between the components of the social system, it turns into a single whole, that is, into society (just as thanks to the interaction of various human organs there is a single human body).

The connections between subsystems and elements of society can be illustrated by various examples. The study of the distant past of mankind allowed scientists to conclude that the moral relations of people in primitive conditions were built on collectivist principles, that is, in modern terms, priority was always given to the team, and not to the individual. It is also known that the moral norms that existed among many tribes in those archaic times allowed the killing of weak members of the clan - sick children, the elderly - and even cannibalism. Have the real material conditions of their existence influenced these ideas and views of people about the limits of the morally permissible? The answer is clear: no doubt they did. The need to jointly obtain material wealth, the doom to an early death of a person who has broken away from the family, and laid the foundations of collectivist morality. Guided by the same methods of struggle for existence and survival, people did not consider it immoral to get rid of those who could become a burden for the team.

Another example may be the relationship between legal norms and socio-economic relations. Let's turn to known historical facts. In one of the first codes of laws of Kievan Rus, which is called Russkaya Pravda, various punishments for murder are provided. At the same time, the measure of punishment was determined primarily by the place of a person in the system of hierarchical relations, his belonging to one or another social stratum or group. So, the fine for killing a tiun (steward) was huge: it was 80 hryvnias and equaled the cost of 80 oxen or 400 rams. The life of a smerd or a serf was estimated at 5 hryvnias, i.e. 16 times cheaper.

Integral, i.e. common, inherent in the whole system, the qualities of any system are not a simple sum of the qualities of its components, but represent a new quality that has arisen as a result of the interconnection, interaction of its components. In its most general form, this is the quality of society as a social system - the ability to create all the necessary conditions for its existence, to produce everything necessary for the collective life of people. In philosophy, self-sufficiency is seen as the main difference between society and its constituent parts. Just as human organs cannot exist outside of an integral organism, so none of the subsystems of society can exist outside the whole - society as a system.

Another feature of society as a system is that this system is self-governing. The administrative function is performed by the political subsystem, which gives consistency to all components that form social integrity.

Any system, be it a technical one (a unit with an automatic control system), or a biological one (an animal), or a social one (society), is in a certain environment with which it interacts. The environment of the social system of any country is both nature and the world community. Changes in the state of the natural environment, events in the world community, in the international arena are a kind of "signals" to which society must respond. Usually it seeks to either adapt to changes in the environment, or to adapt the environment to its needs. In other words, the system responds to "signals" in one way or another. At the same time, it implements its main functions: adaptation; goal achievement, i.e. the ability to maintain its integrity, ensuring the implementation of its tasks, influencing the natural and social environment; maintenance of the sample - the ability to maintain its internal structure; integration - the ability to integrate, that is, to include new parts, new social formations (phenomena, processes, etc.) into a single whole.

Social institutions

Social institutions are the most important component of society as a system.

The word "institute" in Latin instituto means "establishment". In Russian, it is often used to refer to higher educational institutions. In addition, as you know from the basic school course, in the field of law the word "institution" means a set of legal norms that regulate one social relationship or several relationships related to each other (for example, the institution of marriage).

In sociology, social institutions are called historically established stable forms of organizing joint activities, regulated by norms, traditions, customs and aimed at meeting the fundamental needs of society.

- the need for the reproduction of the genus;

− the need for security and social order;

− the need for means of subsistence;

− the need for obtaining knowledge, socialization of the younger generation, training of personnel;

- the need to solve spiritual problems of the meaning of life.

According to the named needs, the society also developed the types of activities, which, in turn, required the necessary organization, streamlining, the creation of certain institutions and other structures, the development of rules that ensure the achievement of the expected result. These conditions for the successful implementation of the main activities were met by historically established social institutions:

− institution of family and marriage;

− political institutions, especially the state;

− economic institutions, primarily production;

− institutes of education, science and culture;

- institute of religion.

Each of these institutions brings together large masses of people to meet a particular need and achieve a specific goal of a personal, group or social nature.

The emergence of social institutions led to the consolidation of specific types of interaction, made them permanent and mandatory for all members of a given society.

So, a social institution is, first of all, a set of persons engaged in a certain type of activity and ensuring, in the process of this activity, the satisfaction of a certain need that is significant for society (for example, all employees of the education system).

Further, the institution is fixed by a system of legal and moral norms, traditions and customs that regulate the corresponding types of behavior. (Remember, for example, what social norms regulate the behavior of people in the family).

Another characteristic feature of a social institution is the presence of institutions equipped with certain material resources necessary for any type of activity. (Think about which social institutions school, factory, police belong to. Give your examples of institutions and organizations related to each of the most important social institutions.)

Any of these institutions is integrated into the socio-political, legal, value structure of society, which makes it possible to legitimize the activities of this institution and exercise control over it.

A social institution stabilizes social relations, brings coherence into the actions of members of society. A social institution is characterized by a clear delineation of the functions of each of the subjects of interaction, the consistency of their actions, and a high level of regulation and control. (Think about how these features of a social institution show up in the education system, particularly in schools.)

Consider the main features of a social institution on the example of such an important institution of society as the family. First of all, each family is a small group of people based on intimacy and emotional attachment, connected by marriage (wife) and consanguinity (parents and children). The need to create a family is one of the fundamental, i.e. fundamental, human needs. At the same time, the family performs important functions in society: the birth and upbringing of children, economic support for minors and the disabled, and much more. Each member of the family occupies a special position in it, which implies appropriate behavior: parents (or one of them) provide a livelihood, run household chores, and raise children. Children, in turn, study, help around the house. Such behavior is regulated not only by intra-family rules, but also by social norms: morality and law. Thus, public morality condemns the lack of care of older family members about the younger ones. The law establishes the responsibility and obligations of spouses in relation to each other, to children, adult children to elderly parents. The creation of a family, the main milestones of family life, are accompanied by traditions and rituals established in society. For example, in many countries, the marriage ritual includes the exchange of wedding rings between spouses.

The presence of social institutions makes people's behavior more predictable and society as a whole more stable.

In addition to the main social institutions, there are non-principal ones. So, if the state is the main political institution, then the non-main ones are the institution of the judiciary or, as in our country, the institution of presidential representatives in the regions, etc.

The presence of social institutions reliably ensures regular, self-renewing satisfaction of vital needs. The social institution makes connections between people not random and not chaotic, but permanent, reliable, stable. Institutional interaction is a well-established order of social life in the main spheres of people's life. The more social needs are met by social institutions, the more developed the society.

In Russia, as a result of the reforms of the late XX century. appeared, for example, such a type of activity as entrepreneurship. The streamlining of this activity led to the emergence of various types of firms, required the issuance of laws regulating entrepreneurial activity, and contributed to the formation of relevant traditions.

In the political life of our country, institutions of parliamentarism, a multi-party system, and the institution of presidency arose. The principles and rules for their functioning are enshrined in the Constitution of the Russian Federation and relevant laws.

In the same way, the institutionalization of other types of activity that have emerged over the past decades has taken place.

It happens that the development of society requires the modernization of the activities of social institutions that have historically developed in previous periods. Thus, in the changed conditions, it became necessary to solve the problems of introducing the younger generation to the culture in a new way. Hence the steps taken to modernize the institution of education, which may result in the institutionalization of the Unified State Examination, the new content of educational programs.

So, we can return to the definition given at the beginning of this part of the paragraph. Think about what characterizes social institutions as highly organized systems. Why is their structure stable? What is the importance of deep integration of their elements? What is the diversity, flexibility, dynamism of their functions?

III. Practical conclusions.

1. Society is a highly complex system, and in order to live in harmony with it, it is necessary to adapt (adapt) to it. Otherwise, you cannot avoid conflicts, failures in your life and work. The condition for adaptation to modern society is knowledge about it, which gives the course of social science.

2. It is possible to understand society only if its quality as an integral system is revealed. To do this, it is necessary to consider various sections of the structure of society (the main areas of human activity, a set of social institutions, social groups), systematizing, integrating the links between them, the features of the management process in a self-governing social system.

3. In real life, you will have to interact with various social institutions. To make this interaction successful, it is necessary to know the goals and nature of the activity that has taken shape in the social institution of interest to you. This will help you to study the legal norms governing this type of activity.

4. In the following sections of the course, which characterize individual areas of human activity, it is useful to revisit the content of this paragraph in order, based on it, to consider each area as part of an integral system. This will help to understand the role and place of each sphere, each social institution in the development of society.

IV. Document.

From the work of the modern American sociologist E. Shils "Society and Societies: Macrosociological Approach".

What is included in societies? As has been said, the most differentiated of these consist not only of families and kinship groups, but also of associations, unions, firms and farms, schools and universities, armies, churches and sects, parties and numerous other corporate bodies or organizations which, in in turn, have boundaries that define the circle of members over which the appropriate corporate authorities - parents, managers, chairmen, etc., etc. - exercise a certain measure of control. It also includes systems formally and informally organized on a territorial basis - communities, villages, districts, cities, districts - all of which also have some features of society. Further, it includes unorganized collections of people within society - social classes or strata, occupations and professions, religions, language groups - which have a culture that is more inherent in those who have a certain status or position than everyone else.

…So, we have seen that society is not just a collection of united people, original and cultural groups interacting and exchanging services with each other. All these collectives form a society by virtue of their existence under a common authority, which exercises its control over the territory marked by boundaries, maintains and propagates a more or less common culture. It is these factors that make a set of relatively specialized original corporate and cultural collectives into a society.

Questions and tasks for the document

1) What components, according to E. Shils, are included in society? Indicate to which spheres of life of society each of them belongs.

2) Select from the listed components those that are social institutions.

3) Based on the text, prove that the author considers society as a social system.

V. Questions for self-examination.

1. What does the term "system" mean?

2. How do social (public) systems differ from natural ones?

3. What is the main quality of society as an integral system?

4. What are the connections and relations of society as a system with the environment?

5. What is a social institution?

6. Describe the main social institutions.

7. What are the main features of a social institution?

8. What is the meaning of institutionalization?

VI. Tasks.

1. Using a systematic approach, analyze Russian society at the beginning of the 20th century.

2. Describe all the main features of a social institution using the example of the institution of education. Use the material and recommendations of the practical conclusions of this paragraph.

3. The collective work of Russian sociologists says: “…society exists and functions in diverse forms… A really important issue is to ensure that society itself is not lost behind special forms, and forests behind trees.” How is this statement related to the understanding of society as a system? Justify your answer.

VII. Thoughts of the wise.

"Man is a social being, and the highest cause of his life, the final goal of his efforts lies not in his personal destiny, but in the social destinies of all mankind."

V. S. Solovyov (1853-1900), Russian philosopher

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Is there a connection between various events and phenomena in the life of society? What gives stability and predictability to the development of society?

In the second part of the definition of "society", given in -1, the idea of the relationship of people and the interaction of various spheres of public life is emphasized. In philosophical literature, society is defined as a "dynamic system". The new concept of "system" may seem complicated, but it makes sense to understand it, since there are many objects in the world that are covered by this concept. Systems are our Universe, and the culture of an individual people, and the activity of man himself. The word "system" of Greek origin, means "a whole made up of parts", "a set". Thus, each system includes interacting parts: subsystems and elements, connections and relations between its parts acquire the main importance. Dynamic systems allow various changes, development, the emergence of new and the withering away of old parts and the connections between them.

Features of the social system

What are the characteristic features of society as a system? How does this system differ from natural systems? A number of such differences have been identified in the social sciences.

First, society as a system is complex, since it includes many levels, subsystems, and elements. So, we can talk about human society on a global scale, about a society within one country, about various social groups in which each person is included (nation, class, family, etc.).

The macrostructure of society as a system consists of four subsystems, which are the main areas of human activity - material and production, social, political, spiritual. Each of these spheres known to you has its own complex structure and is itself a complex system. Thus, the political sphere acts as a system that includes a large number of components - the state, parties, etc. But the state, for example, is also a system with many components.

In other words, society is a complex system of systems, a kind of supersystem.

Secondly, a characteristic feature of society as a system is the presence in its composition of elements of different quality, both material (various technical devices, institutions, etc.) and ideal (values, ideas, traditions, etc.). For example, the economic sphere includes enterprises, vehicles, raw materials, industrial goods, and at the same time economic knowledge, rules, values, patterns of economic behavior, and much more.

From the course of history, you know that certain qualitative changes took place in societies that existed in different eras, while the natural systems of those periods did not undergo significant changes. This fact indicates that society is a dynamic system that has a property that is expressed in science by the concepts of "change", "development", "progress", "regression", "evolution", "revolution", etc. Therefore, a person is a universal element of all social systems, since he is necessarily included in each of them.

Like any system, society is an ordered integrity. This means that the components of the system are not in a chaotic disorder, but, on the contrary, occupy a certain position within the system and are connected in a certain way with other components. Consequently, the system has an integrative quality, which is inherent in it as a whole. None of the components of the system, considered separately, has this quality. It, this quality, is the result of the integration and interconnection of all components of the system. Just as individual human organs (heart, stomach, liver, etc.) do not have the properties of a person, so the economy, the healthcare system, the state and other elements of society do not have the qualities that are inherent in society as a whole. And only thanks to the diverse links that exist between the components of the social system, it turns into a single whole, i.e. into society (as thanks to the interaction of various human organs, a single human body exists).

The connections between subsystems and elements of society can be illustrated by various examples. The study of the distant past of mankind allowed scientists to conclude that. that the moral relations of people in primitive conditions were built on collectivist principles. That is, in modern terms, priority has always been given to the collective, and not to the individual. It is also known that the moral norms that existed among many tribes in those archaic times allowed the killing of weak members of the clan - sick children, the elderly - and even cannibalism. Have the real material conditions of their existence influenced these ideas and views of people about the limits of the morally permissible? The answer is clear: no doubt they did. The need to jointly obtain material wealth, the doom to an early death of a person who has broken away from the family, and laid the foundations of collectivist morality. Guided by the same methods of struggle for existence and survival, people did not consider it immoral to get rid of those who could become a burden for the team.

Integral, i.e. the general qualities of any system inherent in the whole system are not a simple sum of the qualities of its components, but represent a new quality that has arisen as a result of the interconnection, interaction of its components. In its most general form, this is the quality of society as a social system - the ability to create all the necessary conditions for its existence, to produce everything necessary for the collective life of people. In philosophy, self-sufficiency is seen as the main difference between society and its constituent parts. Just as human organs cannot exist outside of an integral organism, so none of the subsystems of society can exist outside the whole - society as a system.

Another feature of society as a system is that this system is self-governing.

The administrative function is performed by the political subsystem, which gives consistency to all components that form social integrity.

Any system, whether technical (a unit with an automatic control system), or biological (animal), or social (society), is in a certain environment with which it interacts. The environment of the social system of any country is both nature and the world community. Changes in the state of the natural environment, events in the world community, in the international arena are a kind of "signals" to which society must respond. Usually it seeks to either adapt to changes in the environment, or to adapt the environment to its needs. In other words, the system responds to "signals" in one way or another. At the same time, it implements its main functions: adaptation; goal achievement, i.e. the ability to maintain its integrity, which ensures the implementation of its tasks, influencing the natural and social environment; maintaining the image shcha - the ability to maintain its internal structure; integration - the ability to integrate, i.e. include new parts, new social formations into a single whole.

Initially, being just a collection of information and empirical observations of the game of dice, the theory of probability has become a solid science. Fermat and Pascal were the first to give it a mathematical framework.

From reflections on the eternal to the theory of probability

Two individuals to whom the theory of probability owes many fundamental formulas, Blaise Pascal and Thomas Bayes, are known as deeply religious people, the latter was a Presbyterian minister. Apparently, the desire of these two scientists to prove the fallacy of the opinion about a certain Fortune, bestowing good luck on her favorites, gave impetus to research in this area. After all, in fact, any game of chance, with its wins and losses, is just a symphony of mathematical principles.

Thanks to the excitement of the Chevalier de Mere, who was equally a gambler and a person who was not indifferent to science, Pascal was forced to find a way to calculate the probability. De Mere was interested in this question: "How many times do you need to throw two dice in pairs so that the probability of getting 12 points exceeds 50%?". The second question that interested the gentleman extremely: "How to divide the bet between the participants in the unfinished game?" Of course, Pascal successfully answered both questions of de Mere, who became the unwitting initiator of the development of the theory of probability. It is interesting that the person of de Mere remained known in this area, and not in literature.

Previously, no mathematician has yet made an attempt to calculate the probabilities of events, since it was believed that this was only a guesswork solution. Blaise Pascal gave the first definition of the probability of an event and showed that this is a specific figure that can be justified mathematically. Probability theory has become the basis for statistics and is widely used in modern science.

What is randomness

If we consider a test that can be repeated an infinite number of times, then we can define a random event. This is one of the possible outcomes of the experience.

Experience is the implementation of specific actions in constant conditions.

In order to be able to work with the results of experience, events are usually denoted by the letters A, B, C, D, E ...

Probability of a random event

To be able to proceed to the mathematical part of probability, it is necessary to define all its components.

The probability of an event is a numerical measure of the possibility of the occurrence of some event (A or B) as a result of an experience. The probability is denoted as P(A) or P(B).

Probability theory is:

reliable the event is guaranteed to occur as a result of the experiment Р(Ω) = 1;
impossible the event can never happen Р(Ø) = 0;
random the event lies between certain and impossible, that is, the probability of its occurrence is possible, but not guaranteed (the probability of a random event is always within 0≤P(A)≤1).

Relationships between events

Both one and the sum of events A + B are considered when the event is counted in the implementation of at least one of the components, A or B, or both - A and B.

In relation to each other, events can be:

Equally possible.
compatible.
Incompatible.
Opposite (mutually exclusive).
Dependent.

If two events can happen with equal probability, then they equally possible.

If the occurrence of event A does not nullify the probability of occurrence of event B, then they compatible.

If events A and B never occur at the same time in the same experiment, then they are called incompatible. Tossing a coin is a good example: coming up tails is automatically not coming up heads.

The probability for the sum of such incompatible events consists of the sum of the probabilities of each of the events:

P(A+B)=P(A)+P(B)

If the occurrence of one event makes the occurrence of another impossible, then they are called opposite. Then one of them is designated as A, and the other - Ā (read as "not A"). The occurrence of event A means that Ā did not occur. These two events form a complete group with a sum of probabilities equal to 1.

Dependent events have mutual influence, decreasing or increasing each other's probability.

Relationships between events. Examples

It is much easier to understand the principles of probability theory and the combination of events using examples.

The experiment that will be carried out is to pull the balls out of the box, and the result of each experiment is an elementary outcome.

An event is one of the possible outcomes of an experience - a red ball, a blue ball, a ball with the number six, etc.

Test number 1. There are 6 balls, three of which are blue with odd numbers, and the other three are red with even numbers.

Test number 2. There are 6 blue balls with numbers from one to six.

Based on this example, we can name combinations:

Reliable event. In Spanish No. 2, the event "get the blue ball" is reliable, since the probability of its occurrence is 1, since all the balls are blue and there can be no miss. Whereas the event "get the ball with the number 1" is random.
Impossible event. In Spanish No. 1 with blue and red balls, the event "get the purple ball" is impossible, since the probability of its occurrence is 0.
Equivalent events. In Spanish No. 1, the events “get the ball with the number 2” and “get the ball with the number 3” are equally likely, and the events “get the ball with an even number” and “get the ball with the number 2” have different probabilities.
Compatible events. Getting a six in the process of throwing a die twice in a row are compatible events.
Incompatible events. In the same Spanish No. 1 events "get the red ball" and "get the ball with an odd number" cannot be combined in the same experience.
opposite events. The most striking example of this is coin tossing, where drawing heads is the same as not drawing tails, and the sum of their probabilities is always 1 (full group).
Dependent events. So, in Spanish No. 1, you can set yourself the goal of extracting a red ball twice in a row. Extracting it or not extracting it the first time affects the probability of extracting it the second time.

It can be seen that the first event significantly affects the probability of the second (40% and 60%).

Event Probability Formula

The transition from fortune-telling to exact data occurs by transferring the topic to the mathematical plane. That is, judgments about a random event like "high probability" or "minimum probability" can be translated to specific numerical data. It is already permissible to evaluate, compare and introduce such material into more complex calculations.

From the point of view of calculation, the definition of the probability of an event is the ratio of the number of elementary positive outcomes to the number of all possible outcomes of experience with respect to a certain event. Probability is denoted by P (A), where P means the word "probability", which is translated from French as "probability".

So, the formula for the probability of an event is:

Where m is the number of favorable outcomes for event A, n is the sum of all possible outcomes for this experience. The probability of an event is always between 0 and 1:

0 ≤ P(A) ≤ 1.

Calculation of the probability of an event. Example

Let's take Spanish. No. 1 with balls, which is described earlier: 3 blue balls with numbers 1/3/5 and 3 red balls with numbers 2/4/6.

Based on this test, several different tasks can be considered:

A - red ball drop. There are 3 red balls, and there are 6 variants in total. This is the simplest example, in which the probability of an event is P(A)=3/6=0.5.
B - dropping an even number. There are 3 (2,4,6) even numbers in total, and the total number of possible numerical options is 6. The probability of this event is P(B)=3/6=0.5.
C - loss of a number greater than 2. There are 4 such options (3,4,5,6) out of the total number of possible outcomes 6. The probability of the event C is P(C)=4/6=0.67.

As can be seen from the calculations, event C has a higher probability, since the number of possible positive outcomes is higher than in A and B.

Incompatible events

Such events cannot appear simultaneously in the same experience. As in Spanish No. 1, it is impossible to get a blue and a red ball at the same time. That is, you can get either a blue or a red ball. In the same way, an even and an odd number cannot appear in a die at the same time.

The probability of two events is considered as the probability of their sum or product. The sum of such events A + B is considered to be an event that consists in the appearance of an event A or B, and the product of their AB - in the appearance of both. For example, the appearance of two sixes at once on the faces of two dice in one throw.

The sum of several events is an event that implies the occurrence of at least one of them. The product of several events is the joint occurrence of them all.

In probability theory, as a rule, the use of the union "and" denotes the sum, the union "or" - multiplication. Formulas with examples will help you understand the logic of addition and multiplication in probability theory.

Probability of the sum of incompatible events

If the probability of incompatible events is considered, then the probability of the sum of events is equal to the sum of their probabilities:

P(A+B)=P(A)+P(B)

For example: we calculate the probability that in Spanish. No. 1 with blue and red balls will drop a number between 1 and 4. We will calculate not in one action, but by the sum of the probabilities of the elementary components. So, in such an experiment there are only 6 balls or 6 of all possible outcomes. The numbers that satisfy the condition are 2 and 3. The probability of getting the number 2 is 1/6, the probability of the number 3 is also 1/6. The probability of getting a number between 1 and 4 is:

The probability of the sum of incompatible events of a complete group is 1.

So, if in the experiment with a cube we add up the probabilities of getting all the numbers, then as a result we get one.

This is also true for opposite events, for example, in the experiment with a coin, where one of its sides is the event A, and the other is the opposite event Ā, as is known,

Р(А) + Р(Ā) = 1

Probability of producing incompatible events

Multiplication of probabilities is used when considering the occurrence of two or more incompatible events in one observation. The probability that events A and B will appear in it at the same time is equal to the product of their probabilities, or:

P(A*B)=P(A)*P(B)

For example, the probability that in No. 1 as a result of two attempts, a blue ball will appear twice, equal to

That is, the probability of an event occurring when, as a result of two attempts with the extraction of balls, only blue balls will be extracted, is 25%. It is very easy to do practical experiments on this problem and see if this is actually the case.

Joint Events

Events are considered joint when the appearance of one of them can coincide with the appearance of the other. Despite the fact that they are joint, the probability of independent events is considered. For example, throwing two dice can give a result when the number 6 falls on both of them. Although the events coincided and appeared simultaneously, they are independent of each other - only one six could fall out, the second die has no influence on it.

The probability of joint events is considered as the probability of their sum.

The probability of the sum of joint events. Example

The probability of the sum of events A and B, which are joint in relation to each other, is equal to the sum of the probabilities of the event minus the probability of their product (that is, their joint implementation):

R joint. (A + B) \u003d P (A) + P (B) - P (AB)

Assume that the probability of hitting the target with one shot is 0.4. Then event A - hitting the target in the first attempt, B - in the second. These events are joint, since it is possible that it is possible to hit the target both from the first and from the second shot. But the events are not dependent. What is the probability of the event of hitting the target with two shots (at least one)? According to the formula:

0,4+0,4-0,4*0,4=0,64

The answer to the question is: "The probability of hitting the target with two shots is 64%."

This formula for the probability of an event can also be applied to incompatible events, where the probability of the joint occurrence of an event P(AB) = 0. This means that the probability of the sum of incompatible events can be considered a special case of the proposed formula.

Probability geometry for clarity

Interestingly, the probability of the sum of joint events can be represented as two areas A and B that intersect with each other. As you can see from the picture, the area of their union is equal to the total area minus the area of their intersection. This geometric explanation makes the seemingly illogical formula more understandable. Note that geometric solutions are not uncommon in probability theory.

The definition of the probability of the sum of a set (more than two) of joint events is rather cumbersome. To calculate it, you need to use the formulas that are provided for these cases.

Dependent events

Dependent events are called if the occurrence of one (A) of them affects the probability of the occurrence of the other (B). Moreover, the influence of both the occurrence of event A and its non-occurrence is taken into account. Although events are called dependent by definition, only one of them is dependent (B). The usual probability was denoted as P(B) or the probability of independent events. In the case of dependents, a new concept is introduced - the conditional probability P A (B), which is the probability of the dependent event B under the condition that the event A (hypothesis) has occurred, on which it depends.

But event A is also random, so it also has a probability that must and can be taken into account in the calculations. The following example will show how to work with dependent events and a hypothesis.

Example of calculating the probability of dependent events

A good example for calculating dependent events is a standard deck of cards.

On the example of a deck of 36 cards, consider dependent events. It is necessary to determine the probability that the second card drawn from the deck will be a diamond suit, if the first card drawn is:

Tambourine.
Another suit.

Obviously, the probability of the second event B depends on the first A. So, if the first option is true, which is 1 card (35) and 1 diamond (8) less in the deck, the probability of event B:

P A (B) \u003d 8 / 35 \u003d 0.23

If the second option is true, then there are 35 cards in the deck, and the total number of tambourines (9) is still preserved, then the probability of the following event is B:

P A (B) \u003d 9/35 \u003d 0.26.

It can be seen that if event A is conditional on the fact that the first card is a diamond, then the probability of event B decreases, and vice versa.

Multiplication of dependent events

Based on the previous chapter, we accept the first event (A) as a fact, but in essence, it has a random character. The probability of this event, namely the extraction of a tambourine from a deck of cards, is equal to:

P(A) = 9/36=1/4

Since the theory does not exist by itself, but is called upon to serve practical purposes, it is fair to note that most often the probability of producing dependent events is needed.

According to the theorem on the product of the probabilities of dependent events, the probability of occurrence of jointly dependent events A and B is equal to the probability of one event A multiplied by the conditional probability of event B (depending on A):

P (AB) \u003d P (A) * P A (B)

Then in the example with a deck, the probability of drawing two cards with a suit of diamonds is:

9/36*8/35=0.0571 or 5.7%

And the probability of extracting not diamonds at first, and then diamonds, is equal to:

27/36*9/35=0.19 or 19%

It can be seen that the probability of occurrence of event B is greater, provided that a card of a suit other than a diamond is drawn first. This result is quite logical and understandable.

Total probability of an event

When a problem with conditional probabilities becomes multifaceted, it cannot be calculated by conventional methods. When there are more than two hypotheses, namely A1, A2, ..., A n , .. forms a complete group of events under the condition:

P(A i)>0, i=1,2,…
A i ∩ A j =Ø,i≠j.
Σ k A k =Ω.

So, the formula for the total probability for event B with a complete group of random events A1, A2, ..., A n is:

A look into the future

The probability of a random event is essential in many areas of science: econometrics, statistics, physics, etc. Since some processes cannot be described deterministically, since they themselves are probabilistic, special methods of work are needed. The probability of an event theory can be used in any technological field as a way to determine the possibility of an error or malfunction.

It can be said that, by recognizing the probability, we somehow take a theoretical step into the future, looking at it through the prism of formulas.

The demographic growth rates among European "farmers" and American hunters were the same.

It is believed that the reason for the significant demographic growth that occurred about 10-12 thousand years ago was the Neolithic revolution - the transition from an appropriating economy (hunting and gathering) to a producing one (agriculture and cattle breeding). The transition to agriculture, as most scientists believe, led to the emergence of the first cities and civilizations.

(Photo by hannahargyle/RooM the Agency/Corbis.)

Neolithic grain grinder. (Photo: José-Manuel Benito / CC BY-SA 2.5 / Wikimedia Commons / https://commons.wikimedia.org/wiki/File:Molino_neol%C3%ADtico_de_vaiv%C3%A9n.jpg.)

However, the results of researchers from the Harvard-Smithsonian Center for Astrophysics and the University of Wyoming, published in the journal Proceedings of the National Academy of Sciences do not fit into this theory. Robert Kelly ( Robert Kelly), professor of anthropology at the University of Wyoming, and his colleagues have performed radiocarbon dating of embers from hearths left by hunter-gatherers in ancient settlements in the territories of Wyoming and Colorado. The age of the remains is from 13 to 6 thousand years. A statistical analysis of the hunter-gatherer population showed that for many years the local population grew at a rate of about 0.041% per year. But exactly at the same rate, the number of the first farmers of Eurasia increased.

That is, in the words of Robert Kelly, "societies that switched to a productive economy grew at the same pace as contemporary societies with an appropriating economy." He notes that a similar rate of population growth (about 0.04%) was recorded in different geographical and climatic conditions, and it remained so until the end of the 18th century. And only in the last 200 years, the growth of the world's population has averaged 1%.

From this we can conclude that, as the authors of the work say, "the emergence of agriculture cannot be directly related to long-term population growth." In their opinion, factors of a global nature, climatic or biological (epidemics, diseases) influenced the population. Specific conditions, however, whether it be the local environment or the type of human activity, did not have a direct impact on demographic growth. However, they do not exclude that the population growth rate in some regions could experience short-term fluctuations.

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