The degree of organization of the system.

The organization or orderliness of the organization of the system is estimated by the formula

R=1-E real/Emax,

where is the real or current entropy value,

The maximum possible entropy or uncertainty in the structure and functions of the system.

If the system is completely deterministic and organized, then and . Reducing the entropy of the system to zero means the complete "overorganization" of the system and leads to the degeneration of the system. If the system is completely disorganized, then

A qualitative classification of systems according to the degree of organization was proposed by V. V. Nalimov, who singled out a class of well-organized and a class of poorly organized, or diffuse systems. Later, a class of self-organizing systems was added to these classes. It is important to emphasize that the name of a system class is not its evaluation. First of all, it can be considered as approaches to displaying an object or a problem being solved, which can be chosen depending on the stage of cognition of the object and the possibility of obtaining information about it.

Well organized systems.

If the researcher manages to determine the elements of the system and their relationship with each other and with the goals of the system and the type of deterministic (analytical or graphical) dependencies, then it is possible to represent the object in the form of a well-organized system. That is, the representation of an object in the form of a well-organized system is used in cases where a deterministic description can be proposed and the validity of its application has been experimentally shown (the adequacy of the model to a real object has been proved).

This representation is successfully used in modeling technical and technological systems. Although, strictly speaking. even the simplest mathematical relationships that reflect real situations are also not absolutely adequate, since, for example, when adding apples, it is not taken into account that they are not exactly the same, and weight can only be measured with some accuracy. Difficulties arise when working with complex objects (biological, economic, social, etc.). Without significant simplification, they cannot be represented as well-organized systems. Therefore, in order to display a complex object in the form of a well-organized system, it is necessary to single out only the factors that are essential for the specific purpose of the study. Attempts to apply models of well-organized systems to represent complex objects are practically often unrealizable, since, in particular, it is not possible to set up an experiment that proves the adequacy of the model. Therefore, in most cases, when representing complex objects and problems at the initial stages of the study, they are displayed by the classes discussed below.

According to the degree of organization (orderliness), information can be divided into documented and undocumented.

Documented information is information recorded on a material carrier by documenting with details that allow it to be identified, to determine such information, or in the manner prescribed by law. Russian Federation cases, its material carrier (Article 2 of the Federal Law of the Russian Federation of July 27, 2006 No. 149-FZ “On Information, Informatization and Information Protection”).

Undocumented information remains outside the scope of legal regulation.

Classification by role in the legal system

According to the role in the legal system, information is divided into legal and non-legal.

Non-legal - is not created as a result of legal activity, but is circulated in accordance with the prescriptions of legal norms. For example, an object civil law- information.

Legal - is created as a result of law-making, law enforcement, law enforcement activities: regulatory legal information and non-normative legal information.

Regulatory legal information is created in the course of law-making activities and is contained in regulatory legal acts of the federal level, constituent entities of the Russian Federation, and local governments. information legal civil

Non-normative legal information is created, as a rule, in the course of law enforcement and law enforcement activities. With the help of this information, legal regulations are implemented. This information is created in the control object and moves in the feedback loop of the legal control system. Non-normative legal information includes: judicial, criminal and prosecutorial statistics; information on the observance of human rights and freedoms (including on the proposal of the Commissioner for Human Rights); information on civil law relations, contractual and other obligations (contracts, agreements, etc. documents); information representing the administrative activities of executive authorities and local self-government in the implementation of regulatory requirements; court information and judiciary(court cases, court decisions, etc.), etc.

In systems theory, the sign of the degree of organization of a system directly intersects with the sign of its complexity of structure and behavior. Therefore, the concepts of complexity and organization can complement each other, and can act independently when characterizing individual manifestations of the system. As a rule, according to the degree of organization, systems are classified into "well organized" systems and "poorly organized" systems.

Under the definition " well organized" systems understand such systems, in the analysis of which it is possible to determine its elements and components, the relationships between them, the rules for combining elements into larger components. At the same time, it is possible to set the goals of the system and determine the effectiveness of their achievement during the functioning of the system.

In this case, the problem situation can be described in the form of a mathematical expression that links the goal with the means, i.e., in the form of an efficiency criterion, a criterion for the functioning of the system, which can be represented by a complex equation or system of equations. The solution of the problem when it is presented in the form of a "well-organized" system is carried out by analytical methods of formalized representation of the system.

Thus, we can talk about the equivalence of "well-organized" systems and simple systems.

It should be noted that in order to display an object in the form of a “well-organized” system, it is necessary to single out only the essential ones and not take into account the relatively unimportant for this purpose of consideration, individual elements, components and their relationships.

For example, solar system can be represented as a "well-organized" system in describing the most significant patterns of planetary motion around the Sun, without taking into account meteorites, asteroids and other small elements of interplanetary space compared to planets.

The technical device of a computer can be cited as a “well-organized” system (without taking into account the possibility of failure of its individual elements and nodes or any random interference coming through the power circuits).

Thus, the description of an object in the form of a "well-organized" system is used in cases where it is possible to offer a deterministic description and experimentally prove the validity of its application, the adequacy of the model to the real process.

"Poorly organized" systems, in contrast to the above, in general, they correspond to “complex” systems, since it is not always possible to analyze them determine the elements and the relationships between them, as well as find out the clear goals of the system and methods for evaluating the effectiveness of their functioning.

In the case of representing an object in the form of a "poorly organized" (or diffuse) system, the task is not to determine all the elements, components, their properties and connections between them and the goals of the system. The system is characterized by a certain set of macro parameters and those patterns that are determined on the basis of the study of not the entire object or a whole class of phenomena, but only its separate part - a sample obtained using certain sampling rules. On the basis of such a selective study, characteristics or patterns (statistical, economic) are obtained and distributed to the entire system as a whole. At the same time, appropriate reservations are made. For example, when obtaining statistical regularities, they are extended to the behavior of the entire system with a certain confidence probability.

The approach to displaying objects in the form of diffuse systems is widely used in describing queuing systems (for example, in telephone networks, etc.), information flows in information systems, description of resource tasks of a sectoral nature, etc.

The division of systems according to the degree of organization is proposed in continuation of the idea of ​​their division into well organized and poorly organized, or diffuse. To these two classes, another class has been added developing (self-organizing) systems. These classes are briefly characterized in Table. 1.4.

Table 1.4

In the proposed classification of systems, the systems that existed by the mid-70s of the 20th century were used. terms, but they are combined into a single classification, in which the selected classes are considered as approaches to displaying an object or solving a problem, and their characteristics are proposed, which allows choosing a class of systems for displaying an object, depending on the stage of its cognition and the possibility of obtaining information about it.

Problem situations with a large initial uncertainty are more consistent with the representation of an object in the form of a third-class system. In this case, modeling becomes, as it were, a kind of “mechanism” for the development of the system. The practical implementation of such a "mechanism" is associated with the need to develop a procedure for building a model of the decision-making process. Building a model begins with the use of a sign system (modeling language), which is based on one of the methods of discrete mathematics (for example, set-theoretic representations, mathematical logic, mathematical linguistics) or special methods of system analysis (for example, simulation dynamic simulation etc.). When modeling the most complex processes (for example, the processes of forming goal structures, improving organizational structures etc.) the "mechanism" of development (self-organization) can be implemented in the form of an appropriate method of system analysis. On the considered idea of ​​displaying an object in the process of representing it by a class of self-organizing systems, the method of gradual formalization of the decision-making model is also based, which is characterized in Ch. four.

Class self-organizing (developing), systems are characterized by a number of features or features that bring them closer to real developing objects (Table 1.5).

Table 1.5

The listed signs of self-organizing (developing) systems have various manifestations, which can sometimes be distinguished as independent features. These features, as a rule, are due to the presence of active elements in the system and are of a dual nature: they are new properties that are useful for the existence of the system, its adaptation to changing environmental conditions, but at the same time cause uncertainty and make it difficult to control the system.

Some of the features considered are characteristic of diffuse systems ( stochastic behavior, instability of individual parameters), but most of them are specific features that significantly distinguish this class of systems from others and make their modeling difficult.

At the same time, when creating and organizing enterprise management, they often try to represent them using the theory of automatic regulation and control, which was developed for closed, technical systems and significantly distorts the understanding of systems with active elements, which can harm the enterprise, make it an inanimate "mechanism", unable to adapt to the environment and develop options for their development.

The considered features are contradictory. In most cases, they are both positive and negative, desirable and undesirable for the system being created. It is not immediately possible to understand and explain the signs of systems, to select and create the required degree of their manifestation. Philosophers, psychologists, specialists in systems theory are studying the reasons for the manifestation of such features of complex objects with active elements, who, in order to explain these features, propose and investigate patterns of systems.

The manifestation of contradictory features of developing systems and the explanation of their patterns on the example of real objects must be studied, constantly monitored, reflected in models, and search for methods and means to regulate the degree of their manifestation.

At the same time, one should keep in mind the important difference between developing systems with active elements and closed ones: trying to understand the fundamental features of modeling such systems, the first researchers already noted that starting from a certain level of complexity, the system is easier to manufacture and put into operation, transform and change than to be represented by a formal model.

With the accumulation of experience in the study and transformation of such systems, this observation was confirmed, and their main feature was realized - fundamental limitation of a formalized description of developing (self-organizing) systems.

This feature, i.e. the need to combine formal methods and methods of qualitative analysis, and is the basis of most models and methods of system analysis. When forming such models, the usual idea of ​​models, which is characteristic of mathematical modeling and applied mathematics, changes. The idea of ​​proving the adequacy of such models also changes.

The variety of systems is quite large, and classification provides essential assistance in their study.
Classification is the division of a set of objects into classes according to some of the most essential features.
It is important to understand that classification is only a model of reality, so it must be treated as such, without requiring absolute completeness from it. It is also necessary to emphasize the relativity of any classifications.
The classification itself acts as a system analysis tool. With its help, the object (problem) of the study is structured, and the constructed classification is a model of this object.
At present, there is no complete classification of systems; moreover, its principles have not been finally developed. Different authors offer different principles of classification, and give different names to those that are similar in essence.

1. Classification by origin.
Depending on the origin, systems are divided into natural and artificial (created, anthropogenic).
Natural systems are systems that objectively exist in reality. in animate and inanimate nature and society.
These systems arose in nature without human intervention.
Examples: atom, molecule, cell, organism, population, society, universe, etc.
Artificial systems are systems created by man.
Examples:
1. Refrigerator, aircraft, enterprise, firm, city, state, party, social organization etc.
2. One of the first artificial systems can be considered a trading system.
In addition, we can talk about the third class of systems - mixed systems, which include ergonomic (machine - human operator), automated, biotechnical, organizational and other systems.

2. Classification according to the objectivity of existence.
All systems can be divided into two large groups: real (material or physical) and abstract (symbolic) systems.
Real systems consist of products, equipment, machines and, in general, natural and artificial objects.
Abstract systems, in fact, are models of real objects - these are languages, number systems, ideas, plans, hypotheses and concepts, algorithms and computer programs, mathematical models, systems of sciences.
Sometimes there are ideal or conceptual systems - systems that express a fundamental idea or exemplary reality - an exemplary version of an existing or projected system.
It is also possible to single out virtual systems - model or mental representations of real objects, phenomena, processes that do not actually exist (they can be both ideal and real systems).

3. Operating systems.
Let us single out the operating systems from the whole variety of created systems. Such systems are able to perform operations, work, procedures, provide a given flow of technological processes, acting according to programs specified by a person. In existing systems, the following systems can be distinguished: 1) technical, 2) ergatic, 3) technological, 4) economic, 5) social, b) organizational and 7) management.
1. Technical systems are material systems, which solve problems according to programs compiled by a person; the person himself is not an element of such systems.
A technical system is a set of interconnected physical elements.
The links in such systems are physical interactions (mechanical, electromagnetic, gravitational, etc.).
Examples: car, refrigerator, computer.
2. Ergatic systems. If there is a person in the system who performs certain functions of the subject, then one speaks of an ergatic system.
An ergatic system is a system whose constituent element is a human operator.
A special case of an ergatic system will be a human-machine system - a system in which a human operator or a group of operators interacts with a technical device in the production process. material assets, management, information processing, etc..
Examples:
1. Chauffeur driving a car.
2. A worker turning a part on a lathe.
3.Technological systems. There are two classes of definition of the concept of "technology":
a) as a certain abstract set of operations.
b) as a certain set of operations with the corresponding hardware and technical devices or tools.
Hence, by analogy with the structure, we can speak of a formal and material technological system.
A technological system (formal) is a set of operations (processes) in achieving certain goals (solutions of certain tasks).
The structure of such a system is determined by a set of methods, techniques, recipes, regulations, rules and norms.
The elements of a formal technological system will be operations (actions) or processes. Previously, the process was defined as a sequential change of states, but here we will consider a different understanding of the process: as a sequential change of operations.
A process is a sequential change of operations (actions aimed at changing the state of an object.
Links in the technological system receive the properties of processed objects or signals transmitted from operation to operation.
A technological system (material) is a set of real devices, devices, tools and materials (technical, system support) that implement operations (system process support) and predetermine their quality and duration.
Example. The formal technological system for the production of borscht is a recipe. The material technological system for the production of borscht is a set of knives, pots, kitchen appliances that implement the recipe. In abstract technology, we talk about the need to boil meat, but we do not specify either the type of pan or the type of stove (gas or electric). In material technology technical support cooking borscht will determine its quality and the duration of certain operations.
The technological system is more flexible than the technical one: with minimal transformations, it can be reoriented to the production of other objects, or to obtain other properties of the latter.
Examples. Technological systems: paper production, car manufacturing, travel arrangements, cash withdrawals from ATMs.
4. The economic system - that is the system of relations (processes) that take shape in the economy. Let's expand that definition.
An economic system is a set of economic relations that arise in the process of production, distribution, exchange and consumption of economic products and are regulated by a set of relevant principles, rules and legislative norms.
5. Social system. Since we are considering only created systems, we will consider the social system in the following context:
The social system is a set of activities aimed at social development people's lives.
Such measures include: improving the socio-economic and production conditions of work, strengthening its creative nature, improving the lives of workers, improving housing conditions, etc.
6. Organizational system. The interaction of the above systems is provided by the organizational system (organizational management system).
An organizational system is a set of elements that ensure the coordination of actions, the normal functioning and development of the main functional elements of an object.
The elements of such a system are management bodies that have the right to make management decisions - these are managers, divisions or even individual organizations (for example, ministries).
Relationships in the organizational system have an information basis and are determined by job descriptions and other regulatory documents that spell out the rights, duties and responsibilities of the management body.
7. Control system. Management is considered as actions or functions that ensure the implementation of specified goals.
The system in which the control function is implemented is called the control system.
The control system contains two main elements: the controlled subsystem (control object) and the control subsystem (performing the control function).
With regard to technical systems, the control subsystem is called the regulation system, and for socio-economic systems, the organizational management system.
A kind of control system is an ergatic system - a man-machine control system.
Example.
Let's consider the work of a store and try to identify the above systems in its work.
The store has a control system consisting of a control subject - management and a control object - all other store systems.
Management is implemented by the organizational management system - an organizational system consisting of the director, his deputies, heads of departments and sections, connected by certain subordination relationships.
The store operates an economic system that includes such economic relations as production (services and, possibly, goods, exchange (money for goods and services), distribution (profits).
Available social system, formulated in the collective and / or labor contracts.
Economic relations of exchange are implemented in the form of some technological systems (the technology of selling goods, the technology of returning money).
Technological systems, in turn, are built on the basis of technical systems (cash registers, barcode scanners, computers, calculators). A cashier working on a cash register is an ergatic system..

4. Centralized and decentralized systems.
A centralized system is a system in which some element plays a major, dominant role in the functioning of the system. Such a main element is called the leading part of the system or its center. At the same time, small changes in the leading part cause significant changes in the entire system: both desirable and undesirable. The disadvantages of a centralized system include a low rate of adaptation (adaptation to changing conditions environment), as well as the complexity of management due to the huge flow of information to be processed in the central part of the systems.
A decentralized system is a system in which there is no main element.
The most important subsystems in such a system have approximately the same value and are not built around a central subsystem, but are connected to each other in series or in parallel.
Examples.
1. Army structures are pronounced centralized systems.
2. The Internet is an almost perfect decentralized system.

5. Classification by dimension.
Systems are divided into one-dimensional and multidimensional.
A system that has one input and one output is called one-dimensional. If there is more than one input or output - multidimensional.
It is necessary to understand the conditionality of the one-dimensionality of the system - in reality, any object has an infinite number of inputs and outputs.

6. Classification of systems according to the homogeneity and diversity of structural elements.
Systems are homogeneous, or homogeneous, and heterogeneous, or heterogeneous, as well as a mixed type.
In homogeneous systems, the structural elements of the system are homogeneous, that is, they have the same properties. In this regard, in homogeneous systems, elements are interchangeable.
Example. A homogeneous computer system in an organization consists of computers of the same type with the same operating systems and application programs. This allows you to replace a failed computer with any other without additional configuration and retraining of the end user.
The term "homogeneous system" is widely used to describe the properties of gases, liquids, or populations of organisms.
Heterogeneous systems consist of heterogeneous elements that do not have the property of interchangeability.
Examples.
1. Heterogeneous network - an information network in which the network layer protocols of various manufacturers operate. A heterogeneous computer network consists of fragments of different topologies and different types of technical means.
2. If the university in the usual sense is a homogeneous education, i.e., it provides training in higher and postgraduate education (which are close both in terms of curricula and in their teaching methods), then the university complex is a heterogeneous system in which training is carried out programs of primary, secondary, higher postgraduate education.

7. Linear and non-linear systems.
A system is called linear if it is described linear equations(algebraic, differential, integral, etc.), otherwise non-linear.
For linear systems the principle of superposition is valid: the reaction of the system to any combination of external influences is equal to the sum of the reactions to each of these influences applied to the system separately. Suppose that after changing the input variable by Δх, the output variable changes by Δу. If the system is linear, then after two independent changes in the input variable by Δx 1 and Δх 2 . such that Δх 1 +Δх 2 =Δх, the total change in the output variable will also be equal to Δу.
Most complex systems are non-linear. In this regard, to simplify the analysis of systems, a linearization procedure is often used, in which a nonlinear system is described by approximately linear equations in a certain (working) range of input variables. However, not every nonlinear system can be linearized; in particular, discrete systems cannot be linearized.

8. Discrete systems.
Among nonlinear systems, a class of discrete systems is singled out.
A discrete system is a system containing at least one element of a discrete action.
A discrete element is an element whose output value changes discretely, i.e., in jumps, even with a smooth change in input values.
All other systems are referred to as continuous systems.
Continuous system ( continuous system) consists only of elements of continuous action, i.e., elements whose outputs change smoothly with a smooth change in input values.

9. Causal and purposeful systems.
Depending on the ability of the system to set a goal for itself, causal and goal-directed (purposeful, active) systems are distinguished.
Causal systems include a wide class of non-living systems:
Causal systems are systems in which purpose is not intrinsically inherent.
If such a system has an objective function (for example, an autopilot), then this function is set externally by the user.
Purposeful systems are systems capable of choosing their behavior depending on an inherent goal.
In purposeful systems, the goal is formed within the system.
Example. The system "aircraft-pilots" is able to set itself a goal and deviate from the route.
An element of purposefulness is always present in a system that includes people (or, more broadly, living beings). The question most often consists in the degree of influence of this purposefulness on the functioning of the object. If we are dealing with manual production, then the influence of the so-called human factor is very large. An individual, a group of people or the whole team is able to set the goal of their activity, which is different from the goal of the company.
Active systems, which primarily include organizational, social and economic, in foreign literature called "soft" systems. They are able to deliberately provide false information and deliberately not carry out plans, tasks, if it is beneficial for them. An important property of such systems is foresight, which ensures the system's ability to predict the future consequences of decisions. This, in particular, makes it difficult to use feedback to control the system.
In addition, sometimes in practice, systems are conditionally divided into systems striving for a goal - goal-oriented, and systems that are focused, first of all, not on goals, but on certain values ​​- value-oriented.

10. Large and complex systems.
Quite often, the terms "large system" and "complex system" are used interchangeably. At the same time, there is a point of view that large and complex systems are different classes of systems. At the same time, some authors associate the concept of “large” with the size of the system, the number of elements (often relatively homogeneous), and the concept of “complex” with the complexity of relationships, algorithms, or the complexity of behavior. There are more convincing justifications for the difference between the concepts of "large system" and "complex" "system".

10.1. Large systems.
The concept of "large system" began to be used after the appearance of the book of R.Kh. Hood and R.Z. Macola. This term was widely used during the formation systems studies in order to emphasize the fundamental features of objects and problems that require a systematic approach.
As signs of a large system, it was proposed to use various concepts:
o the concept of a hierarchical structure, which, naturally, narrowed the class of structures with which the system can be displayed;
o the concept of a “man-machine” system (but then fully automatic complexes fell out);
o the presence of large flows of information;
or a large number algorithms for its processing
U.R. Ashby believed that the system is large from the point of view of the observer, whose capabilities it surpasses in some aspect important for achieving the goal. At the same time, the physical dimensions of an object are not a criterion for classifying an object as a class of large systems. One and the same material object, depending on the purpose of the observer and the means at his disposal, can be displayed or not displayed by a large system.
Yu.I. Chernyak also explicitly connects the concept of a large system with the concept of an “observer”: to study a large system, unlike a complex one, an “observer” is needed (meaning not the number of people involved in the study or design of the system, but the relative homogeneity of their qualifications). : for example, an engineer or an economist). He emphasizes that in the case of a large system, the object can be described, as it were, in one language, that is, with the help of a single modeling method, albeit in parts, to subsystems. More Yu.I. Chernyak proposes to call a large system "one that cannot be studied otherwise than by subsystems."

10.2. Classification of systems by complexity.
There are a number of approaches to separating systems by complexity, and, unfortunately, there is no single definition of this concept, and there is no clear boundary separating simple systems from complex ones. Various authors have proposed various classifications of complex systems.
For example, a relatively small amount of information required for its successful management is considered a sign of a simple system. Systems in which there is not enough information for effective management are considered complex.
G.N. Povarov estimates the complexity of systems depending on the number of elements included in the system:
o small systems (10-10 3 elements);
o complex (10 4 -10 6);
o ultra-complex (10 7 -10 30 elements);
o supersystems (10 30 -10 200 elements).
In particular, Yu.I. Chernyak calls a complex system that is built to solve a multi-purpose, multi-aspect problem and reflects an object from different angles in several models. Each of the models has its own language, and a special metalanguage is needed to coordinate these models. At the same time, it was emphasized that such a system has a complex, composite goal, or even different goals, and, moreover, many structures at the same time (for example, technological, administrative, communication, functional, etc.).
B.C. Fleishman takes the complexity of the system behavior as the basis for classification.
One of the interesting classifications by difficulty levels was proposed by K. Boulding (Table 1). In this classification, each subsequent class includes the previous one.
Conventionally, two types of complexity can be distinguished: structural and functional.
structural complexity. Art. Veer proposes to divide systems into simple, complex and very complex.
Simple systems are the least complex systems.
Complex - these are systems that are distinguished by a branched structure and a great variety of internal connections.

Table 1. Classification of systems according to the level of complexity of K. Boulding.

A very complex system is a complex system that cannot be described in detail.
Undoubtedly, these divisions are rather arbitrary and it is difficult to draw a line between them. (Here the question immediately comes to mind: how many stones does a pile start with?)
Later St. Veer proposed to classify as simple systems those that have up to 10 3 states, as complex - from 10 3 to 10 6 states, and as very complex - systems with over a million states.
One way to describe complexity is to estimate the number of elements that make up the system (variables, states, components) and the variety of interdependencies between them. For example, the complexity of a system can be quantified by comparing the number of system elements (n) and the number of links (m) using the following formula:
where n(n -1) is the maximum possible number of connections.
An entropy approach can be applied to assess the complexity of a system. It is believed that the structural complexity of the system should be proportional to the amount of information required to describe it (removal of uncertainty). In this case, the total amount of information about the system S, in which the a priori probability of the occurrence of the ith property is equal to p(s i), is defined as

functional complexity. Speaking about the complexity of systems, Art. Veer reflected only one side of the complexity - the complexity of the structure - structural complexity. However, it should be said about another complexity of systems - functional (or computational).
For quantification functional complexity, you can use an algorithmic approach, for example, the number of arithmetic-logical operations required to implement the function of the system for converting input values ​​to output values, or the amount of resources (counting time or memory used) used in the system when solving a certain class of problems.
It is believed that there are no data processing systems that could process more than 1.6 10 17 bits of information per second per gram of their mass. Then a hypothetical computer system with a mass equal to the mass of the Earth, for a period approximately equal to the age of the Earth, can process about 10 98 bits of information (the Bremmermann limit). In these calculations, each cell was used as an information cell. quantum level in the atoms that make up the earth. Tasks that require processing more than 1093 bits are called transcomputing. In practical terms, this means that, for example, a complete analysis of a system of 100 variables, each of which can take 10 different values, is a transcomputational problem.
Example. If the system has two inputs that can be in two possible states, then options states are four. With 10 inputs of options, there are already 1024, and with 20 (which corresponds to a small real deal) - there are already 2 20 options. When there is a real operational plan for a small corporation, in which at least a thousand independent events(inputs), then there are 2 1000 options! Significantly larger than the Bremmermann limit.
In addition, there is such a type of complexity as dynamic complexity. It occurs when the relationships between elements change. For example, in a team of employees of a company, the mood may change from time to time, so there are many options for connections that can be established between them. Trying to give an exhaustive description of such systems can be compared to finding a way out of a labyrinth that completely changes its configuration as soon as you change direction. Chess is an example.
Small and large, complex and simple. The authors of the book propose to consider four options for the complexity of systems
1) small simple;
2) small complex;
3) large simple;
4) large complex.
In this case, the selection of a system by one or another class in the same object depends on the point of view of the object, i.e., on the observer.
Examples:
1. It has long been known that the townsfolk are always ready to give advice in the field of education, treatment, governing the country - for them these are always small simple systems. Whereas for educators, doctors and statesmen, these are large complex systems.
2. Serviceable Appliances for the user small simple systems, but faulty - small complex. And for the master, the same faulty devices are small simple systems.
3. A cipher lock for the owner of the safe is a small simple system, and for a kidnapper it is a large simple one.
Thus, the same object can be represented by systems of different complexity. And it depends not only on the observer, but also on the purpose of the study. In this regard, V. A. Kartashev writes: “The primary consideration of even the most complex formations at the level of establishing their main, main relationships leads to the concept of a simple system”
Example. With a stratified description of the enterprise at the topmost stratum, it can be described as a small simple system in the form of a “black box” with basic inputs and outputs.

11. Determinism.
Consider another classification of systems proposed by St. Birom.
If the inputs of an object uniquely determine its outputs, that is, its behavior can be uniquely predicted (with probability 1), then the object is deterministic; otherwise, it is non-deterministic (stochastic).
Mathematically, determinism can be described as a strict functional relationship Y = F(X), and stochasticity arises as a result of adding random variableε: Y = F(X) + ε
Determinism is characteristic of less complex systems;
stochastic systems are more difficult than deterministic systems because they are more difficult to describe and study
Examples:
1. A sewing machine can be attributed to a deterministic system: by turning the handle of the machine at a given angle, we can say with confidence that the needle will move up and down a known distance (the case of a faulty machine is not considered)
2. An example of a non-deterministic system is a dog, when a bone is handed to it, it is impossible to unambiguously predict the dog's behavior.
An interesting question is about the nature of stochasticity. On the one hand, stochasticity is a consequence of randomness.
Randomness is a chain of unrevealed patterns hidden beyond the threshold of our understanding.
On the other hand, the approximate measurements. In the first case, we cannot take into account all the factors (inputs) acting on the object, and we also do not know the nature of its non-stationarity. In the second, the problem of the unpredictability of the output is related to the inability to accurately measure the values ​​of the inputs and the limited accuracy of complex calculations.
Examples. Art. Veer offers the following table with examples of systems:

12. Classification of systems according to the degree of organization.
12.1 The degree of organization of the system.
The organization or orderliness of the organization of the system R is estimated by the formula
R \u003d 1-E real / E max,
where Ereal is the real or current value of entropy,
Emax - the maximum possible entropy or uncertainty in the structure and functions of the system.
If the system is completely deterministic and organized, then E real = 0 and R = 1. Reducing the entropy of the system to zero means the complete "overorganization" of the system and leads to the degeneration of the system. If the system is completely disorganized, then
R=0 and E real = E max.
A qualitative classification of systems according to the degree of organization was proposed by V. V. Nalimov, who singled out a class of well-organized and a class of poorly organized, or diffuse systems. Later, a class of self-organizing systems was added to these classes. It is important to emphasize that the name of a system class is not its evaluation. First of all, it can be considered as approaches to displaying an object or a problem being solved, which can be chosen depending on the stage of cognition of the object and the possibility of obtaining information about it.

12.2. Well organized systems.
If the researcher manages to determine the elements of the system and their relationship with each other and with the goals of the system and the type of deterministic (analytical or graphical) dependencies, then it is possible to represent the object in the form of a well-organized system. That is, the representation of an object in the form of a well-organized system is used in cases where a deterministic description can be proposed and the validity of its application has been experimentally shown (the adequacy of the model to a real object has been proved).
This representation is successfully used in modeling technical and technological systems. Although, strictly speaking. even the simplest mathematical relationships that reflect real situations are also not absolutely adequate, since, for example, when adding apples, it is not taken into account that they are not exactly the same, and weight can only be measured with some accuracy. Difficulties arise when working with complex objects (biological, economic, social, etc.). Without significant simplification, they cannot be represented as well-organized systems. Therefore, in order to display a complex object in the form of a well-organized system, it is necessary to single out only the factors that are essential for the specific purpose of the study. Attempts to apply models of well-organized systems to represent complex objects are practically often unrealizable, since, in particular, it is not possible to set up an experiment that proves the adequacy of the model. Therefore, in most cases, when representing complex objects and problems at the initial stages of the study, they are displayed by the classes discussed below.

12.3. Poorly organized (or diffuse) systems.
If the task is not set to determine all the considered components and their connections with the goals of the system, then the object is presented as a poorly organized (or diffuse) system. To describe the properties of such systems, two approaches can be considered: selective and macroparametric.
With a selective approach, regularities in the system are revealed on the basis of studying not the entire object or class of phenomena, but by studying a fairly representative (representative) sample of components that characterize the object or process under study. The sample is determined using some rules. The characteristics or regularities obtained on the basis of such a study are extended to the behavior of the system as a whole.
Example. If we are not interested in the average price of bread in any city, then we could sequentially go around or call all the city's outlets, which would require a lot of time and money. Or you can go the other way: collect information in a small (but representative) group of outlets, calculate the average price and generalize it to the whole city.
At the same time, we must not forget that the obtained statistical regularities are valid for the entire system with some probability, which is estimated using special techniques studied by mathematical statistics.
With the macroparametric approach, the properties of the system are evaluated using some integral characteristics (macroparameters).
Examples:
1. When using a gas for applied purposes, its properties are not determined by an accurate description of the behavior of each molecule, but are characterized by macro parameters - pressure, temperature, etc. Based on these parameters, devices and devices are developed that use the properties of the gas, without examining the behavior of each molecule.
2. When assessing the quality level of the health care system of the state, the UN uses as one of the integral characteristics the number of children who die before the age of five per thousand newborns.

Displaying objects in the form of diffuse systems is widely used in determining the throughput of systems of various kinds, in determining the number of staff in service, for example, repair shops of an enterprise and in service institutions, in the study of documentary information flows, etc.

12.4. self-organizing systems.
The class of self-organizing, or developing, systems is characterized by a number of features, features, which, as a rule, are due to the presence of active elements in the system that make the system purposeful. This implies the features of economic systems, as self-organizing systems, in comparison with the functioning of technical systems:
o non-stationarity (variability) of individual parameters of the system and the stochasticity of its behavior;
o uniqueness and unpredictability of the system behavior in specific conditions. Due to the presence of active elements of the system, a kind of "free will" appears, but at the same time, its possibilities are limited by the available resources (elements, their properties) and structural connections characteristic of a certain type of systems;
o the ability to change its structure and form behaviors while maintaining integrity and basic properties (in technical and technological systems, a change in structure, as a rule, leads to a disruption in the functioning of the system or even to the cessation of existence as such);
o the ability to resist entropic (system-destroying) tendencies. In systems with active elements, the regularity of the increase in entropy is not observed, and even negentropic tendencies are observed, i.e., self-organization proper;
o ability to adapt to changing conditions. This is good in relation to disturbing influences and interference, but it is bad when adaptability also manifests itself in relation to control actions, making it difficult to control the system;
o the ability and desire for goal setting;
o fundamental disequilibrium.
It is easy to see that although some of these features are also characteristic of diffuse systems (stochastic behavior, instability of individual parameters), however, for the most part they are specific features that significantly distinguish this class of systems from others and make their modeling difficult.
The considered features are contradictory. In most cases they are both positive and negative, desirable and undesirable for the system being created. It is not immediately possible to understand and explain them in order to select and create the required degree of their manifestation.
At the same time, one should keep in mind the important difference between open developing systems with active elements and closed ones. Trying to understand the fundamental features of modeling such systems, the first researchers already noted that, starting from a certain level of complexity, the system is easier to manufacture and put into operation, transform and change than to be displayed by a formal model. With the accumulation of experience in the study and transformation of such systems, this observation was confirmed, and their main feature was realized - the fundamental limitation of a formalized description of developing, self-organizing systems.
On this occasion, von Neumann expressed the following hypothesis: “We do not have complete confidence that in the field of complex problems a real object cannot be the simplest description of itself, that is, that any attempt to describe it using ordinary verbal or formal logical method will not lead to something more complex, confusing and difficult to implement ... ".
The need to combine formal methods and methods of qualitative analysis is the basis of most models and methods of system analysis. When forming such models, the usual idea of ​​models, which is characteristic of mathematical modeling and applied mathematics, changes. The idea of ​​proving the adequacy of such models also changes.
The main constructive idea of ​​modeling when displaying an object by a class of self-organizing systems can be formulated as follows: by accumulating information about the object, fixing all the new components and connections and applying them, you can get mappings of the successive states of the developing system, gradually creating an increasingly adequate model of the real, studied or created object. In this case, information can come from specialists various areas knowledge and accumulate over time as it arises (in the process of knowing the object).
The adequacy of the model is also proved, as it were, sequentially (as it is formed) by evaluating the correctness of the reflection in each subsequent model of the components and relationships necessary to achieve the goals.

Summary
1. When studying any objects and processes, including systems, classification is of great help - the division of a set of objects into classes according to some, the most significant features.
2. Depending on the origin, systems can be natural (systems that objectively exist in living and inanimate nature and society) and artificial (systems created by man).
3. According to the objectivity of existence, all systems can be divided into two large groups: real (material or physical) and abstract (symbolic) systems.
4. Among the variety of systems being created, of particular interest are the existing systems, which include technical, technological, economic, social and organizational.
5. According to the degree of centralization, centralized systems are distinguished (having in their composition an element that plays the main, dominant role in the functioning of the system) and decentralized (not having such an element).
6. Distinguish between one-dimensional systems (having one input and one output) and multidimensional (if there are more than one input or output).
7. Systems are homogeneous, or homogeneous, and heterogeneous or heterogeneous, as well as mixed.
8. If the system is described by linear equations, then it belongs to the class of linear systems, otherwise - non-linear.
9. A system that does not contain a single element of a discrete action (the output value of which changes in jumps even with a smooth change in the input values) is called continuous, otherwise it is discrete.
10. Depending on the ability of the system to set a goal for itself, there are causal systems (incapable of setting a goal for themselves) and goal-oriented systems (capable of choosing their behavior depending on the inherent goal).
11. There are large, very complex, complex and simple systems.
12. By the predictability of weekend values system variables for known input values, deterministic and stochastic systems are distinguished.
13. Depending on the degree of organization, there are classes of well-organized systems (their properties can be described as deterministic dependencies), poorly organized (or diffuse) and self-organizing (including active elements)
14. Starting from a certain level of complexity, the system is easier to manufacture and put into operation, to transform and change than to be displayed by a formal model, since there is a fundamental limitation of a formalized description of developing self-organizing systems.
15. In accordance with the von Neumann hypothesis, the simplest description of an object that has reached a certain threshold of complexity is the object itself, and any attempt at a rigorous formal description leads to something more difficult and confusing.