It is called a systemic view of the interconnections of various theories. General systems theory
The usual interpretation of the concepts discussed below ( element, connection etc.) does not always coincide with their meaning as special terms for the system description and analysis of objects. Therefore, we briefly consider the basic concepts that help clarify the idea of the system.
It is usually customary to divide concepts into two groups (Fig. 1.3): 1) concepts included in the definitions of the system and characterizing its structure; 2) concepts that characterize the functioning and development of the system.
Rice. 1.3
Concepts characterizing the structure of the system
The concepts included in the definition of a system are closely related and, according to L. von Bertalanffy, cannot be defined independently, but are defined, as a rule, one through the other, clarifying each other, and therefore the sequence of their presentation adopted here should be considered conditional.
Element. An element is usually understood as the simplest, indivisible part of a system. However, the answer to the question of what is such a part can be ambiguous.
Example
As elements of the table, one can name "legs, boxes, a lid, etc.", or "atoms, molecules", depending on what task the researcher faces.
Similarly, in the enterprise management system, the elements can be considered the divisions of the management apparatus, or each employee or each operation that he performs. A typical error was associated with a lack of understanding of this problem when examining an existing control system as the first stage of developing an automated control system: engineers, in accordance with their approach to ensuring completeness, analyzed all documents, up to the details, which significantly delayed the work, while for the development of technical specifications for the creation of an automated control system of such detail was not required.
So let's take the following definition: element – this is the limit of the division of the system in terms of the aspect of consideration, solving a specific problem, a goal.
To help in the selection of elements in the analysis of specific problem situations, it is possible, as shown in Chap. 3, use the information approach, and in particular the measure of perception information J= A/ΔA, where DA is the minimum amount of material property A (quantum), up to which the researcher is interested in information about this property when forming a model. Examples of using this method for determining the element base will be given in Chap. 6–8 (in particular, when modeling a market situation).
The system can be divided into elements in various ways, depending on the formulation of the task, the goal and its refinement in the process of conducting a systematic study. If necessary, you can change the principle of dismemberment, highlight other elements and use the new dismemberment to get a more adequate idea of the analyzed object or problem situation.
When defining an element, it was necessary to use the concept of goal, which will be described below (the concepts included in the definition of the system, as noted above, cannot be defined independently of each other), so an attempt was made not to use the concept of goal, but to put next to it the concepts aspect consideration, tasks, although it is more accurate to use the concept of goal.
Components and subsystems. Sometimes the term "element" is used in a broader sense, even in cases where the system cannot be immediately divided into components that are the limit of its division. However, with a multilevel partition of the system, it is better to use other terms provided in the theory of systems: it is customary to first divide complex systems into subsystems, or at Components.
The concept of "subsystem" implies that a relatively independent part of the system is singled out, which has the properties of the system, and in particular, has a subgoal, to which the subsystem is oriented, as well as other properties - integrity, communication, etc., determined by the patterns of systems considered in paragraph 1.6.
If parts of the system do not have such properties, but are simply collections of homogeneous elements, then such parts are usually called components.
When dividing the system into subsystems, it should be borne in mind that, just as when dividing into elements, the allocation of subsystems depends on the goal and may change as it is refined and the researcher's ideas about the analyzed object or problem situation develop.
Connection. The concept of "connection" is included in any definition of a system and ensures the emergence and preservation of its integral properties. This concept simultaneously characterizes both the structure (statics) and the functioning (dynamics) of the system.
Communication is defined as a limitation of the degree of freedom of elements. Indeed, the elements, entering into interaction (connection) with each other, lose some of their properties, which they potentially possessed in a free state.
In system definitions, the terms "relationship" and "relationship" are usually used interchangeably. However, there are different points of view: some researchers believe connection special case relations; others, on the contrary, attitude considered as a special case communications; others propose to use the concept of "relationship" to describe the statics of the system, its structure, and the concept of relation to characterize some actions in the process of functioning (dynamics) of the system. The question of the sufficiency and completeness of the network of connections for the system to be considered a system has not been resolved (and, apparently, can hardly be resolved in a general way). One of the approaches to solving this problem is proposed, for example, by V.I. Nikolaev and V. M. Brook who believe that in order for the system not to fall apart, it is necessary to ensure that the total strength (power) of the connections between the elements of the system is exceeded, i.e. internal connections, over the total power of connections between the elements of the system and the elements of the environment, i.e. external relations:
Unfortunately, in practice, such measurements (especially in organizational systems) are difficult to implement, but it is possible to assess the trends in this ratio using indirect factors.
Connections can be characterized by direction, strength, character (or type). On the basis of the first feature, the connections are divided into directed and non-directed. According to the second - on strong and weak (sometimes they try to introduce a "scale" of the strength of connections for a specific task). According to the nature (kind), there are connections of subordination, generation (or genetic), equal (or indifferent), management.
Relationships in specific systems can be simultaneously characterized by several of these features.
An important role in system modeling is played by the concept feedback, whose models are given in paragraph 2.6. Feedback is the basis of self-regulation, development of systems, their adaptation to changing conditions of existence.
Multi-loop models for managing economic systems were proposed, for example, in the dictionary-reference book on mathematics and cybernetics in economics. When developing models for the functioning of complex self-regulating, self-organizing systems, as a rule, both negative and positive feedbacks are simultaneously present in them. On the use of these concepts, in particular, simulation dynamic modeling is based.
Target. The concept of "goal" and related concepts of "expediency" and "purposefulness" underlie the development of the system.
Much attention is paid to the study of these concepts in philosophy, psychology, and cybernetics.
The process of goal formation and the corresponding process of substantiating goals in organizational systems is very complex. Throughout the entire period of development of philosophy and theory of knowledge, ideas about the goal have been developing (the history of the development of the concept of "goal" can be found in the book M. G. Makarova ).
An analysis of the definitions of the goal and related concepts shows that, depending on the stage of cognition of the object, the stage of system analysis, various shades are put into the concept of "goal" (Fig. 1.4) - from ideal aspirations (goal - " expression of activity of consciousness" ; "a person and social systems have the right to formulate goals, the achievement of which, as they know, is impossible, but which can be continuously approached"), to specific goals - final results, achievable within a certain time interval, sometimes formulated even in terms of final product activities .
In some definitions, the goal is, as it were, transformed, taking on various shades within the conventional "scale" - from idea
al aspirations for material embodiment, the final result of activity.
For example, M. G. Makarov , along with the above definition, calls the goal "what seeks, what worships and for what fights Human" ( "struggles" implies reachability in a certain time interval); L . A. Rastrigin and P. S. Grave , the goal is understood as a "model of the desired future" (in this case, various shades of realizability can be invested in the concept of "model") and, in addition, a concept is introduced that characterizes the type of goal, and in addition, the concept of "dream" is introduced - it is a goal not supported by the means to achieve it". The contradiction contained in the concept of "goal" - the need to be an incentive to action "leading reflection"(term introduced P. K. Anokhin), or " leading idea, and at the same time the material embodiment of this idea, i.e. to be achievable, has manifested itself since the emergence of this concept: for example, the ancient Indian concept of "artha" included at the same time the meanings of the terms "motive", "cause", "desire", "goal" and even - "method".
In Russian, there was no term "purpose" at all. This term is borrowed from German and has a meaning close to the concepts of "target", "finish", "point of impact". There are several terms in the English language that reflect different shades of the concept of purpose, within the "scale" under consideration.
Example
Purpose(goal - intention, purposefulness, will), object and objective(goal - direction of action, direction of movement), aim(goal - aspiration, sight, indication), goal(goal - destination, task), target(target - target for shooting, task, plan), end(goal - finish, end, end, limit).
The essence of the dialectical interpretation of the concept of goal is revealed in the theory of knowledge, which shows the relationship of concepts goals, evaluations, means, integrity(and her "self-movement").
The study of the relationship between these concepts shows that, in principle, the behavior of the same system can be described both in terms of a goal or goal functionals that connect goals with the means to achieve them (such a representation is called axiological [53]), and without mentioning the concept of goal, in terms of the direct influence of some elements or the parameters that describe them on others, in terms of "state space" (or causally). Therefore, the same situation, depending on the inclination and previous experience of the researcher, can be represented in one way or another. In most practical situations a better understanding and description of the state of the system and its future allows a combination of these ideas.
In order to reflect the dialectical contradiction contained in the concept of "goal", the following definition is given in the TSB: the goal is " preconceived result of the conscious activity of a person, a group of people" .
"Thinkable in advance", but still the "result", the embodiment of the idea; it is also emphasized that the concept of purpose is associated with a person, his "conscious activity", i.e. with the presence of consciousness, and to characterize purposeful, negentropic tendencies at lower stages of the development of matter, it is customary to use other terms.
The considered understanding of the goal is very important in organizing the processes of collective decision-making in control systems.
In real situations, it is necessary to specify in what sense the concept of "goal" is used at this stage of the consideration of the system, which should be reflected to a greater extent in its formulation - ideal aspirations, that will help a team of decision makers see perspectives, or real possibilities, ensuring the timeliness of the completion of the next stage on the way to the desired future.
The analysis of the definitions of the concept of "goal" and the graphical interpretation of the "blurring" of the philosophical interpretations of the goal (see Fig. 1.4) have become an important step towards the practical implementation of goal formation processes.
In later works V. A. Chabrovsky, G. M. Vapne, A. M. Gendina a conception of two different concepts of a goal, which is very useful for practical application, was developed: the "goal of activity" (actual, specific goal) and the infinite in content "goal - aspiration" (goal - ideal, potential goal); the concept of analysis of the process of formulating and structuring goals from the standpoint of dialectical logic is proposed and the idea of the unity of the goal, the means (variant) of achieving it and the evaluation criterion is expressed.
Structure. The system can be represented, as already noted, by a simple enumeration of elements or black box(model "input - output"). However, most often, when studying an object, such a representation is not enough, since it is required to find out what the object is, what in it ensures the fulfillment of the set goal, obtaining the required results. In these cases, the system is displayed by dividing it into subsystems, components, elements with relationships that can be of a different nature, and the concept of "structure" is introduced.
Structure(from lat. "structure", meaning structure, arrangement, order) reflects "certain relationships, the relative position of the components of the system, its device, structure" .
At the same time, in complex systems, the structure does not include all the elements and connections between them (in the limiting case, when they try to apply the concept of structure to simple, completely deterministic objects, the concepts of structure and system coincide), but only the most essential components and connections that change little when the current functioning of the system and ensure the existence of the system and its basic properties. In other words, the structure characterizes the organization of the system, the stable ordering of elements and relationships.
Structural connections are relatively independent of the elements and can act as an invariant in the transition from one system to another, transferring the patterns identified and reflected in the structure of one of them to others. In this case, the systems can have a different physical nature.
One and the same system can be represented by different structures depending on the stage of cognition of objects or processes, on the aspect of their consideration, the purpose of creation. At the same time, as research develops or in the course of designing, the structure of the system may change.
Structures, especially hierarchical ones, as shown below, can help unravel the uncertainty of complex systems. In other words, structural representations of systems are a means of their study.
In this regard, it is useful to identify certain types (classes) of structures and study them, which is discussed in more detail in paragraph 1.3.
- TSB. - 2nd ed. - T. 46. - S. 498.
- TSB. - 2nd ed. - T. 41. - S. 154.
Lecture 2TO.rtf
Lecture 2. System views
Formation of system views .
Concepts characterizing the structure of systems.
System classification .
Properties of the system.
Formation of system views
The concepts of "system" and "systematic" play an important role in modern science and practice. Since the middle of the XX century. intensive developments are underway in the field of a systematic approach to research and systems theory. At the same time, the very concept of a system has a long history. Initially, systemic representations were formed within the framework of philosophy: back in the ancient world, the thesis was formulated that the whole is greater than the sum of its parts. Ancient philosophers (Plato, Aristotle, etc.) interpreted the system as a world order, that systemicity is a property of nature.
The principles of systematicity were actively studied in philosophy (for example, I. Kant sought to substantiate the systematic nature of the process of cognition itself) and in the natural sciences. Our compatriot E. Fedorov at the end of the XIX century. came to the conclusion that nature is systematic in the process of creation crystallography.
The principle of consistency in economics was also formulated by A. Smith, who concluded that the effect of the actions of people organized in a group is greater than the sum of single results.
Various areas of systematic research led to the conclusion that this is a property of nature and a property of human activity (Fig. 2.1).
Rice. 2.1. Consistency as a universal property of matter
Systems theory serves as a methodological basis for control theory. This is a relatively young science, the organizational formation of which took place in the second half of the 20th century. The Austrian scientist L. von Bertalanffy is considered to be the founder of systems theory. The first international symposium on systems was held in London in 1961. The first report was made by the outstanding English cyberneticist S. Veer, which can be considered evidence of the epistemological closeness of cybernetics and systems theory.
The central concept of systems theory is a system (from the Greek systema - "a whole made up of parts"). A system is an object of an arbitrary nature that has a pronounced system property that none of the parts of the system has in any way of its division, a property that is not derived from the properties of the parts.
The above definition of the system cannot be considered exhaustive - it reflects only a certain general approach to the study of objects. In the literature on system analysis, you can find many definitions of the system. (See: for example, Uyomov A.I. System approach and general theory of systems. - M., 1978. See also Appendix 5)
In this manual, we will use the following working definition of a system: "A system is an integral set of interrelated elements that has a certain structure and interacts with the environment in order to achieve a goal." Analyzing this definition, we can identify several basic concepts: integrity, totality, structuredness, interaction with the external environment, the presence of a goal, etc. They represent a system of concepts, i.e., the internal organization of some stable object, the integrity of which is the system. The very possibility of identifying stable objects in the field of study is determined by the property of the integrity of the system, the goals of the observer and his ability to perceive reality.
Let's consider some basic terms and concepts widely used in system research.
^ State of the system - an ordered set of essential properties that it possesses at a certain point in time.
Properties of the system- a set of parameters that determine the behavior of the system.
Behavior systems - the actual or potential operation of the system.
Action- an event occurring with the system, caused by another event.
Event- change at least one property of the system.
Concepts characterizing the structure of systems
Under element It is customary to understand the simplest indivisible part of the system. The concept of indivisibility is associated with the goal of considering an object as a system. Thus, an element is the limit of system division from the point of view of solving a specific problem.
The system can be divided into elements not immediately, but by successive division into subsystems, larger than the elements, but smaller than the system as a whole. The possibility of dividing the system into subsystems is associated with the isolation of a set of elements capable of performing relatively independent functions aimed at achieving the overall goal of the system. For a subsystem, a subgoal should be formulated, which is its system-forming factor.
If the task is not only to isolate the system from the environment and study its behavior, but also to understand its internal structure, it is necessary to study structure systems. The term "structure" comes from the Latin structura - “structure”, “location”, “order”. The structure of the system includes its elements, the links between them and the attributes of these links. In most cases, the concept of "structure" is usually associated with a graphical display, but this is not necessary. The structure can be represented in the form of set-theoretic descriptions, matrices, graphs, etc.
Connection - a concept expressing necessary and sufficient relations between elements. The connection attributes are:
orientation;
force;
character.
By strength of manifestation connections are divided into weak and strong.
By character links are divided into ties of subordination and communications onbirth. The former can be divided into linear and functional; the latter characterize the cause-and-effect relationship.
Relationships between elements are characterized by a certain order, internal properties, and focus on the functioning of the system. Such features of the system are called its organization.
Structural bonds are relatively independent of the elements and can act as an invariant in the transition from one system to another. This means that the regularities revealed in the study of systems representing objects of one nature can be used in the study of systems of another nature. Communication can also be represented and considered as a system that has its own elements and connections.
The concept of "structure" in the narrow sense of the word can be identified with the concept of "system-forming relations", i.e. structure can be considered as a system-forming factor,
In the broad sense of the word, structure is understood as the totality of relations between elements, and not just system-forming relations.
The method of isolating system-forming relations from the environment depends on whether we are talking about designing a system that does not yet exist or about analyzing a systemic representation of a known object, material or ideal. There are different types of structures. The most famous of them are shown in Fig. 2.2.
Rice. 2.2. Types of structures
System classification
Consider first some types of systems. abstract systems are systems all of whose elements are concepts
Specific systems are systems whose elements are physical objects. They are divided into natural(arising and existing without human intervention) and artificial(man-made).
open systems - exchanging matter, energy and information with the external environment.
^ Closed systems are systems that have no exchange with the external environment.
In its pure form, open and closed systems do not exist.
Dynamic systems occupy one of the central places in the general theory of systems. Such a system is a structured object that has inputs and outputs, an object into which, at certain moments, you can enter and from which you can output matter, energy, information. Dynamic systems are presented as systems in which processes proceed continuously in time, and as systems in which all processes occur only at discrete moments of time. Such systems are called discrete dynamical systems. Moreover, in both cases it is assumed that the behavior of the system can be analyzed in a certain period of time, which is directly defined by the term "dynamic".
^ Adaptive Systems - systems operating under conditions of initial uncertainty and changing external conditions. The concept of adaptation was formed in physiology, where it is defined as a set of reactions that ensure the adaptation of the body to changes in internal and external conditions. In the theory of adaptation management, they call the process of accumulation and use of information in a system aimed at achieving an optimal state with initial immediacy and changing external conditions.
^ Hierarchical systems - systems, the elements of which are grouped by levels, vertically correlated with one another; in this case, the elements of the levels have branching outputs. Although the concept of "hierarchy" was constantly present in scientific and everyday life, a detailed theoretical study of hierarchical systems began recently. Considering hierarchical systems, let us turn to the principle of opposition. The object of opposition will be systems with a linear structure (radial, centralized). For systems with centralized control, the unambiguity of control actions is characteristic. Unlike them, there are hierarchical systems, systems of an arbitrary nature (technical, biological, social, and others), which have a multi-level and branched structure in functional, organizational or other terms. Hierarchical systems are the subject of special attention in the theory and practice of management due to their universal nature and a number of advantages compared to, for example, linear structures. Among these advantages: freedom of local influences, no need to pass very large information flows through one control point, increased reliability. In addition, if one element of the centralized system fails, the entire system will also fail; if one element of the hierarchical system fails, the probability of failure of the entire system is negligible. All hierarchical systems have a number of characteristics:
sequential vertical arrangement of levels that make up the system (subsystem);
priority of actions of top-level subsystems (the right to intervene);
the dependence of the actions of the upper-level subsystem on the actual performance by the lower levels of their functions;
relative independence of subsystems, which makes it possible to combine centralized and decentralized management of a complex system.
Let us consider some types of classification of systems according to various criteria.
Classification of systems by origin (Fig. 2.3).
Classification of systems according to the description of variables (Fig. 2.4).
Classification of systems according to the method of control (Fig. 2.5).
Classification of systems according to the type of their operators (Fig. 2.6).
In addition to the considered classifications of systems, they can be divided into simple and complex, deterministic and probabilistic, linear and non-linear, etc.
System Properties
Analysis of the working definition of the system allows us to highlight some of its general properties:
any system is a complex of interrelated elements;
the system forms a special unity with the external environment;
any system is an element of a system of a higher order;
the elements that make up the system, in turn, act as systems of a lower order.
Element B, which serves as an element of system A, in turn, is a lower-level system that consists of its own elements, including, for example, element C. And if we consider element B as a system interacting with the external environment, then the latter in In this case, it will represent system B (an element of system A). Therefore, the feature of the unity of the system with the external environment can be interpreted as the interaction of elements of the system of a higher order. Similar reasoning can be carried out for any element of any system.
The study of the properties of the system involves, first of all, the study of the relationship of parts and the whole. This means that:
1) the whole is primary, and the parts are secondary;
2) system-forming factors are the conditions for the interconnection of parts within one system;
3) parts of the system form an inseparable whole, so the impact on any of them affects the entire system;
4) each part of the system has its own purpose in terms of the goal towards which the activity of the whole is directed;
5) the nature of the parts and their functions are determined by the position of the parts as a whole, and their behavior is regulated by the relationship of the whole and its parts;
6) the whole behaves like a single entity, regardless of the degree of complexity.
From the whole variety of properties of systems for the study of organizational processes, it is advisable first of all to single out such properties as emergence, equifinality and homeostasis.
emergence is one of the most essential properties of systems. This is the irreducibility of the properties of the system to the properties of its elements; in other words, emergence is the presence of new qualities of the whole that are absent from its constituent parts. Thus, the properties of the whole are not a simple sum of the properties of its constituent elements, although they depend on them. At the same time, the elements integrated into the system may lose the properties inherent in them outside the system, or acquire new ones.
equifinality- one of the least studied properties of the system, characterizing the limiting capabilities of systems of a certain class of complexity. L. von Bertalanffy, who proposed this term, defined equifinality in relation to an open system as the ability of a system (in contrast to the equilibrium states in closed systems, completely determined by the initial conditions) to achieve a state independent of time and initial conditions, which is determined solely by the parameters of the system. The need to introduce this concept arises starting from a certain level of system complexity. equifinality- the internal predisposition of the system to achieve a certain limiting state, independent of external conditions. Idea equifinality consists in studying the parameters that determine a certain limiting level of organization.
The organization, being a holistic entity, always strives to reproduce itself, restore the lost balance, overcome resistance, in particular the external environment. This property of an organization is called homeostasis.
In the most general and broadest sense of the word, a systematic study of objects and phenomena of the world around us is understood as a method in which they are considered as parts or elements of a single, holistic education. These parts or elements, interacting, determine new properties of the system that are absent from its individual elements. With this understanding of the system, we constantly met in the course of presenting all the previous material. However, it is applicable only to characterize systems consisting of homogeneous parts with a well-defined structure. Nevertheless, in practice, systems are often also referred to as sets of heterogeneous objects combined into a single whole to achieve a specific goal.
The main thing that defines the system is the interconnection and interaction of parts within the framework of the whole. If such an interaction exists, then it is permissible to speak of a system, although the degree of interaction of its parts may be different. You should also pay attention to the fact that each individual object, object or phenomenon can be considered as a certain integrity, consisting of parts, and, therefore, explored as a system.
The concept of a system and the system method as a whole were formed gradually, as science and practice mastered different types, types and forms of interaction and association of objects and phenomena. Now we have to get acquainted in more detail with various attempts to clarify both the very concept of a system and the formation of a system method.
18.1. The formation of a systematic research method
The roots of a systematic approach to the study of the surrounding world go back to ancient times. In an implicit form, it was widely used in an-
science, although the term "system" itself appeared much later. The ancient Greeks considered nature and the world as a whole, in which objects, phenomena and events are connected by many different connections. The basis of such unity among the early Greek philosophers is a certain material principle: water for Thales, air for Anaximenes, and fire for Heraclitus. However, this idea, which is true in general, was not revealed in the concrete connections of phenomena and processes, and was not proved in particular. This is quite understandable, because the ancient Greeks did not have specific sciences, and everything that could be called positive knowledge, along with natural-philosophical speculations, was part of an undifferentiated philosophy. The only exception was mathematics, in which they created the famous axiomatic method of constructing knowledge, which still serves as the most important means of logical systematization and substantiation of not only mathematical, but any knowledge in general.
With the transition to the experimental study of nature and the emergence of experimental natural science in the 17th century. there is a division of knowledge into separate areas of nature, groups of phenomena, branches and scientific disciplines. A disciplinary method of building and developing scientific knowledge begins, when each science carefully and thoroughly studies its subject, using specific research methods, without being interested in either the goals and objectives or the methods of cognition of other sciences. Such an approach, as noted already in Chapter 1, had certain advantages, but at the same time limited the possibilities of researchers to the narrow boundaries of their discipline and thus prevented the establishment of links between other disciplines. As a result, a single nature was artificially divided among the disparate sciences.
Despite this, the differentiation of science continued to grow, the number of individual scientific disciplines increased more and more, and, accordingly, the ties and mutual understanding of scientists weakened. Over time, this situation became more and more intolerable, and despite the resistance of certain groups of scientists, integrative, interdisciplinary methods and theories arose, with the help of which, using general concepts and principles, the problems that were put forward before the sciences that studied the interconnected processes and forms of the movement of matter, and then more general theories. So, in the late XIX - early XX century. biophysics and biochemistry, geophysics and geochemistry, chemical physics and physical chemistry, and others arose.
The real breakthrough in systems research occurred after the end of World War II, when a powerful system
a new movement that contributed to the introduction of ideas, principles and methods of systematic research not only in the natural sciences, but also in the socio-economic and human sciences. It was the systems approach that contributed to the fact that each science began to consider as its subject the study of systems of a certain type that are in interaction with other systems. According to the new approach, the world appeared as a huge set of systems of the most diverse concrete content and generality, united into a single whole - the Universe.
18.2. Specificity of the system research method
The above intuitive definition of a system is sufficient to distinguish systems from such collections of objects and phenomena that are not systems. There is no special term for them in our literature. Therefore, we will denote them by the term borrowed from the English literature aggregates. It is unlikely that anyone would call a bunch of stones a system, while a physical body consisting of a large number of interacting molecules, or a chemical compound formed from several elements, and even more so a living organism, population, species and other communities of living beings, everyone will intuitively consider a system.
What are we guided by when classifying some sets of objects as systems, and others as aggregates? Obviously, in the first case, we notice a certain integrity, the unity of the elements that make up the system, and in the second, such unity and interconnection are absent, and therefore we should talk about a simple set, or aggregate, of elements.
Thus, the systemic approach is characterized by a holistic consideration, the establishment of the interaction of the constituent parts or elements of the totality, the irreducibility of the properties of the whole to the properties of the parts.
Throughout the presentation, we have met with numerous physical, chemical, biological and ecological systems, the properties of which cannot be explained by the properties of their elements. In contrast, the properties of simple collections, or aggregates, arise from the summation of the properties of their constituent parts. Thus, for example, the length of a body consisting of several parts, or its weight, can be found by summing, respectively, the lengths and weights of its parts. In contrast, the temperature of water obtained by mixing its different volumes heated to different degrees
souls cannot be calculated in this way. It is often said, therefore, that if the properties of simple collections additive those. are summarized or made up of the properties or magnitudes of their parts, then the properties of systems as integral formations are non-additive.
However, it should be noted that the difference between systems and aggregates, or simply collections of objects, is not absolute, but relative character and depends on how the population is approached to study. After all, even a bunch of stones can be considered as some kind of system, the elements of which interact according to the law of universal gravitation. Nevertheless, here we do not find the emergence of new integral properties that are inherent in real systems. This distinctive feature of systems, which consists in the presence of new integrative, integral properties that arise as a result of the interaction of their constituent parts or elements, should always be borne in mind when defining systems.
In recent years, many attempts have been made to give a logical definition to the concept of a system. Since the typical way in logic is the definition through the nearest genus and specific difference, the most general concepts of mathematics and even philosophy were usually chosen as the generic concept. In modern mathematics, such a concept is the concept of a set, introduced at the end of the last century by the German mathematician G. Kantor (1845-1918) to denote any set of mathematical objects that have some common property. Therefore, R. Fagin and A. Hall used the concept of a set to logically define a system.
"A system," they write, "is a set of objects together with relationships between objects and between their attributes (properties)."
Such a definition cannot be called correct, if only because the most diverse collections of objects can be called sets, and for many of them it is possible to establish certain relationships between objects, so that the specific difference for systems (differentia specified) not specified. The point, however, is not so much in the formal incorrectness of the definition, but in its substantive inconsistency with reality. Indeed, it does not note that the objects that make up the system interact in such a way that they cause the emergence of new, integral, system properties. Apparently, such an extremely broad concept as a system cannot be defined purely logically through other existing concepts. Therefore, it should be recognized as the original and undefined concept, the content of which can be explained using the
ditch. This is exactly what is usually done in science when one has to deal with its original, initial concepts, for example, with a set in mathematics or mass and charge in physics.
For a better understanding of the nature of systems, it is necessary to consider first their structure and structure, and then their classification.
System structure characterized by the components from which it is formed. Such components are: subsystems, parts or elements of the system, depending on what is taken as the basis for division.
Subsystems constitute parts of the system that have a certain autonomy, but at the same time they are subordinate to the system and controlled by it. Usually subsystems are allocated in a special way organized systems, which are called hierarchical.
Elements usually called the smallest units of the system, although in principle any part can be considered as an element, if we ignore its size.
A typical example is the human body, which consists of the nervous, respiratory, digestive, and other subsystems, often referred to simply as systems. In turn, subsystems contain in their composition certain organs, which consist of tissues, and tissues - from cells, and cells - from molecules. Many living and social systems are built on the same hierarchical principle, where each level of organization, having a certain autonomy, is at the same time subordinate to the previous, higher level. Such a close relationship and interaction of various components provide the system as a holistic, unified education with the best conditions for existence and development.
Structure systems are the totality of those specific relationships and interactions, due to which new integral properties arise that are inherent only in the system and are absent from its individual components. In Western literature, such properties are called emergent, or arising as a result of interaction and inherent only in the system. Depending on the specific nature of the interaction of components, different types of systems are distinguished: electromagnetic, atomic, nuclear, chemical, biological and social. Within the framework of these types, it is possible, in turn, to consider individual types of systems.
In principle, each individual object can be approached from a systemic point of view, since it represents a certain holistic formation capable of independent existence. So, for example, a water molecule formed from two water atoms
of hydrogen and one oxygen atom, is a system, the components of which are interconnected by the forces of electromagnetic interaction. The whole world around us, its objects, phenomena and processes turn out to be a combination of the most diverse systems in terms of their specific nature and level of organization. Every system in this world interacts with other systems.
The system and its environment. For a more thorough study, those systems are usually singled out with which the given system interacts directly and which are called environment or external environment systems. All real systems in nature and society are, as already mentioned, open and, therefore, interacting with the environment through the exchange of matter, energy and information. The concept of a closed or isolated system is a far-reaching abstraction that does not adequately reflect reality, since no real system can be isolated from the influence of other systems that make up its environment. In inorganic nature, open systems can exchange either matter with the environment, as happens in chemical reactions, or energy, when the system receives fresh energy from the environment and dissipates “waste” energy in it in the form of heat. In living nature, systems exchange with the environment, in addition to matter and energy, also information, through which control and transmission of hereditary traits from organisms to descendants takes place. Of particular importance is the exchange of information in socio-economic and cultural-humanitarian systems, where such an exchange serves as the basis for all communicative activities of people.
System classification can be done for a variety of reasons. First of all, all systems can be divided into systems material and ideal or conceptual. Material systems include the overwhelming majority of systems of inorganic, organic and social character. All material systems, in turn, can be divided into basic classes according to the form matter movement, which they represent. In this regard, one usually distinguishes between gravitational, physical, chemical, biological, geological, ecological and social systems. Among the material systems, there are also artificial, technical and technological systems specially created by society that serve to produce material goods.
All these systems are called material or objective because their content and properties do not depend on the cognizing subject. However, the subject can get to know them deeper, more fully and more accurately.
properties and regularities with the help of the conceptual systems he creates. Such systems are called ideal precisely because they represent a reflection of material, objectively existing systems in nature and society.
The most typical example of a conceptual system is a scientific theory, which expresses, with the help of its concepts, generalizations and laws, objective, real connections and relationships that exist in specific natural and social systems.
The systemic nature of a scientific theory is expressed in its very construction, when its individual concepts and judgments are not simply listed, but are combined within a certain integral structure. For these purposes, several basic, or initial, concepts are usually singled out, on the basis of which, first, other, derivative, or secondary, concepts are determined according to the rules of logic. Similarly, among all the judgments of the theory, some initial or basic judgments are selected, which in mathematical theories are called axioms, and in natural science theories - laws or principles. So, for example, in classical mechanics such basic judgments are the three basic laws of mechanics, in the special theory of relativity - the principles of constancy of the speed of light and relativity. In mathematical theories of physics, the corresponding laws are often expressed using systems of equations, as done by J.K. Maxwell in his theory of electromagnetism. In biological and social theories, one usually confines oneself to verbal formulations of laws. On the example of Charles Darwin's evolutionary theory, we have seen that its main content can be expressed using three basic principles or even the only principle of natural selection.
All our knowledge, not only in the field of science, but also in other areas of activity, we strive to systematize in a certain way, so that the logical interconnection of individual judgments, as well as the entire structure of knowledge as a whole, becomes clear. A separate, isolated judgment is not of particular interest to science. Only when it can be logically connected with other elements of knowledge, in particular with the judgments of the theory, does it acquire a certain meaning and significance. Therefore, the most important function of scientific knowledge is precisely in systematization of all accumulated knowledge, in which individual judgments expressing knowledge about specific facts are combined within a certain conceptual system.
Other classifications, as the basis for division, consider signs that characterize the state of the system, its behavior,
interaction with the environment, purposefulness and predictability of behavior and other properties.
The simplest classification is the division of systems into static and dynamic, which to a certain extent is conditional, since everything in the world is in constant change and movement. Since, however, even in mechanics we distinguish between statics and dynamics, it seems expedient to consider specifically also static systems.
Among dynamical systems, one usually singles out deterministic and stochastic systems. Such a classification is based on the nature of predicting the dynamics or behavior of systems. As noted in previous chapters, predictions based on the study of the behavior of deterministic systems are quite unambiguous and reliable. Such systems are the dynamical systems studied in classical mechanics and astronomy. In contrast, stochastic systems, which are most often called probabilistic-statistical systems, deal with massive or repetitive random events and phenomena. Therefore, the predictions in them, as noted in previous chapters, are not reliable, but only probabilistic.
According to the nature of interaction with the environment, systems are distinguished, as we already know, open and closed (isolated), and sometimes allocate partially open systems. Such a classification is basically conditional, because the concept of closed systems arose in classical thermodynamics as a certain abstraction that turned out to be inconsistent with objective reality, in which the vast majority of systems, if not all of them, are open.
Many complex systems found in the social world are targeted those. focused on achieving one or more goals, and in different subsystems and at different levels of the organization, these goals can be different and even come into conflict with each other.
The classification of systems makes it possible to consider the set of systems existing in science retrospectively, i.e. retroactively, and therefore does not represent for the researcher such interest, as the study of the method and prospects of a systematic approach in the specific conditions of its application.
18.3. Method and perspectives of systemic research
In an implicit form, the systems approach in its simplest form has been used in science from the very beginning of its inception. Even when individual sciences were engaged in the accumulation and generalization of the original factual material, the idea of systematization and unity underlay all searches for new facts and bringing them into a single system of scientific knowledge.
However, the emergence of the system method as a special method of research is attributed by many to the time of the Second World War and the ensuing peace period. During the war, scientists were faced with problems of a complex nature, which require taking into account the relationship and interaction of many factors within the framework of the whole. Such problems included, in particular, the planning and conduct of military operations, issues of supply and organization of the army, decision-making in difficult conditions, etc. On this basis, one of the first systemic disciplines arose, called operations research. The application of systemic ideas to the analysis of economic and social processes contributed to the emergence game theory and decision theory.
Perhaps the most significant step in the formation of the ideas of the systems method was the appearance cybernetics as a general theory of control in technical systems, living organisms and society. It most clearly shows a new approach to the study of control systems that differ in specific content. Although separate control theories existed in technology, biology, and social sciences, nevertheless, a unified, interdisciplinary approach made it possible to reveal deeper and more general patterns of control, which were obscured by a mass of minor details in a specific study of private control systems. Within the framework of cybernetics, it was clearly shown for the first time that the management process from the most general point of view can be considered as a process of accumulation, transfer and transformation information. The control itself can be displayed using a specific sequence algorithms or precise prescriptions through which the achievement of the goal is carried out. Shortly thereafter, algorithms were used to solve various other problems of a mass nature, for example, traffic control, technological processes in metallurgy and mechanical engineering, organization of product distribution, traffic control, and numerous similar processes.
The advent of high-speed computers was the necessary technical base with which it was possible to process
typify various algorithmically described processes. Algorithmization and computerization of a whole range of production, technical, managerial and other processes was, as is known, one of the constituent elements of the modern scientific and technological revolution, which linked together new achievements in science with the results of the development of technology.
In order to better understand the essence of the system method, it is necessary to note from the very beginning that the concepts, theories and models on which it is based are applicable to the study of objects and phenomena of the most specific various content. For these purposes, it is necessary to abstract, digress from the specific content of individual, particular systems and identify the general, essential that is inherent in all systems of a certain kind.
The most common way to achieve this goal is mathematical modeling. With the help of a mathematical model, the most significant quantitative and structural relationships between the elements of some related systems are displayed. Then this model is calculated on a computer and the calculation results are compared with observational and experimental data. The discrepancies that arise are eliminated by making additions and changes to the original model.
Appeal to mathematical models is dictated by the very nature of system research, in the process of which one has to deal with the most general properties and relationships of various specific, particular systems. Unlike the traditional approach, which operates on two or more variables, the system method involves the analysis of a whole set of variables. The connection between these numerous variables, expressed in the language of various equations and their systems, is a mathematical model. This model is first put forward as a hypothesis, which must be further verified with the help of experience.
Obviously, before constructing a mathematical model of any system, it is necessary to identify the general qualitatively homogeneous, which is inherent in different types of systems of the same type. Until the systems are studied at a qualitative level, there can be no question of any quantitative mathematical model. Indeed, in order to express any dependencies in mathematical form, it is necessary to find homogeneous properties for different specific systems of objects and phenomena, for example, dimensions, volume, weight, etc. Using the chosen unit of measurement, these properties can be represented as numbers and then the relationship between the properties can be expressed as a dependency.
bridges between the mathematical equations and functions that represent them. The construction of a mathematical model has a significant advantage over simply describing systems in qualitative terms because it makes it possible to make accurate predictions about the behavior of systems that are much easier to test than highly uncertain and general qualitative predictions. Thus, in the mathematical modeling of systems, the effectiveness of the unity of qualitative and quantitative research methods, which characterizes the main path of development of modern scientific knowledge, is most clearly manifested.
Let us now turn to the question of advantages and prospects of the system method research.
First of all, we note that the emergence of the systemic method itself and its application in natural science and other sciences mark a significantly increased maturity of the current stage of their development. Before science could move on to this stage, it had to explore the individual aspects, features, properties and relationships of certain objects and phenomena, to study the parts in abstraction from the whole, the simple separated from the complex. Such a period, as noted in Chapter 1, corresponded to a disciplinary approach, when each science focused all attention on the study of the specific laws of the range of phenomena it studied. Over time, it became obvious that such an approach does not make it possible to reveal the deeper patterns inherent in a wide class of interrelated phenomena, not to mention the fact that it leaves in the shadow the relationship of different classes of phenomena, each of which was the subject of a separate study of a separate science.
Interdisciplinary The approach, which replaced the disciplinary one, has been increasingly used to establish patterns inherent in different areas of phenomena, and has been further developed in various forms of system research both in the process of its formation and in specific applications.
The systemic method has gone through different stages, which is reflected in the very terminology, which, unfortunately, is not distinguished by unity. From the point of view of practical significance, we can distinguish:
system engineering, engaged in research, design and construction of the latest technical systems, which take into account not only the operation of mechanisms, but also the actions of a person - the operator who controls them. This direction develops some principles of organization and self-organization, identified by cybernetics, and is currently becoming increasingly important in
connection with the introduction of human-machine systems, including computers operating in a dialogue mode with the researcher;
system analysis, which deals with the study of complex and multilevel systems. Although such systems usually consist of elements of a heterogeneous nature, they are connected and interact with each other in a certain way and therefore require a holistic, systemic analysis. These include, for example, the organization system of a modern factory or plant, in which production, supply of raw materials, marketing of goods and infrastructure are combined into a single whole;
systems theory, which studies the specific properties of systems consisting of objects of a single nature, such as physical, chemical, biological and social systems.
If systems engineering and systems analysis are actually applications of some system ideas in the field of organization of production, transport, technology and other sectors of the national economy, then systems theory explores the general properties of systems studied in the natural, technical, socio-economic and human sciences.
The question may arise: if the specific properties of the systems mentioned above are studied in separate sciences, then why is a special system method needed? In order to answer it correctly, it is necessary to state clearly what exactly the particular sciences and systems theory study when applied to the same field of phenomena. If it is important for a physicist, biologist or sociologist to reveal specific, specific connections and patterns of the systems under study, then the task of the systems theorist is to identify the most general properties and relationships of such systems, to show how the general principles of the system method are manifested in them. In other words, with a systems approach, each specific system acts as a special case of the general theory of systems.
Speaking about the general theory of systems, one should be aware of the nature of its generality. The point is that in recent years there have been many projects for the construction of such general theories, the principles and statements of which claim to be universal. One of the initiators of the creation of such a theory, L. von Bertalanffy, who made a significant contribution to the dissemination of systemic ideas, formulates its tasks as follows: “The subject of this theory is the establishment and derivation of those principles that are valid for“ systems ”in general ... We can ask the question of principles applicable to systems in general, regardless of their physical, biological or social nature. If we pose such a problem and define the concept of a system in an appropriate way, we will find that there are models that
principles and laws that apply to generalized systems regardless of their particular form, elements or "forces" that compose them.
The question is, what character should such a not just general, but, in fact, universal theory of systems have? Obviously, in order to be applicable anywhere and everywhere, such a theory must be abstracted from any specific, private and special properties of individual systems. But in this case, from its concepts and principles it is impossible to logically deduce the specific properties of individual systems, as advocates of a general, or, one might say, universal, theory insist on this. Another thing is that some general system concepts and principles can be used to better understand and explain specific systems.
The fundamental role of the system method is that it achieves the most complete expression unity scientific knowledge. This unity is manifested, on the one hand, in the interconnection of various scientific disciplines, which is expressed in the emergence of new disciplines at the "junction" of old ones (physical chemistry, chemical physics, biophysics, biochemistry, biogeochemistry, etc.), in the emergence of interdisciplinary areas of research (cybernetics, synergetics, environmental programs, etc.). On the other hand, a systematic approach makes it possible to identify unity and interrelationships within individual scientific disciplines. As noted above, the properties and patterns of real systems in nature are reflected primarily in the scientific theories of individual disciplines of natural science. These theories, in turn, are connected with each other within the framework of the respective disciplines, and the latter constitute natural science as the doctrine of nature as a whole. So, the unity that is revealed in a systematic approach to science lies primarily in the establishment of connections and relationships between the most diverse in complexity of organization, level of knowledge and integrity of coverage of conceptual systems, with the help of which the growth and development of our knowledge about nature is displayed. The more extensive the system under consideration, the more complex it is in terms of the level of knowledge, hierarchical organization, the greater the range of phenomena it is able to explain. Thus, the unity of knowledge is directly dependent on its consistency.
From the standpoint of systemicity, unity and integrity of scientific knowledge, it becomes possible to correctly approach the solution of such problems as reduction, or reduction of some theories of natural science to others, synthesis, or unification of theories that seem far from each other, their confirmation and refutation by observational and experimental data.
Reduction, or the reduction of some theories to others, is a completely acceptable theoretical procedure, because it expresses a tendency to establish the unity of scientific knowledge. When Newton created his mechanics and the theory of gravitation, he thereby demonstrated the unity of the laws of motion of terrestrial and celestial bodies. Similarly, the use of spectral analysis to establish the unity of chemical elements in the structure of celestial bodies was a major achievement in physics. In our time, the reduction of certain properties and regularities of biological systems to physical and chemical properties has become the basis for landmark discoveries in the field of the study of heredity, the synthesis of protein bodies, and evolution.
However, reduction is acceptable and effective only when it is used to explain phenomena and systems of the same type in terms of content. Indeed, when Newton managed to reduce the laws of motion of celestial mechanics to the laws of terrestrial mechanics and establish unity between them, it turned out to be possible only because they describe the same type of processes of mechanical motion of bodies. The more some processes differ from others, the more qualitatively they are heterogeneous, the more difficult it is to reduce them. Therefore, the laws of more complex systems and forms of motion cannot be completely reduced to the laws of lower forms or simpler systems. Discussing the concept of atomism, we were convinced that, despite the huge success in explaining the properties of complex substances through the simple properties of their constituent atoms, this concept has certain limits. After all, the general, integral properties of systems are not reduced to the sum of the properties of their components, but arise as a result of their interaction. Such a new, systematic approach radically undermines the idea of the former natural-science picture of the world, when nature was considered as a simple set of various processes and phenomena, and not closely interconnected and interacting systems, different both in terms of organization level and in their complexity.
18.4. System method and modern scientific outlook
The widespread dissemination of ideas and principles of the systemic method contributed to the emergence of a number of new problems of an ideological nature. Moreover, some Western leaders of the systems approach began to consider it as a new scientific philosophy, which, in contrast to the previously dominant philosophy of positivism, which emphasized the priority analysis and reduction, the main emphasis is on
synthesis and anti-reductionism. In this regard, the old philosophical problem of the ratio parts and the whole.
Many supporters of mechanism and physicalism argue that the parts play a decisive role in this relationship, since it is from them that the whole arises. But at the same time, they ignore the indisputable fact that, within the framework of the whole, the parts not only interact with each other, but also experience the action of the whole. Trying to understand the whole by analysis parts fails precisely because it ignores synthesis, which plays a decisive role in the emergence of each system. Any complex substance or chemical compound differs in its properties from the properties of its constituent simple substances or elements. Each atom has properties that are different from the properties of its constituent elementary particles. In short, any system is characterized by special holistic, integral properties that are absent from its components.
The opposite approach, based on the priority of the whole over the part, has not received wide distribution in science because it cannot rationally explain the process of the emergence of the whole. Often, therefore, his supporters resorted to the assumption of irrational forces, such as entelechy, vital force, and so on. In philosophy, such views are defended by supporters holism(from Greek - whole), who believe that the whole always precedes the parts and is always more important than the parts. When applied to social systems, such principles justify the suppression of the individual by society, ignoring its desire for freedom and independence.
At first glance, it may seem that the concept of holism about the priority of the whole over the part is consistent with the principles of the system method, which also emphasizes the great importance of the ideas of integrity, integration and unity in the knowledge of the phenomena and processes of nature and society. But on closer examination, it turns out that holism exaggerates the role of the whole in comparison with the part, the importance of synthesis in relation to analysis. Therefore, it is the same one-sided concept as atomism and reductionism.
The systems approach avoids these extremes in the knowledge of the world. He proceeds from the fact that the system as a whole does not arise in some mystical and irrational way, but as a result of a specific, specific interaction of quite specific real parts. It is due to this interaction of parts that new integral properties of the system are formed. But the newly emerged integrity, in turn, begins to influence the parts, subordinating their functioning to the tasks and goals of a single, holistic
systems. We noted that not every collection or whole forms a system, and in this connection we introduced the concept of an aggregate. But any system is a whole formed by its interconnected and interacting parts. Thus, the process of cognition of natural and social systems can be successful only when the parts and the whole in them are studied not in opposition, but in interaction with each other, the analysis will be accompanied by synthesis.
Basic concepts and questions
Aggregate Set
Additivity Subsystem
External environment System
Determinism Systems Analysis
Hierarchy Systems Engineering
Stochastic Information
Mathematical Modeling Structure
1. What is the specificity of system research?
2. What is the difference between a system and a unit?
3. What is the difference between the structure and structure of the system?
4. What is the basis for the application of mathematics in systems research?
5. What are the advantages of a systematic research method?
6. Can the system method be applied to a single subject?
7. What is the difference between systems engineering and systems analysis?
8. Is it possible to construct a universal systems theory?
9. How does a systems approach differ from reductionism and holism?
10. What is the ideological significance of the system method?
Literature
Main:
Blauberg I.V., Yudin E.G. Formation and essence of the system approach. M., 1973.
Ruzavin G.I. System approach and unity of scientific knowledge // Unity of scientific knowledge. M., 1988. S. 237-252.
Philosophy of Science. Modern philosophical problems of areas of scientific knowledge. M., 2005.
Additional:
System Research. Methodological problems: Yearbook. M., 1982.
Philosophy: Encyclopedic Dictionary / Ed. A.A. Ivin. M., 2004.
Iskander Khabibrakhmanov wrote material on the theory of systems, the principles of behavior in them, relationships and examples of self-organization for the “Games Market” column.
We live in a complex world and do not always understand what is happening around. We see people who become successful without deserving it and those who are really worthy of success, but remain in obscurity. We are not sure about tomorrow, we are closing more and more.
To explain things we don't understand, we invented shamans and fortune-tellers, legends and myths, universities, schools and online courses, but it didn't seem to help. When we were in school, we were shown the picture below and asked what would happen if we pulled a string.
Over time, most of us have learned to give the correct answer to this question. However, then we went out into the open world, and our tasks began to look like this:
This led to frustration and apathy. We have become like the wise men in the parable of the elephant, each of whom sees only a small part of the picture and cannot draw a correct conclusion about the object. Each of us has our own misunderstanding of the world, it is difficult for us to communicate it with each other, and this makes us even more alone.
The fact is that we live in the age of a double paradigm shift. On the one hand, we are moving away from the mechanistic paradigm of society inherited from the industrial age. We understand that inputs, outputs and capacities do not explain the diversity of the world around us, and often it is much more influenced by the socio-cultural aspects of society.
On the other hand, a huge amount of information and globalization lead to the fact that instead of an analytical analysis of independent quantities, we must study interdependent objects, indivisible into separate components.
It seems that our survival depends on the ability to work with these paradigms, and for this we need a tool, just as we once needed tools for hunting and tilling the land.
One such tool is systems theory. Below there will be examples from systems theory and its general provisions, there will be more questions than answers and, hopefully, there will be some inspiration to learn more about it.
Systems theory
Systems theory is a fairly young science at the junction of a large number of fundamental and applied sciences. This is a kind of biology from mathematics, which deals with the description and explanation of the behavior of certain systems and the commonality between this behavior.
There are many definitions of the concept of a system, here is one of them. System - a set of elements that are in relationships, which forms a certain integrity of structure, function and processes.
Depending on the objectives of the research, the systems are classified:
- by the presence of interaction with the outside world - open and closed;
- by the number of elements and the complexity of the interaction between them - simple and complex;
- if possible, observations of the entire system - small and large;
- by the presence of an element of randomness - deterministic and non-deterministic;
- by the presence of goals in the system - casual and purposeful;
- according to the level of organization - diffuse (random walks), organized (the presence of a structure) and adaptive (the structure adapts to external changes).
Also, systems have special states, the study of which gives an understanding of the behavior of the system.
- sustainable focus. With small deviations, the system returns to its original state again. An example is a pendulum.
- Unstable focus. A small deviation brings the system out of equilibrium. An example is a cone placed with a point on a table.
- Cycle. Some states of the system are cyclically repeated. An example is the history of different countries.
- Complex behavior. The behavior of the system has a structure, but it is so complex that it is not possible to predict the future state of the system. An example is stock prices on the stock exchange.
- Chaos. The system is completely chaotic, there is no structure in its behavior.
Often when working with systems, we want to make them better. Therefore, we need to ask ourselves the question in what special state we want to bring it. Ideally, if the new state of interest to us is a stable focus, then we can be sure that if we achieve success, then it will not disappear the next day.
Complex systems
We are increasingly seeing complex systems around us. Here I did not find sounding terms in Russian, so I have to speak in English. There are two fundamentally different concepts of complexity.
The first (complicatedness) - means some complexity of the device, which is applied to fancy mechanisms. This kind of complexity often makes the system unstable to the slightest changes in the environment. So, if one of the machines stops at the plant, it can disable the entire process.
The second (complexity) - means the complexity of behavior, for example, biological and economic systems (or their emulations). On the contrary, this behavior persists even with some changes in the environment or the state of the system itself. So, when a major player leaves the market, the players will share his share less among themselves, and the situation will stabilize.
Often complex systems have properties that can lead the uninitiated into apathy, and make working with them difficult and intuitive. These properties are:
- simple rules for complex behavior,
- butterfly effect or deterministic chaos,
- emergence.
Simple rules for complex behavior
We are used to the fact that if something exhibits complex behavior, then it is most likely complex internally. Therefore, we see patterns in random events and try to explain things that are incomprehensible to us by the machinations of evil forces.
However, this is not always the case. A classic example of a simple internal structure and complex external behavior is the game "Life". It consists of a few simple rules:
- the universe is a checkered plane, there is an initial arrangement of living cells.
- at the next moment of time, a living cell lives if it has two or three neighbors;
- otherwise it dies of loneliness or overpopulation;
- in an empty cell, next to which there are exactly three living cells, life is born.
In general, writing a program that will implement these rules will require five to six lines of code.
At the same time, this system can produce quite complex and beautiful patterns of behavior, so without seeing the rules themselves it is difficult to guess them. And it's certainly hard to believe that this is implemented in a few lines of code. Perhaps the real world is also built on a few simple laws that we have not yet deduced, and the entire boundless variety is generated by this set of axioms.
Butterfly Effect
In 1814, Pierre-Simon Laplace proposed a thought experiment, which consisted in the existence of an intelligent being capable of perceiving the position and speed of every particle of the universe and knowing all the laws of the world. The question was the theoretical ability of such a being to predict the future of the universe.
This experiment caused a lot of controversy in scientific circles. Scientists, inspired by progress in computational mathematics, tended to answer yes to this question.
Yes, we know that the principle of quantum uncertainty excludes the existence of such a demon even in theory, and predicting the position of all particles in the world is fundamentally impossible. But is it possible in simpler deterministic systems?
Indeed, if we know the state of the system and the rules by which they change, what prevents us from calculating the next state? Our only problem might be a limited amount of memory (we can store numbers with limited precision), but all calculations in the world work this way, so this should not be a problem.
Not really.
In 1960, Edward Lorenz created a simplified weather model, consisting of several parameters (temperature, wind speed, pressure) and the laws by which the state at the next time is obtained from the current state, representing a set of differential equations.
dt = 0.001
x0 = 3.051522
y0 = 1.582542
z0 = 15.623880
xn+1 = xn + a(-xn + yn)dt
yn+1 = yn + (bxn - yn - znxn)dt
zn+1 = zn + (-czn + xnyn)dt
He calculated the values of the parameters, displayed them on the monitor and built graphs. It turned out something like this (graph for one variable):
After that, Lorentz decided to rebuild the graph, taking some intermediate point. It is logical that the graph would have turned out exactly the same, since the initial state and the transition rules have not changed in any way. However, when he did, something unexpected happened. In the graph below, the blue line represents the new set of parameters.
That is, at first both graphs go very close, there are almost no differences, but then the new trajectory moves further and further away from the old one, starting to behave differently.
As it turned out, the reason for the paradox lay in the fact that in the computer's memory all data was stored with an accuracy of up to the sixth decimal place, and was displayed with an accuracy of up to the third. That is, a microscopic change in the parameter led to a huge difference in the trajectories of the system.
It was the first deterministic system to have this property. Edward Lorenz gave it the name The Butterfly Effect.
This example shows us that sometimes events that seem unimportant to us end up having a huge impact on outcomes. The behavior of such systems is impossible to predict, but they are not chaotic in the truest sense of the word, because they are deterministic.
Moreover, the trajectories of this system have a structure. In three-dimensional space, the set of all trajectories looks like this:
What is symbolic, it looks like a butterfly.
emergence
Thomas Schelling, an American economist, looked at maps of the distribution of racial classes in various American cities, and observed the following pattern:
This is a map of Chicago, and here the places where people of different nationalities live are shown in different colors. That is, in Chicago, as in other cities in America, there is a fairly strong racial segregation.
What conclusions can we draw from this? The first thing that comes to mind is: people are intolerant, people do not accept and do not want to live with people who are different from them. But is it?
Thomas Schelling proposed the following model. Imagine a city in the form of a checkered square, people of two colors (red and blue) live in the cells.
Then almost every person from this city has 8 neighbors. It looks something like this:
Moreover, if a person has less than 25% of neighbors of the same color, then he randomly moves to another cell. And so it continues until each resident is satisfied with his situation. The inhabitants of this city cannot be called intolerant at all, because they only need 25% of people like them. In our world, they would be called saints, a real example of tolerance.
However, if we start the process of moving, then from the random location of the inhabitants above, we will get the following picture:
That is, we get a racially segregated city. If, instead of 25%, each resident wants at least half of the neighbors like him, then we will get almost complete segregation.
At the same time, this model does not take into account such things as the presence of local temples, shops with national utensils, and so on, which also increase segregation.
We are accustomed to explaining the properties of a system by the properties of its elements and vice versa. However, for complex systems, this often leads us to incorrect conclusions, because, as we have seen, the behavior of the system at the micro and macro levels can be opposite. Therefore, often going down to the micro level, we try to do the best, but it turns out as always.
This property of a system, when the whole cannot be explained by the sum of its elements, is called emergence.
Self-organization and adaptive systems
Perhaps the most interesting subclass of complex systems are adaptive systems, or systems capable of self-organization.
Self-organization means that the system changes its behavior and state, depending on changes in the external world, it adapts to changes, constantly transforming itself. Such systems everywhere, almost any socio-economic or biological, just like the community of any product, are examples of adaptive systems.
Here is a video of the puppies.
At first, the system is in chaos, but when an external stimulus is added, it becomes more orderly and quite nice behavior appears.
Ant Swarm Behavior
The foraging behavior of an ant swarm is a perfect example of an adaptive system built around simple rules. When looking for food, each ant wanders randomly until it finds food. Having found food, the insect returns home, marking the path it has traveled with pheromones.
At the same time, the probability of choosing a direction when wandering is proportional to the amount of pheromone (smell strength) on this path, and over time, the pheromone evaporates.
The efficiency of the ant swarm is so high that a similar algorithm is used to find the optimal path in graphs in real time.
At the same time, the behavior of the system is described by simple rules, each of which is critical. So the randomness of the wander allows finding new food sources, and the evaporability of the pheromone and the attractiveness of the path, proportional to the strength of the smell, allows you to optimize the length of the route (on a short path, the pheromone will evaporate more slowly, since new ants will add their pheromone).
Adaptive behavior is always somewhere between chaos and order. If there is too much chaos, then the system reacts to any, even insignificant, change and cannot adapt. If there is too little chaos, then stagnation is observed in the behavior of the system.
I have seen this phenomenon in many teams, where having clear job descriptions and tightly regulated processes made the team toothless, and any outside noise unsettled them. On the other hand, the lack of processes led to the fact that the team acted unconsciously, did not accumulate knowledge, and therefore all its unsynchronized efforts did not lead to a result. Therefore, the construction of such a system, and this is the task of most professionals in any dynamic field, is a kind of art.
In order for the system to be capable of adaptive behavior, it is necessary (but not sufficient):
- openness. A closed system cannot adapt by definition because it knows nothing about the outside world.
- Presence of positive and negative feedbacks. Negative feedbacks keep the system in a favorable state as they reduce the response to outside noise. However, adaptation is also impossible without positive feedbacks that help the system move to a new, better state. When it comes to organizations, processes are responsible for negative feedbacks, while new projects are responsible for positive feedbacks.
- Variety of elements and relationships between them. Empirically, increasing the variety of elements and the number of connections increases the amount of chaos in the system, so any adaptive system must have the necessary amount of both. Diversity also allows for a smoother response to change.
Finally, I would like to give an example of a model that emphasizes the need for a variety of elements.
It is very important for a bee colony to maintain a constant temperature in the hive. Moreover, if the temperature of the hive falls below the desired for a given bee, she begins to flap her wings to warm the hive. Bees have no coordination and the desired temperature is built into the bee's DNA.
If all the bees have the same desired temperature, then when it drops below, all the bees will begin to flap their wings at the same time, quickly warm the hive, and then it will also quickly cool down. The temperature graph will look like this:
And here is another graph where the desired temperature for each bee is randomly generated.
The temperature of the hive is kept at a constant level, because the bees are connected to the heating of the hive in turn, starting from the most "freezing".
That's all, finally, I want to repeat some of the ideas that were discussed above:
- Sometimes things are not quite what they seem.
- Negative feedback helps you stay put, positive feedback helps you move forward.
- Sometimes, to make it better you need to add chaos.
- Sometimes simple rules are enough for complex behavior.
- Appreciate variety, even if you're not a bee.
Two heads and six legs; four walk, and two lie still
Self-esteem - what is it: concept, structure, types and levels
Cassandra's Path, or Pasta Adventures War on Earth and Underground