Topic 2. System properties. System classification
So, the state of the system is a set of essential properties that the system has at each moment of time.
Under property understand the side of an object that determines its difference from other objects or similarity with them and manifests itself when interacting with other objects.
Characteristic- something that reflects some property of the system.
What properties of systems are known.
From the definition of "system" it follows that the main property of the system is integrity, unity, achieved through certain relationships and interactions of the elements of the system and manifested in the emergence of new properties that the elements of the system do not possess. This property emergence(from eng. emerge- appear, appear
1. Emergence - the degree of irreducibility of the properties of the system to the properties of the elements of which it consists.
2. Emergence is a property of systems that causes the emergence of new properties and qualities that are not inherent in the elements that make up the system.
Emergence is a principle opposite to reductionism, which states that the whole can be studied by dividing it into parts and then, by determining their properties, determine the properties of the whole.
The property of emergence is close to the property of system integrity. However, they cannot be identified.
Integrity system means that each element of the system contributes to the implementation of the target function of the system.
Integrity and emergence are the integrative properties of the system.
The presence of integrative properties is one of the most important features of the system. Integrity is manifested in the fact that the system has its own pattern of functionality, its own purpose.
organization- a complex property of systems, consisting in the presence of structure and functioning (behavior). The indispensable property of systems is their components, namely those structural formations that make up the whole and without which it is not possible.
Functionality- this is a manifestation of certain properties (functions) when interacting with the external environment. Here, the goal (purpose of the system) is defined as the desired end result.
Structurality- this is the ordering of the system, a certain set and arrangement of elements with links between them. There is a relationship between the function and structure of the system, as between the philosophical categories of content and form. A change in the content (functions) entails a change in the form (structure), but vice versa.
An important property of the system is the presence of behavior - actions, changes, functioning, etc.
It is believed that this behavior of the system is associated with the environment (environment), i.e. with other systems with which it comes into contact or enters into certain relationships.
The process of purposeful change in time of the state of the system is called behavior. Unlike control, when a change in the state of the system is achieved due to external influences, behavior is implemented exclusively by the system itself, based on its own goals.
The behavior of each system is explained by the structure of lower-order systems that make up this system, and the presence of equilibrium signs ( homeostasis). In accordance with the sign of equilibrium, the system has a certain state (states), which are preferable for it. Therefore, the behavior of systems is described in terms of the restoration of these states when they are disturbed as a result of a change in the environment.
Another property is the property of growth (development). Development can be seen as an integral part of behavior (and the most important).
One of the primary, and, therefore, fundamental attributes of the system approach is the inadmissibility of considering an object outside of it. development, which is understood as an irreversible, directed, regular change in matter and consciousness. As a result, a new quality or state of the object arises. Identification (perhaps not quite strict) of the terms "development" and "motion" allows us to express ourselves in such a sense that the existence of matter, in this case, a system, is unthinkable outside development. It is naive to imagine development occurring spontaneously. In the boundless multitude of processes that at first glance seem to be something like Brownian (random, chaotic) movement, with close attention and study, at first, the contours of tendencies appear, and then quite stable patterns. These regularities by their nature act objectively, i.e. do not depend on whether we desire their manifestation or not. Ignorance of the laws and patterns of development is wandering in the dark.
“Who does not know in which harbor he sails,
there is no tailwind for that.”
Seneca
The behavior of the system is determined by the nature of the reaction to external influences.
The fundamental property of systems is sustainability, i.e. the ability of the system to withstand external disturbing influences. It depends on the lifetime of the system.
Simple systems have passive forms of stability: strength, balance, controllability, homeostasis. And for complex ones, active forms are decisive: reliability, survivability and adaptability.
If the listed forms of stability of simple systems (except for strength) concern their behavior, then the determining form of stability of complex systems is mainly structural in nature.
Reliability- the property of preserving the structure of systems, despite the death of its individual elements by replacing or duplicating them, and survivability- as an active suppression of harmful qualities. Thus, reliability is a more passive form than survivability.
Adaptability- the ability to change behavior or structure in order to maintain, improve or acquire new qualities in a changing environment. A prerequisite for the possibility of adaptation is the presence of feedback.
Any real system exists in the environment. The connection between them is so close that it becomes difficult to determine the boundary between them. Therefore, the selection of the system from the environment is associated with a certain degree of idealization.
There are two aspects of interaction:
In many cases, it takes on the character of an exchange between the system and the environment (substance, energy, information);
The environment is usually a source of uncertainty for systems.
The impact of the environment can be passive or active (antagonistic, purposefully counteracting the system).
Therefore, in the general case, the environment should be considered not only indifferent, but also antagonistic in relation to the system under study.
Many are familiar with the phrase from the film by Andrew and Lawrence Wachowski: "The Matrix is a system. It is our enemy." However, it is worth understanding the concepts, terms, as well as the capabilities and properties of the system. Is she as scary as she is presented in many films and literary works? The characteristics and properties of the system and examples of their manifestation will be discussed in the article.
Term meaning
The word "system" of Greek origin (σύστημα), meaning in literal translation a whole consisting of connected parts. However, the concept behind this term is much more multifaceted.
Although in modern life almost all things are considered as it is impossible to give the only correct definition of this concept. Oddly enough, this is due to the penetration of systems theory into literally everything.
Even at the beginning of the twentieth century, there were discussions about the difference between the properties of linear systems studied in mathematics, logic, and the characteristics of living organisms (an example of scientific validity in this case is the theory of functional systems by P. K. Anokhin). At the present stage, it is customary to single out a number of meanings of this term, which are formed depending on the analyzed object.
In the twenty-first century, a more detailed explanation of the Greek term has appeared, namely: "a wholeness consisting of elements that are interconnected and are in certain relations." But this general description of the meaning of the word does not reflect the properties of the system analyzed by the observer. In this regard, the concept will acquire new facets of interpretation depending on the object under consideration. Only the concepts of integrity, the basic properties of the system and its elements will remain unchanged.
Element as part of the whole
In systems theory, it is customary to consider the whole as the interaction and relationships of certain elements, which, in turn, are units with certain properties that are not subject to further division. The parameters of the part under consideration (or properties of a system element) are usually described using:
- functions (performed by the considered unit of action within the system);
- behavior (interaction with the external and internal environment);
- state (condition for finding an element with changed parameters);
- process (changing element states).
It is worth paying attention to the fact that the element of the system is not equivalent to the concept of "elementary". It all depends on the scale and complexity of the object in question.
If we discuss the system of human properties, then the elements will be such concepts as consciousness, emotions, abilities, behavior, personality, which, in turn, can themselves be represented as an integrity consisting of elements. From this follows the conclusion that the element can be considered as a subsystem of the object under consideration. The initial stage in system analysis is the determination of the composition of "integrity", that is, the clarification of all its constituent elements.
Links and resources as backbone properties
Any systems are not in an isolated state, they constantly interact with the environment. In order to isolate any "integrity", it is necessary to identify all the links that unite the elements into a system.
What are connections and how do they affect the properties of the system.
Communication - mutual dependence of elements on the physical or semantic level. In terms of importance, the following links can be distinguished:
- Structures (or structural): mainly characterize the physical component of the system (for example, due to changing bonds, carbon can act as graphite, like diamond, or like gas).
- Functioning: guarantee the operability of the system, its vital activity.
- Inheritance: cases where the element "A" is the source for the existence of "B".
- Developments (constructive and destructive): take place either in the process of complicating the structure of the system, or vice versa - simplification or decay.
- Organizational: these include social, corporate, role-playing. But the most interesting group is the control links as allowing to control and direct the development of the system in a certain direction.
The presence of certain connections determines the properties of the system, displays the dependencies between specific elements. You can also track the use of resources needed to build and operate the system.
Each element is initially equipped with certain resources that it can transfer to other participants in the process or exchange them. Moreover, the exchange can occur both within the system and between the system and the external environment. Resources can be classified as follows:
- Material - are objects of the material world: warehouses, goods, devices, machines, etc.
- Energy - this includes all types known at the present stage of the development of science: electrical, nuclear, mechanical, etc.
- Information.
- Human - a person acts not only as an employee performing certain operations, but also as a source of intellectual funds.
- Space.
- Time.
- Organizational - in this case, the structure is considered as a resource, the lack of which can even lead to the collapse of the system.
- Financial - for most organizational structures are fundamental.
Levels of systematization in systems theory
Since systems have certain properties and features, they can be classified, the purpose of which is to select appropriate approaches and means for describing integrity.
Main criteria for system typing
There is a categorization regarding interaction with the external environment, structure and spatio-temporal characteristics. The system functionality can be assessed according to the following criteria (see table).
| Criteria | |
| Interaction with the external environment | Open - interacting with the external environment Closed - showing resistance to the effects of the external environment Combined - contain both types of subsystems |
| Integrity structure | Simple - including a small number of elements and relationships Complex - characterized by heterogeneity of connections, a plurality of elements and a variety of structures Large - differ in the multiplicity and heterogeneity of structures and subsystems |
| Functions performed | Specialized - narrow specialization Multifunctional - structures that perform several functions at the same time Universal (for example, combine) |
| System development | Stable - the structure and functions are unchanged Developing - have a high complexity, undergo structural and functional changes |
| Organization of the system | Well organized (you can pay attention to the properties of information systems, which are characterized by a clear organization and ranking) Poorly organized |
| Complexity of system behavior | Automatic - a programmed response to external influences, followed by a return to homeostasis Decisive - based on constant reactions to external stimuli Self-organizing - flexible responses to external stimuli Foresight - surpass the external environment in the complexity of the organization, able to anticipate further interactions Transforming - complex structures not related to the material world |
| The nature of the relationship between elements | Deterministic - the state of the system can be predicted for any moment Stochastic - their change is random |
| Managment structure | Centralized decentralized |
| Purpose of the system | Managers - the properties of the control system are reduced to the regulation of information and other processes Producing - characterized by obtaining products or services Servicing - support for system performance |
System Property Groups
It is customary to call a property some characteristic features and qualities of an element or integrity that appear when interacting with other objects. It is possible to single out groups of properties that are characteristic of almost all existing communities. In total, twelve general properties of systems are known, which are divided into three groups. See the table for information.
Static property group
From the name of the group it follows that the system has some features that are always inherent in it: in any given period of time. That is, these are the characteristics without which the community ceases to be such.
Integrity- this is a property of the system, which allows you to distinguish it from the environment, to determine the boundaries and distinctive features. Thanks to it, the existence of established links between elements at each selected point in time is possible, which allow realizing the goals of the system.
openness- one of the properties of the system, based on the law of the relationship of everything that exists in the world. Its essence is that it is possible to find connections between any two systems (both incoming and outgoing). As you can see, upon closer examination, these interactions are different (or asymmetric). Openness indicates that the system does not exist in isolation from the environment and exchanges resources with it. The description of this property is usually referred to as a "black box model" (with an input that denotes the impact of the environment on integrity, and an output that is the impact of the system on the environment).
Internal heterogeneity of systems. AT As an illustrative example, consider the properties of the human nervous system, the stability of which is ensured by a multi-level, heterogeneous organization of elements. It is customary to consider three main groups: properties of the brain, individual structures of the nervous system, and specific neurons. Information about the constituent parts (or elements) of the system allows you to map the hierarchical relationships between them. It should be noted that in this case, the "distinguishability" of the parts, and not their "separability" is considered.
Difficulties in determining the composition of the system are for the purposes of the study. After all, one and the same object can be considered from the point of view of its value, functionality, complexity of the internal structure, etc. In addition to everything, the ability of the observer to find differences between the elements of the system plays an important role. Therefore, the model of a washing machine for a seller, a technical worker, a loader, a scientist will be completely different, since the listed people consider it from different positions and with different set goals.
Structured- a property that describes the relationship and interaction of elements within the system. Connections and relationships of elements constitute the model of the system under consideration. Thanks to structuredness, such property of an object (system) as integrity is supported.
Dynamic Properties Group
If static properties are what can be observed at any single moment in time, then dynamic properties are classified as mobile, that is, manifested in time. These are changes in the state of the system over a certain period of time. A clear example is the change of seasons in some observed area or street (static properties remain, but dynamic effects are visible). What properties of the system belong to the group under consideration?
Functionality- is determined by the impact of the system on the environment. A characteristic feature is the subjectivity of the researcher in the selection of functions, dictated by the goals set. So, the car, as you know, is a "means of transportation" - this is its main function for the consumer. However, when choosing, the buyer can be guided by such criteria as reliability, comfort, prestige, design, as well as the availability of related documents, etc. In this case, the versatility of such a system as a car is revealed, and the subjectivity of functionality priorities system of major, minor and minor functions).
Stimulability- manifests itself everywhere as an adaptation to external conditions. A striking example is the properties of the nervous system. The impact of an external stimulus or environment (stimulus) on an object contributes to a change or correction of behavior. This effect was described in detail in his studies by IP Pavlov, and in the theory of system analysis it is called stimulability.
Variability of the system over time. If a the system functions, changes are inevitable both in interaction with the environment and in the implementation of internal connections and relations. The following types of variability can be distinguished:
- high-speed (fast, slow, etc.);
- structural (changes in the composition, structure of the system);
- functional (replacing some elements with others or changing their parameters);
- quantitative (an increase in the number of elements of the structure that does not change it);
- qualitative (in this case, the properties of the system change with the observed growth or decline).
The nature of the manifestation of these changes can be different. It is obligatory to take into account this property in the analysis and planning of the system.
Existence in a changing environment. Both the system and the environment in which it resides are subject to change. For the integrity to function, it is necessary to determine the ratio of the rate of changes of internal and external. They may coincide, may differ (lead or lag). It is important to correctly determine the ratio, taking into account the characteristics of the system and the environment. A good example is driving a car in extreme conditions: the driver acts either ahead of the curve or in accordance with the situation.
Group of synthetic properties
Describes the relationship between the system and the environment in terms of a common understanding of integrity.
emergence- a word of English origin, translated as "arise". The term refers to the appearance of certain properties that appear only in the system due to the presence of connections of certain elements. That is, we are talking about the emergence of properties that cannot be explained by the sum of the properties of the elements. For example, car parts are not able to drive, let alone carry out transportation, but assembled into a system, they are able to be a means of transportation.
Indivisibility into parts is property, logically, follows from emergence. Removal of any element from the system affects its properties, internal and external relations. At the same time, the element "sent to free float" acquires new properties and ceases to be a "link in the chain". For example, a car tire on the territory of the former USSR often appears in flowerbeds, sports fields, and "bungee". But removed from the car system, it lost its functions and became a completely different object.
Inherence is an English term (Inherent), which translates as "an integral part of something." The degree of "inclusion" of elements in the system depends on the performance of the functions assigned to it. On the example of the properties of elements in the periodic system of Mendeleev, one can verify the importance of taking into account inherence. So, the period in the table is built on the basis of the properties of the elements (chemical), primarily the charge of the atomic nucleus. Properties follow from its functions, namely the classification and ordering of elements in order to predict (or find) new links.
Expediency - any artificial system is created with a specific purpose, whether it is a solution to a problem, the development of specified properties, the release of the required product. It is the goal that dictates the choice of structure, composition of the system, as well as connections and relationships between internal elements and the external environment.
Conclusion
The article outlines twelve system properties. The classification of systems, however, is much more diverse and is carried out in accordance with the goal pursued by the researcher. Each system has properties that distinguish it from many other communities. In addition, the listed properties can manifest themselves to a greater or lesser extent, which is dictated by external and internal factors.
Properties determined by the interaction of the part and the whole, include :
integrity;
integrativity;
communication;
hierarchy.
Property integrity assumes that:
the whole is not a simple sum of parts, since the system must be considered as a unity;
an integral system is such a system in which the internal connections of the parts among themselves are predominant in relation to the movement of these parts and to the external influence on them;
in order for something integral to be perceived as a system, it must have boundaries separating it from the external environment.
Integrity Property manifests itself in the emergence of new integrative qualities in the system that are not characteristic of its components, i.e. in emergence . At the same time, the elements combined into the system may lose a number of properties that are inherent in them outside the system, i.e. the system, as it were, suppresses some properties of its elements.
For example, the production system during working hours uses only those knowledge and skills of workers (system elements) that are necessary for the implementation of the production process and suppresses their other abilities (vocal, choreographic).
The property of integrity is associated with the purpose for which the system is created. At the same time, objects (parts) function in time as a whole - each object, subsystem, cell, work for the sake of a single goal facing the system as a whole.
Dual in relation to the integrity property is the property physical additivity (or independence, or summativity). The properties of physical additivity are manifested in a system that, as it were, has broken down into independent elements. Strictly speaking, any system is always between the extreme states of absolute integrity and absolute additivity. In this case, the term "progressive factorization" refers to the system's desire to increase the degree of independence of elements, and the term "progressive systematization" refers to the system's desire to reduce the independence of elements, i.e. to greater integrity.
Property of integrativity means the presence of system-forming, system-preserving factors, among which an important role is played by the heterogeneity and inconsistency of elements, on the one hand, and their desire to join coalitions, on the other.
Communication means that the system is not isolated from other systems, it is connected by many communications with the environment, which, in turn, is a complex and heterogeneous formation. This environment contains:
a higher-order system that sets requirements and restrictions for an object;
underlying systems;
systems of the same level with the considered object.
Communication characterizes the complex unity of the system with the environment.
Hierarchy is a necessary property of systems and manifests itself in the existence of several levels of interaction:
each level of hierarchical ordering has complex relationships in the higher and lower levels. Even if there are no explicit links between the elements of the same level of the hierarchy (horizontal links), they still appear through the higher level. In particular, it depends on the higher level, for example, which of the departments will be encouraged, and which will be assigned a non-prestigious job. This concretization of the property of hierarchy explains the heterogeneity of the use of the concepts "goal" and "means", "system" and "subsystem" in complex organizational systems.
a higher hierarchical level has a guiding effect on the lower level subordinate to it. This effect is manifested in the fact that the subordinate members of the hierarchy acquire new properties that they do not have in an isolated state, i.e. the property of emergence manifests itself at each level of the hierarchy;
for systems with uncertainty, hierarchy means, as it were, the division of a “large” uncertainty into smaller ones that are better amenable to research and evaluation. At the same time, even if these minor uncertainties cannot be fully disclosed and explained, nevertheless, hierarchical ordering partially removes the general uncertainty and provides at least controlled control over decision-making.
Other properties of the systems include:
historicity , based on the fact that time is an indispensable characteristic of the system, which is expressed in the assessment of the life cycle of a product, technology, enterprise, etc.;
self-organization , i.e. the ability of the system to resist entropy tendencies, to adapt to external disturbances, changing its structure if necessary. Information is lost in various ways, which leads to an increase in the entropy of the system, but in order to acquire new information and reduce the entropy, new measurements must be made, i.e. expend energy. Entropy and information thus serve as an expression of two opposite tendencies in development processes. If the system evolves in the direction of orderliness, then its entropy decreases, but this requires purposeful efforts, the introduction of information, i.e. management;
homeostasis - means the property of the system to maintain its parameters and functions within a certain range. It is based on the stability of the internal environment of the object in relation to the impact of the external environment. That is, in the homeostat, the controlled variable is maintained at the required level by the self-regulation mechanism. Here, the control body is built directly into the system, being an integral part of it. This is an ideal combination inherent in natural, primarily biological, systems, to which systems created by man aspire.
equifinality characterizing the limiting capabilities of systems. The complexity of the system structure determines the complexity of its behavior, which in turn means the limit of reliability, noise immunity, controllability and other qualities of the system, i.e. limiting viability and potential efficiency of complex systems, in this case, control systems and their organizational structures.
The problem of integrity has attracted the attention of philosophers since ancient times. Aristotle was probably the first to draw attention to the fact that the whole is "greater" than the sum of its parts, and tried to show the relative independence of the whole as an entity from changes occurring in its parts. Further development of the concept of integrity is associated with the names of Leibniz, Kant and especially Hegel.
The sharp increase in interest in the problem of integrity within the framework of cybernetics and general systems theory is due to the development of the functional approach and the concept of open systems. A number of monographs by Soviet philosophers are devoted to the analysis of the concept of integrity in philosophy and special sciences, and to the identification of its role in scientific knowledge.
Integrity is usually considered from the point of view of its relationship to parts, while trying to reveal the continuity and interdependence of parts and the whole. Let us consider integrity in its relation to the external environment, to the environment, i.e. in a functional aspect. This integrity is called functional. From this point of view, it acts, first of all, as a factor that determines the individualization of an object, a thing. Due to integral properties, the object is what it is. Outside of integral properties, the totality of external relations and connections of the subject is destroyed. Consequently, the object itself also disappears. The integral properties of the objects of reality in their functional aspect make these objects fundamentally cognizable.
In general systems theory, the concept functional integrity from the very beginning is put in the basis of the theory. It plays a fundamental role here along with the principle of hierarchy. Analyzing the concept of a system, VN Sadovsky considers integrity and hierarchy as equal components and puts them side by side from the point of view of fundamental importance for systems theory. He writes: “The starting points for the metatheoretical analysis of the concept of “system” are the principles of integrity and hierarchy, according to which the primacy of the system as a whole over its elements and the fundamental hierarchical organization of any system are affirmed”, This indicates that there is an organic connection between the principle of integrity and the principle of hierarchy .
The hierarchical structure of systems in the methodological context acts as a consequence of the functional nature of integrity. Indeed, by analyzing the nature of the hierarchy in each specific case, one can be convinced that integrity as a characteristic of the system's connection with the environment initially appears in the form of a hierarchical factor.
From this point of view, a relatively isolated object, considered within the framework of a wider object-environment system, can be treated as a level of hierarchy in this latter system.
The second level is the environment. Accordingly, the "object-environment" system can be represented by two concentric circles.
If the part of the environment in which the system functions (more precisely, its immediate environment) can in turn be described as an integrity, then we get a three-level hierarchical structure, which can be depicted, respectively, by three concentric circles. Etc.
Functional integrity determines the relative independence, autonomy of individual subsystems within the hierarchical structure. This autonomy is, in a certain sense, inevitable, just as it is inevitable that every object, once it exists, has integral characteristics, some behavior of its own.
However, it is necessary to make a reservation right away. These integral characteristics and this own behavior can be attributed to an object only within the framework of an external, phenomenological description. With a more rigorous, essential approach, the so-called intrinsic characteristics of an object reveal a much more complex nature, acting as a synthetic result of the relationship between the object and the environment, as the structural properties of this relationship.
Thus, the autonomy, integrity, behavioral characteristics of any level in a hierarchical system cannot be understood by studying the structure of this level only.
Level functions have an interlevel nature, acting as structural properties of the entire hierarchical system, and from this point of view, they represent the basis for conducting a structural analysis of the system. At the same time, the structure of the system can be considered as the result of functional synthesis, i.e. synthesis of integral properties of elements and levels of the system.
Let us consider in more detail the problem of generating integral properties in the system. In constructive terms, integrity always arises in the process of forming a system.
Strengthening the factors that determine the functional integrity of the elements of the system is expedient only on the condition that at the same time there is a strengthening of interlevel relations and connections. At the same time, the degree of manifestation of the hierarchical structure of the system increases. If there is no strengthening of interlevel relations and connections, then the factors of the functional integrity of the system are weakened and the system may disintegrate.
One of the most common causes of increased factors functional integrity in biological and socio-economic systems - specialization elements. In this case, the integrity of the entire system is ensured by the existence of clear links between the elements, the specialization of which makes them absolutely necessary for each other in the interests of the system.
The emergence of the hierarchical structure of the economy as a result of the social division of labor can serve as an example that refutes the widely held opinion that hierarchical structures are formed solely as a result of the limited capabilities of the elements of the system for processing information. Of course, it cannot be denied that the information factor plays a certain role in the formation of hierarchical structures, but apparently it is not decisive. Experience in the practical design of production control systems shows that attempts to replace the primary regulators with one centralized regulator and a sufficiently productive (in terms of the amount of information processed) computer usually end in failure.
Noting the insufficiency of the information approach to explain the nature of hierarchical structures, V. L. Harton writes: “By using control devices with any speed, any complex hierarchical system, apparently, cannot be transformed into a simple, single-level system. The minimum number of levels is determined by the variety of control algorithms, the varying degree of interconnection of these algorithms. At the same time, the variety of control algorithms is associated with a variety, a different quality of the elements of the system, which gives rise to a variety, a different character of the connections between the elements. In organisms and production systems, the heterogeneity of elements appears precisely as a result of their functional differentiation and specialization. The very process of building information systems for data processing for decision-making uses functional integrity as a fundamental hierarchical factor. Thus, the concept of integrity and hierarchy are inextricably linked.
Integrity- the main common feature that is present in almost all definitions and theoretical models of the concept of "system". This attribute is sought to be expressed explicitly or at least implicitly in all definitions of the concept of a system.
Definition 1.35. The integrity of the system is understood as the internal unity and fundamental irreducibility of the properties of the system to the sum of the properties of its constituent elements.
However, the means by which they try to express integrity are different and not always unambiguous.
In the simplest case, it is believed that the presence of connections and relations between the elements of the system just expresses its integrity, so that no special means, except for setting these relations, are required. In this case, the attribute of integrity is not introduced into the definition of the system. This is typical for definitions that have developed outside the systemic approach. It is clear that not all relations give integrity to the set of elements. Therefore, special relations are distinguished, which are called backbone.
To isolate a system in a complex object, such relations are chosen that are essential in this problem. As signs that characterize the integrity of systems, they use such as unity of purpose, functional purpose, certain functions, the presence of an environment with which the system interacts as a whole. We emphasize that all these signs are not universal.
The following two statements follow from the property of integrity:
· the system in relation to the environment will be perceived as a whole (holistic) and the interaction of internal connections over external connections should prevail in the system, and the integration of the elements of the environment should resist the perturbing effect of the environment;
· within the framework of this whole, the properties and functions of the elements of the system are determined, and any decomposition of the system can be carried out to the minimum elements of the system, which still retain the property of the integrity of the system.
The pattern of integrity is manifested in the system in the emergence of new integrative qualities that are not characteristic of its constituent components. To better understand the pattern of integrity, it is necessary to consider its two sides:
· the properties of the system (the whole) are not the sum of the properties of elements or parts (the irreducibility of the whole to a simple sum of parts);
· the properties of the system (whole) depend on the properties of the elements, parts (a change in one part causes a change in all other parts and in the entire system).
An essential manifestation of the regularity of integrity is the new relationship of the system as a whole with the environment, different from the interaction of individual elements with it.
The property of integrity is related to the purpose for which the system is intended to fulfill.
It is very relevant to assess the degree of integrity of the system during the transition from one state to another. In this regard, there is an ambivalent attitude to the laws of integrity. They call it physical additivity, independence, summativity, isolation. property of physical additivity manifests itself in the system, as if disintegrated into independent elements.
Strictly speaking, any system is always between the extreme points of the conditional scale:
absolute integrity - absolute additivity.
The considered stage of the development of the system can be characterized by the degree of manifestation in it of one or another property and the tendency to its increase or decrease.
To evaluate these phenomena, A. Hall introduced such regularities as "progressive factorization"(the desire of the system to a state with more and more independent elements) and "progressive systematization"(the desire of the system to reduce the independence of elements, i.e., to greater integrity). There are methods for introducing comparative quantitative estimates of the degree of integrity, the coefficient of use of elements in general from the point of view of a specific goal.
As a rule, the unification of elements into a system is carried out as a result of the formation of a coordinated interaction (addition of efforts) into something new, which has integrative quality that these elements did not possess before the unification. The functional integrity of the system characterizes the completeness of its internal structure. It is the system that acts as a whole in relation to the environment: when the external environment disturbs, internal connections between its elements are manifested, and the stronger these connections, the more stable the system is to external disturbances. In other words, a set of interrelated structural elements forms a system only when the relations between the elements give rise to a new special quality of integrity, called systemic.
The properties of the system as a whole are determined not only by the properties of its individual elements, but also by the properties structures systems.
Integrity is a multifaceted phenomenon. One of the most important elements of integrity integration ensures the cohesion of the parts into a whole, and as a result of such cohesion, the properties of the parts are modified and appear as qualitatively different properties characteristic of the existing integrity and different from the properties of individual elements (some sources use the term "emergence"). Integration is also manifested in the functional orientation of the interactions of the elements of the system to the preservation and development of integrity by removing the actual contradictions of the system.
An essential feature of integrity is relative isolation of the system from the environment. This indicates that the system has some outer border(separating it from the environment), which is due to the functional separability of the system from the environment, and contacts with the environment are carried out selectively, which allows you to exchange matter, energy and information with the environment without mixing with the environment and maintaining the qualitative individuality of the system.
The environment is understood as a set of objects outside the given system.
Often isolated near environment, which is defined as a subset of objects that have a significant impact on the system and/or are affected by it.
Thus, the concept of integrity, one way or another, is included in almost all definitions of the system and determines its properties.
System properties can be classified into four types.
1. Holistic system properties (integrative). These are properties that belong to the system under consideration as a whole, but do not belong to its constituent parts.
2. Incoherent properties of the system. These are properties that belong to the component parts, but do not belong to the system as a whole.
3. Holistic-non-holistic properties. These are properties that belong both to the system as a whole and to its elements.
4. "Non-existent" properties of the system. These are properties that do not belong to either the system as a whole or its elements.
Figure 1.17 shows the structure of the system, taking into account its connections with the external environment and elements that ensure its integrity.
The integrity of a system of any nature is provided by the following four elements: energy, matter, information, knowledge. They are pairwise conjugate components. Information and knowledge represent the content essence of the system, energy and matter constitute the form of the system. Energy, as a kind of physical field, represents the dynamic component of the system, and matter, which has a rest mass, represents the static component of the system. Knowledge as a system component represents structured or strategic information, and information, for its part, represents updated knowledge.
Fig.1.17. General structure of the system
From a formal point of view, any system can be understood as some kind of mathematical model. For example, the representation of the system as a "black box" in an abstract form can be defined as follows.
Definition 1.36.The system in a broad sense is the equivalent of the concept of a mathematical model and a pair of sets is given U, Y(U- many inputs; Y is a set of outputs) and a relation that formalizes the connection (dependence) between inputs and outputs.
The connection of systems is also a system and is defined by a relation. For example, series connection of systems, there is a relation , such that there are , satisfying the conditions , , where relation that defines the relationship between and . Thus, it is possible to define arbitrarily complex systems based on simple.
The above definition reflects in an abstract form the attributes (properties) inherent in our intuitive understanding of the system.
There is a definition of the system associated with the concretization of the concept of a model by endowing it with some properties. One of these properties is integrity.
Definition 1.37. The system is a model that has the properties of integrity, structuredness and purposefulness.
Let's give another definition of integrity.
Definition 1.38.Integrity (unity) means that the system is separated from the external environment: the environment can have an action (action) on it only through its inputs and perceive responses (reaction) to these actions through its outputs.
Target. The use of the concept of "goal" and the related concepts of purposefulness, purposefulness, expediency are constrained by the difficulty of their unambiguous interpretation in specific conditions. This is due to the fact that the process of goal formation and the corresponding process of justifying goals in organized systems is very complex and not fully understood. Much attention is paid to his research in psychology, philosophy, and cybernetics.
The following definition of purpose can be given.
Definition 1.39. The goal is a subjective image of a non-existent state of the environment or an object that would solve the problem that has arisen.
In practical applications, a goal is an ideal aspiration that allows the team to see the prospects or real opportunities that ensure the timely completion of the next stage on the path to ideal aspirations.
The connection between the goal and the system is ambiguous: different systems can be oriented towards the same goal; one system can and often does have several different purposes. If we expand the concept of goal, considering any future state of the system as an objective goal, then we can say about the purposefulness of natural systems.
Examples of systems that achieve certain goals are presented in Table 1.5.
Table 1.5
A special class is formed by socio-technical systems, which include not only technology, but individuals and teams associated with the operation of the system. One of the most common classes of such systems is organizational systems or organizations consisting of groups of people whose activities are consciously coordinated to perform certain functions or to achieve common goals using certain technical methods or technologies. The ideological basis for determining the purpose of the socio-technical system is its valuable system awns. It is the object of system analysis at the stage of identifying the corresponding reality of the goals of the persons who enter the system, because the officially declared goals may not coincide with the corresponding reality.
Purposefulness- requires setting a certain goal, the achievement of which indicates the correct operation of the system.
As already mentioned above, an important property of the system is structuredness.
Structuredmeans that the system is internally divided into several subsystems, connected and interacting with each other in the same way as the whole system interacts with the external environment.
Wednesday.The environment is the environment with which the system interacts.. Systems interacting with the environment are called open(Unlike closed, which have no environment).
The environment for one of the subsystems can be the rest of the subsystems or some of them. The typology of the environment is shown in Figure 1.18.
Definition 1.40. The environment is understood as a set of objects outside the given element (system) that influence the element (system) and are themselves under the influence of the element (system).
The environment is also a system.
A deeper understanding of the environment shows that the environment appears to be heterogeneous.
It has the following characteristics:
· some set of organized systems and chaotic formations. At the same time, organized systems give the environment organization, predetermination, and chaotic formations - unpredictability, randomness;
· many factors that affect the system. The environment is not all the objects that surround the system, but only those related to its life. Either these are objects and systems that fall, as they say, into the sphere of “system interests”, or those in whose sphere of interest this system falls;
· the system affects the environment through its functions. At the same time, the external organizing functions influence the environment, and the internal functions influence the internal one;
· the system uses the environment as a source, storage and means of processing resources, means of life. The environment replenishes the system, ensures its renewal, the sphere of life, the manifestation of functions;
· the system is constantly changing its boundaries in relation to the environment.
This shows her dynamism. It can receive or capture elements from the environment and appropriate them, introduce them into the internal environment.
The system is separated from the environment by boundaries.
Fig.1.18. Environment typology
The boundaries of the system can be defined as any objects in which a given object does not exist and which have the least difference from them.
Determining the boundaries of the system is fundamentally important for both its knowledge and management. In this case, the boundaries of the system, first of all, are established in space. To find the boundaries of the system and build its plan, it is necessary to attach a kind of ruler to each object of the system - a system-forming factor. The construction of a spatial model of a system with the definition of boundaries is studied by a special branch of knowledge called the topology of systems.
System model. A system model is understood as a description of the system that displays a certain group of properties. Deepening the description - detailing the system model. Creating a system model allows you to predict its behavior in a certain range of conditions.
Concepts characterizing the functioning and development of the system . The processes occurring in systems, as a rule, cannot be represented in the form of mathematical relationships or even algorithms. Therefore, in order to somehow characterize the functioning of the system, they use special terms borrowed by systems theory from the theory of automatic control, biology, and philosophy.
These concepts include:
· condition;
· behavior;
· equilibrium;
· stability;
· development;
· system functioning model.
State. The state usually characterizes an instant photo, a "cut" of the system, a stop in its development.
The state of the system is determined either by:
· through input actions and output signals (results);
· through macro parameters, macro properties of the system.
The macro parameters of the system include: pressure, velocity, acceleration - for physical systems; productivity, production cost, profit - for economic systems.
Definition 1.41.The state of the system is understood as an ordered set of values of internal and external parameters that determine the course of processes occurring in the system.
The state of the system can be more fully defined if we consider the elements (components, functional blocks) that determine the state, take into account that the "inputs" can be divided into control and perturbing (uncontrolled) and that the "outputs" (output results, signals) depend on the elements, control and uncontrolled impacts.
Thus, the state of the system is a set of essential properties that the system has at a given time.
The set of system states can be countable, continuum or finite.
Behavior. If a system is capable of changing from one state to another, then the system is said to have behavior.
Definition 1.42.The behavior of a system is a sequence of reactions of the system to external influences unfolded in time.
The concept of "behavior" is used when the patterns (rules) of the transition from one state to another are unknown. If they talk about the behavior of the system, then they find out its nature, algorithm.
System functioning model – it is a model that predicts the change in the state of the system over time.
Equilibrium. The concept of equilibrium is defined as the ability of a system in the absence of external perturbing influences (or under constant influences) to maintain its state for an arbitrarily long time. This state is called the equilibrium state.
Sustainability . Stability is understood as the ability of a system to return to a state of equilibrium after it has been brought out of this state under the influence of external disturbances. This ability is usually inherent in systems with a constant control action, if the deviations do not exceed a certain limit.
Definition 1.43.The state of equilibrium to which the system is able to return is called the stable state of equilibrium.
Equilibrium and stability in economic and organized systems are much more complex concepts than in engineering, and until recently they were used only for some preliminary description of the concept of the system. Recently, there have been attempts to formalize these processes in complex organized systems, helping to identify the parameters that affect their course and interconnection.
Development. This concept helps to explain complex thermodynamic and informational processes in nature and society. The study of the development process, the relationship between development and stability, the study of the mechanisms underlying them are the most difficult tasks of systems theory. Allocate a special class developing systems, which have special properties and require the development and use of special approaches and their modeling.
The above formal definitions of a system are quite general. Almost all types of mathematical models of systems fall under them: differential and difference equations, regression models, queuing models, finite and stochastic automata, deductive systems, etc.
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Holistic system and quantitative measurement of its state. Living organism as a expressed integral system
A.P. Khuskivadze
Annotation.
The substantiation of the notion "Theory of integrity" is given. Questions of similarities and differences between the general theory of systems by L. von Bertalanffy, the unified field theory and the theory of integrity are considered.
The concept of an integral system is formulated and it is shown that a living organism is a pronounced integral system. A method for quantitative measurement of the state of an integral system is given.
The work was done at the intersection of fundamental medicine, biology, physics and philosophy. It is of interest, first of all, for specialists working in the field of evidence-based medicine.
Key words: general systems theory, integral system, mathematical description, quantitative indicators of the state of the integral system, probabilistic limit of truth cognition.
All rights to the materials of the article are reserved.
1. General systems theory L. Von Bertalanffy, unified field theory and integrity theory
In the second half of the twentieth century, the phrase "General Systems Theory" took root in biology, medical science and philosophy. Many mathematicians also began to use this phrase. However, most mathematicians still prefer to talk about "Mathematical thorns of systems". In physics, as a rule, they operate with the phrase: "Unified field theory" or "Theory of everything (Eng. Theory of everything, TOE)".
All these theories, in essence, set themselves the same task: to find the most general laws of nature. The difference between these theories is in the approaches to solving the problem. Thus, the unified field theory sees the way to solve the problem in the study of the very deep processes occurring in inanimate nature. Logic works intuitively here: “Inanimate nature is primary, and living nature is secondary. Consequently, the patterns common to all inanimate nature must be common to all living nature.” It must be assumed that it was precisely this logic that W. Heisenberg was guided by, seeing ways to solve the so-called. "problems of the central order" in the knowledge of the mysteries of the atom.
The “Problem of the central order” is understood as the problem of finding a pattern that determines the significant difference, which exists between the durations of existence whole andits constituent parts. For example, hundreds and thousands of people die, but the biological species continues to exist, many streets collapse, but on the whole the city continues to exist, etc. .
As you can see, the phrase "Problem of the central order" denotes the same problem of searching for general laws of nature.
The general theory of systems sees the way to solve the problem in the study of processes that occur both in living and inanimate nature. equally. Of course, the deep processes occurring in all manifestations - forms - of inanimate nature in the same way, will occur in the same way in all forms of living nature. However, general systems theory proceeds from the fact that in addition to these processes, there are general processes that are far not deep. For example, we all know that if a person's brain is left without oxygen for five minutes, then both the brain and the person themselves will die. Similarly, if he stops the supply of electricity and gas to the blast furnace and let it cool down, then it will stop completely. A stopped blast furnace, as you know, is not restored, but it is preferred to rebuild it.
What do the human brain and the blast furnace of a metallurgical plant have in common?
The human brain and the blast furnace of a steel plant have one thing in common: they are both expressed integral systems, serving, for their part, the most important elements of the respective integral formations.
The meaning of the phrase "Expressed integral system" seems to be intuitively clear. A strict definition of the concept denoted by this phrase is given in. Intuitively, the meaning of the phrase is also clear: "The most important element of the corresponding holistic education." However, relying on this intuitive idea alone, it is impossible to properly formalize the common thing that unites the human brain and the blast furnace of a metallurgical plant.
It must be assumed that when the creator of the general theory of systems, a biologist by profession, von Bertalanffy, spoke about the tasks facing this theory, he, first of all, had in mind the study of the common that unites various forms alive nature, i.e. . expressed integrity living organisms.
The pronounced integrity, as mentioned above, is also characteristic of the blast furnace of a metallurgical plant.
Therefore, integrity is a characteristic not only of living nature. It is also characteristic of inanimate nature.
It can be shown that integrity is the most common way of being our reality.
Indeed, each biological species, as is known, is a holistic formation, elementarybricks served couples compiled by representatives opposite sexes this biological species.
Representatives of the opposite sexes of a biological species, of course, can create other integral formations. There are, for example, integral formations. indicated by phrases: "Men's football team", "Women's volleyball team", "Family", "Parents", etc. All these integral formations, apparently, are composed by people, i.e. representatives of the same biological species. However, when it comes to a holistic formation, designated by the phrase "Biological species", then it is the pairs made up by representatives of the opposite sexes of this biological species that act as elementary building blocks.
Particular attention should be paid to the following: when they say that our reality is a unity of opposites, they always mean not heap opposite sides, and properly organized holistic education. At the same time, these integral formations can be composed not only by realities of one nature. Examples of integral formations are both realities such as "Human Society" and "The World of Animals", and realities like "Moscow City" and "Volga River", etc.
All examples given above refer to "shallow" processes. And what happens in the microcosm?
It turns out that all the so-called strongly interacting elementary particles - hadrons - are the same expressed integral systems as living organisms are: just as the functional parts of a living organism cannot exist outside this organism, so quarks cannot exist outside the hadron, to which they belong to .
We can say that everything that we see around us, and everything that we do not see, but exists objectively, is a kind of integral formation. More precisely, it is a holistic formation with a probability: 0.5 ≤ P
So, integrity is something common that is equally characteristic of both living and inanimate nature. Consequently, the regularities of integrity should be regularities that are equally valid for both living and inanimate nature. The study of these regularities is the task of integrity theory.
As can be seen, the theory of integrity, in contrast to the general theory of systems and the unified field theory, is limited to the study of some regularities of the integrity of the forms of existence of animate and inanimate nature. Therefore, this theory is part both the general theory of von Bertalanffy systems and the unified field theory, i.e. it represents an even more general theory.
It should be noted that the phrase "Theory of integrity", firstly, is laconic. Secondly, which is much more important, in this phrase the emphasis is on the most important thing: - the most general property of living and inanimate nature, i.e. about their integrity
In conclusion, let us pay attention to the difference in the language means used in the unified field theory and in integrity theory.
The unified field theory, as is known, operates with the conceptual apparatus of modern physics. This is a language understandable to physicists and those mathematicians who work at the intersection of physics and mathematics.
The theory of integrity, as mentioned above, is part of the general theory of systems. BUT
in the general theory of systems, besides mathematicians and physicists, biologists, physicians, sociologists and philosophers work. The founder of the general theory of systems, Von Bertalanffy, as mentioned above, is a biologist. It is clear that in the general theory of systems a language tool is required that is equally understandable to all: biologists, physicians, physicists, mathematicians, sociologists and philosophers. Such a language tool is currently the conceptual apparatus of modern mathematical statistics.
In addition to the conceptual apparatus of mathematical statistics, we very rarely have to operate with such very general concepts of set theory as "Open set", "Intersection of sets", "Relationship", etc. We operate with these last concepts, in particular, when formalizing such fundamental concepts for the theory of integrity as the concepts of "System" and "Functional element of the system" .
The concept of a holistic system
The first attempts at a mathematical definition of the concept of "Integral System" were made by us in. Later, having familiarized ourselves with the works of Academician V.G. Afanasyev and other philosophers, we came to the conclusion that the concept of "Integral System" is a philosophical concept that is not amenable to mathematical formalization. Hence the idea to single out a class of so-called empirical integral systems. However, further studies have shown that the concept of an integral system is still quite formalizable. Below we operate with the mathematical concept of an integral system introduced by us in .
The concept of "set", as is known, is the primary mathematical concept. If the set is binary, then it is said to be attitude.
So let
They are scalar measured quantities, each j-th of which has three or more possible values.
Denote
Y = í y j ; j = 1..N) (1)
A, A j ; j = 1..N
Non-empty finite sets, and
H and H j ; j = 1..N
Non-empty finite sets of relations such that for each pair
takes place
S j = S j 0 Û y j = y j 0 ,
and the pair s = satisfies the condition
s = s 0 Û Y = Y 0 ,
those. generally take place
s = s 0 Û Y = Y 0 and S j = S j0 Û y j = y j 0 ; j = 1..N, (2)
s 0 , Y 0 , S j 0 and y j 0
are fixed values
s, Y, S j and y j
respectively.
Definition 1
Let (2) take place and at the same time
2 ≤ N and s = s 0 Û S j = S j 0 for all j = 1.. N (3)
Then and only then we say that the pair s is system functional elements
Definition 2
Let the pair s be a system, i.e. the set of conditions (2) and (3) is satisfied.
Then and only then they say that the set (1) is the general set of primary indicators of the state of the system s and write:
Y = Y(G) º í y j ; j = 1..N(G)), (4)
where N(G) is the volume of Y(G).
According to (1) and (4) we have
Therefore, we can say that the system s consists of N(G) number of functional elements.
2 ≤ N(G) ≤ M(A) ,
where M(A) is the volume of A.
Due to the fact that
H ¹ Æ , (5)
the elements of the system s, in contrast to the elements of the set A, are always mutually connected. This interconnectedness is expressed in the fact that the processes occurring in the elements of the system s are in one or another, non-zero, degrees are consistent.
In general, if condition (5) is satisfied, then we can say that the system s is in one or another non-zero, the degree of holistic. Otherwise, we can say that the system s is not complete. For example, a corpse is most likely not an integral system.
According to V.G. Afanasiev, the main sign of the integrity of the system s is the presence of the so-called. single integrative quality(EIC) . Under the EIC of a system s, we understand the quality that this system manifests itself to the extent that this quality is manifested by each of its functional elements, i.e. takes place
g = g 0 Û g j = g 0 for all j = 1..N(G), (6)
g is the measure of manifestation of the UIC by the system s: 0 £ g £ 1;
g 0 is a fixed value of g ;
g j is the measure of UIC manifestation by the j -th functional element of the system s.
The second important sign of the integrity of the system s, according to V.G. Afanasiev, is her historicity, i.e. that for this system the condition
is performed within a well-defined time interval from t to t n,
t to - the time of the appearance of the system s: t to ≥ 0;
t n - the time of the disappearance of the system s: t to
Definition 3.
Let, at the moment of time t = t 0 (t to £ t 0 £ t n), condition (6) is satisfied,
t 0 is a fixed value of t.
Let, at the same time, inequality (7) hold at the time t = t 0 .
Then, and only then, is the system s said to change environment of their existence at time t = t 0 reacts as one.
Under the environment of existence of the system s understand the totality of internal and external factors (conditions) under which inequality (7) takes place.
Any other environment is not an environment for the existence of the system s and, therefore, it cannot react to a change in such an environment as a whole.
Definition 4.
Let the system s at the moment of time t = t 0 (t k £ t 0 £ t n) react as a whole to a change in the environment of its existence.
Then, and only then, we say that the system s at time t = t 0 is complete system.
About the value g 0 say she is actual value g at t = t 0 . It is also said that g 0 is a characteristic actual state of the whole system s at the moment of time
If g \u003d g 0 \u003d 1, then we can say that the integral system s at the time t \u003d t 0 is in the best - normal- condition. In general, the value of g can be said to be
measure of proximity of the actual state of the integral system s to its possible normal state at time t = t 0 .
Similarly, the quantity g j can be said to be a measure of the closeness of the actual state j -th functional element of the integral system s to its possible normal state at time t = t 0 .
So, the measure of the manifestation of the UIC and the measure of the proximity of the actual state to a possible normal state are two different names for the same value. The first name, perhaps, makes sense to apply among philosophers, and the second - among biologists, physicians, engineers, sociologists and physicists.
In general, according to (7), we have
g min £ g £ 1, (8)
g min - minimum allowable at time t = t 0 the value of g for the whole system s.
g j ≥ 0; j = 1..N(G)
However, for an integral system s, according to (1) and (3), we have
gj ≥ gjmin > 0; j = 1.. N(G) (9)
It is said that the jth functional element of the system s for t = t 0 is active, if
g min £ g j £ g
Denote
h j = 1 if g min £ g j £ g
h j = 0, in all other cases
According to (6), we have
g = 1 z g j = 1; j = 1..N(G)
With this in mind, from (11) and (12) we obtain
m = N(G) for g = 1 and m
those. generally
m £ N(G)
g min £ g j
g j = 1 for j = m + 1, m + 2,.., N(G)
The quantity m is said to be the quantity active functional elements of the system s at t = t 0 .
Taking into account (13), dependence (6) can be rewritten in the form
g = 1 Û g j = 1 for all j = 1.. m (14)
As can be seen, in order to achieve the goal
at t = t 0 it is necessary and sufficient to achieve a set of goals
g j → 1; j = 1.. m (16)
2. Measuring a single integrative quality
Let, given a set of data
M j1 , S j 1 and N j 1 ; j = 1..N (17)
M j1 is the sample arithmetic mean of the value y j н Y, which serves as a characteristic of the actual state of the j-th functional element of the integral system s at t = t 0 ;
Y- studied a set of quantitatively measured quantities serving at t = t 0 as primary indicators of the state of the integral system s: Y 0í Y í Y(G);
Y 0 - the general set of quantitatively measured values that serve as primary indicators at t \u003d t 0 actual states active functional elements of the integral system s: h j = 1 for y j н Y 0 ; j = 1..m;
S j 1 is the sample standard deviation of the value y j н Y, which serves as a characteristic of the actual state of the j-th functional element of the integral system s at t = t 0 ;
N j 1 is the sample size of the measurement results of the quantity y j О Y during the time from t j0 – Δ j0 to t 0: N j 1 ≥ 1 ;
Δ j0 is the time interval during which the state of the j-th functional element of the integral system s remains practically unchanged;
N is the volume of Y: m £ N £ N(G).
M j0 , S j 0 and N j 0 ; j = 1..N, (18)
serving as selective characteristics normal states of a typical representative of a homogeneous group of integral systems to which system s belongs in the normal state.
Denote
δ j * = 
and τ j * = τ(P,(N j 0 + N j 1 – 2)),
τ j * - critical value of the Student's criterion for a given confidence probability P and degree of freedom N j 0 + N j 1 – 2.
P ≥ 0.95 and N j 0 >> 1 ; j = 1..N
Let us assume that the samples, according to which the populations (11) and (12) are established, are representative with probability P and the condition
Then you can operate on the dependency:
│M j1 - M j0 │
If this condition is satisfied, then with probability P. it is asserted that the value y j н Y is within the limits generally accepted statistical norm and write:
g j = 1 for │M j1 - M j0 │
Denote.
d j 1 = S j 1 and t j 1 = t(P, 2(N j 1 – 2)),
t j 1 - critical value of Student's criterion for given confidence probability P and degree of freedom 2(N j 1 – 1).
d j 1 t j 1 > 0 (21)
Denote.
δ j = δ j * and τ j = τ j * for d j 1 t j 1 £ δ j * τ j *
δ j = d j 1 and τ j = t j 1 for d j 1 t j 1 > δ j * τ j *
According to (2), (14), and (15), we have
0 £ δ j * τ j * (23)
Hence
│M j1 - M j0 │
From here and from (13) we have
g j = 1 for │M j1 - M j0 │
Denote
A j = (M j 0 - Δ j , M j 0 + Δ j), (24)
Δ j = δ j τ j (25)
For a given confidence probability P, all values of the quantity y j н Y in the region A j are in fact indistinguishable from each other. However, in closed areas
A j * =
the following three values of y j н Y differ from each other:
y j = M j 0 - Δ j , y j = M j 0 and y j = M j 0 + Δ j
This means that in the region A j * the quantity y j н Y most accurately measured in units of Δj. But then this value in the rest of the area of its assignment should be measured in units of Δ j . Otherwise, the condition of equal accuracy of the measurement will not be fulfilled and, therefore, the values of the quantity y j н Y, set in the area A j * , will not be comparable with the values from the rest of the area of its setting.
According to (16) and (18), we have
Δj > 0; j = 1..N
This indicates that in general
where P max is the maximum possible value of P for system s at t = t 0 .
Denote by Δ j (G) the value of Δ j such that
Δ j = Δ j (G) at P = P max
The value of Δ j (G) is objectivelocal - local - unit of measurement of the quantity y j О Y in the system s at t = t 0 .
The value of Δ j is said to be evaluationΔj(G). It is also said that Δ j is subjective local - local - unit of measurement of the quantity y j О Y in the system s at t = t 0 .
If the condition is met
M j1 О A j ,
then with probability P. it is asserted that the quantity y j н Y is within the limits its subjective individual norm and write:
MZ j = M j1 for M j1О A j and MZ j = M j0 for M j1П A j , (26)
MZ j - subjective point individual norm quantities y j н Y for system s with
Denote
a = max(a j ; j = 1..N(G)), (28)
a j = at £ 0.5 and a j = 0.5 at > 0.5 (29)
According to (16), (20), (21) and (22) we have
Denote
3 £ NO £ PO £ PZ(G)
PZ(G) is the maximum possible value of PO for system s at t = t 0:
PO = PZ at P = Pmax
The value of PZ(G) is the probabilistic limit of knowledge of the truth in the system s at t = t 0 .
The value of PO, unlike PZ(G), depends on the confidence level P. The value of PO is said to be subjective the probability of actually knowing the truth in system s at t = t 0 . It is also said that PO is the probability of making the best decision in the system s at t = t 0 .
Denote
MZ j = MZ j (G) for PO = PZ(G)
The value of MZ j (G) is objective point individual norm
y j н Y for system s at t = t 0 .
According to (26), we have
M j 1 = MZ j for M j 1О A j
or, taking into account (24) and (25),
│M j1 - M j0 │
For a given confidence probability P in the open area A j, all values of the quantity y j О Y, as mentioned above, are in fact indistinguishable from each other. In view of this
a j = a jmin for M j 1 = MZ j and a j ≥ a jmin for M j 1 ¹ MZ j ,
where a jmin is the value of a j such that
a j = a jmin for │M j1 - M j0 │
In general, in a complete system, there are:
a jmin = a min for all j = 1..N(G)
a j > a min for j = 1..m and a j = a min for j = m +1, m +2, ..,N(G)
and hence
a = max(a j ; j = 1..N(G)) = max(a j ; j = 1..N) = max(a j ; j = 1.. m) (33)
Due to this, in order to achieve the goal (15), it is enough that the goals (16) are realized. This has long been known to physicians: in each pathology, the doctor always achieves the goals (16) for those indicators of the state of human health that, in this pathology, generally deviate from their statistical norms.
Denote
ΔO j = (1 – PO) MZ j
Taking into account (25), (28), and (29), we can check that
ΔO j ≥ Δ j = δ j τ j ; j = 1..N
and hence
│M i1 – M i0 │≥ ΔO i Þ │M j1 - M j0 │≥ δ j τ j for all i,j = 1..N (G)
So, in order to fulfill the condition
│M j1 - M j0 │≥ δ j τ j for all i,j = 1..N (G)
it is quite enough that there is at least one i = i 0 such that the condition
│M i1 – M i0 │≥ ΔO i at i = i 0 . (34)
This indicates that each value ΔO i contains information about the state of the entire set of functional elements of the system s, i.e. it is a system-wide feature.
The quantity y j н Y, according to (34), in the region
AO j =
has three different distinct values:
y j = M i 0 - ΔO i , y j = M i 0 and y j = M i 0 + ΔO i
Therefore, in the case when dependence (34) is operated on, the value must be measured in units of ΔO i .
Denote
ΔO j = ΔO j (G) at PO = PZ and MZ j = MZ j (G); j = 1..N ,
ΔO j = (1 – PO) MZ j
The value of ΔO j (G) is objective system unit of measurey j н Y for system s at t = t 0 .
We can say about the value of ΔO j that it is an estimate of ΔO j (G). One can also say that ΔO j is subjective system unit of measure y j н Y for system s at t = t 0 .
Denote
MO j = round(, 2) ∆O j ; j = 1..N
aO j = ΔO j if MO j ≤ MZ j and aO j = 2 MZ j - ΔO j if MO j > MZ j ; j = 1..N
Let MO j (G) be the value of MO j such that
MO j = MO j (G) for PO = PZ(G)
If system s is a typical representative, then there will be
MO j (G) = M j 1 (G),
where M j 1 (G) is the general average of M j 1 .
│MO j (G) - M j 1 (G)│≥ 0
The value of MO j (G) is the same objective characteristic of the state of the system s, which is the value of M j 1 (G) for a typical representative.
We can say that MO j (G) is an objective individual characteristic of the actual state system s at t = t 0 . And about the value of MO j, we can say that it is subjective individual characteristic of the actual state system s at t = t 0 .
The quantity aO j is said to be subjective maximum allowable the value of the quantity y j О Y for the system s at t = t 0 and write:
g j = g min at MO j = aO j (36)
Denote
dO j = +1 if MO j ≤ MZ j and dO j = -1 if MO j > MZ; j = 1..N ; (37)
βO1 j = 1 if (MO j -aO j) dO j ≥ 0 and βO1 j = 0 if (MO j - aO j) dO j
βO j = βO1 j , if │MO j - aO j │βO1 j ≤ │MZ j - aO j │
and j = 1..N (39)
βO j = 0 if │MO j - aO j │βO1 j > │MZ j - aO j │;
βO j 0 = 1 if (│MO j - aO j │ ≤ │MZ j - aO j │) Ù (βO1 j = 1)
βO j 0 = 0 – in all other cases;
SO j = S 11 if S 11 > 0 and N j1 ≥ 2
SO j = S 10 - in all other cases;
δO j = SO j ; j =1..N
γO j = 1 if │MO j - MZ j │
γO j = [(NO - 2) βO j + 1] if │MO j - MZ j │≥ δO j tO j
According to (30), we have
γO j = at βO j = 0
From here and from (23), (28) and (29) we have
g min = 1 – PO
and, therefore, according to (24),
g min = 0.5 Û PO = 0.5
According to (25), (28), and (30), we have
γO j = 1 for MO j = MZ j and γO j = g min for MO j = aO j (43)
Denote
The set of conditions (1), (2), (3), (4), (6) and (32) will be satisfied if we assume that in general
h j = βO j 0 ; j = 1..N
γ j = γO j ; j = 1..N
With this in mind, from (6), (30), (34) and (36) we obtain
γ j = 1 if │MO j - MZ j │
γ j = [(NO - 2) βO j + 1] if │MO j - MZ j │≥ δO j tO j
h j = 1 if (│MO j - aO j │ ≤ │MZ j - aO j │) Ù (βO1 j = 1)
h j = 0 – in all other cases.
According to the above algorithm, when determining γ, each value y j н Y is successively measured in three different units of measurement:
Δ(P) j , Δ j and ΔO j ; j = j0 ; j 0 = 1..N,
Δ(П) j is the accuracy of the measuring device of the value y j н Y used in the collection of initial data
B jk = (b jl k ; j = 1..N jk); k = 0.1; j = j0 ; j 0 = 1..N; (47)
Δ j is the measurement accuracy of the quantity y j О Y, established as a result of data analysis (46);
ΔO j - measurement accuracy of the quantity y j н Y, established as a result of the analysis all collections of data
B jk = (b jl k ; j = 1..N jk); k = 0.1; j = 1..N (48)
At the same time, there is
ΔO j ≥ Δj ≥ Δ(П) j > 0; j = j0 ; j 0 = 1..N
The value Δ j is the local unit of measure y j О Y, and the value ΔO j is the system unit of measure y j О Y.
As you can see, the local unit of measurement Δ j of the value y j О Y is used locally – elemental- system control level s, and the system unit of measurement ΔO j - at the upper control level of this system.
As a result of data analysis (47), at the local level of control, in addition to Δ j , the value MZ j is also set, which serves as a subjective point individual norm of the value y j О Y in the system s at t = t 0 .
As a result of data analysis (48) on systemic control level, except for the values
ΔO j ; j = 1..N
set and values
MO j ; j = 1..N
serving as subjective point individual characteristics of the actual state of the system s at t = t 0 .
ΔO j ≥ ΔZ j ≥ Δ j ≥ Δ(P) j > 0; j = 1..N, (49)
ΔZ j is the value of ΔO j such that
MZ j = round(, 2) ΔZ j with ΔO j =ΔZ j ; j = 1..N
and, therefore, according to (35), we have
MO j = MZ j at ΔO j =ΔZ j ; j = 1..N
However, if at t = t 0 the system s is in the normal state in the broad sense and, consequently, γ = 1, then
ΔO j = ΔZ j = Δ j ≥ Δ(П) j > 0 for all j = 1..N, (50)
those . in the normal state at both levels of control of the system s each value
y j О Y is measured in the same units ΔZ j .
It should be noted that in modern social systems, as a rule, there is:
ΔO j >ΔZ j > 0; j = 1..N
So, if sets (10) and (11) are given, then using relation (46) it is possible to quantitatively measure how close the actual state of the integral system s is to its possible normal state at a given time.
A detailed justification for the method for determining the value of γ is given in.
Conclusion
1. Using the conceptual apparatus of mathematical statistics, we describe general patterns of processes occurring in complete systems and an algorithm for determining the value of γ was compiled,
γ is a quantitative measure of the proximity of the actual state of the system to its possible normal state at a given time:
γ min £ γ £ 1,
γ min is the minimum possible value of γ for the system at a given time:
0.5 ≥ γ min > 0.
2. This algorithm, representing a sequence of objective laws of nature, determines the value of γ with the accuracy with which the actual and possible normal state of the system is examined.
At the same time, the algorithm is applicable to any system of animate and inanimate nature, which is integral with the probability PO = PO(G),
PO(G) - the probability of actual knowledge of the truth in the system at a given time
0.5 £PO(G) £PZ(G)
PZ(G) is the probabilistic limit of knowledge of the truth in the system at a given time.
3. The system for which PZ(G) = 0.5 is the simplestcomplete system. The simplest integral systems are, for example, pairs: "Man + woman" and "Electron + positron".
For the simplest integral system, we have
PO(G) = PZ(G) = 0.5
and ultimately
γ = γmin = 0.5,
those. these systems have only one indefinite- condition. This state is indeterminate in the sense that it is and is not normal in the same measure.
4. For each biological and other complex system, the value of PZ(G) is an increasing function of time t until the moment t = t n is reached, where t n is the beginning of the time period when the value of PZ(G) becomes closest to 1.
During the time from t \u003d t n to t \u003d t to the value of PZ (G) remains unchanged, where t to - the end of the time period when the value of PZ (G) is closest to 1. About the period of time from t n to t to say he is the heyday of the whole system. It is believed that for modern healthy for a person, this is the period from t n \u003d 25 years to t k \u003d 45 years.
From the moment t = t n for a complex system, the value of PZ(G) becomes a decreasing function of time t until the moment when PZ(G) = 0.5 is reached.
5. The position "Our reality is the unity of opposites" is equivalent to the position: "Our reality is the unity of the simplest integral systems." It follows from this that each complex system is a well-defined unity of the corresponding simplest integral systems.
6. The simplest integral systems of inanimate nature are primary, and the simplest integral systems of living nature are secondary. In view of this, each complex system, being historical, in the end, becomes a set - a bunch - of the simplest integral systems of inanimate nature.
Thus, any complex system eventually turns into a bunch of the simplest integral systems of inanimate nature.
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