Analysis. Under analysis understand the division of an object (mentally or actually) into its component parts for the purpose of studying them separately. Such parts can be some material elements of the object or its properties, characteristics, relationships, etc. Analysis is a necessary stage in the knowledge of the object.
In progress synthesis the component parts (sides, properties, features, etc.) of the object under study, dissected as a result of analysis, are brought together. On this basis, further study of the object takes place, but as a single whole. At the same time, synthesis does not mean a simple mechanical connection of separated elements into unified system. It reveals the place and role of each element in the system of the whole, establishes their interrelation and interdependence, i.e., it allows us to understand the true dialectical unity of the object being studied.
Analysis and synthesis are also successfully used in the sphere of human mental activity, that is, in theoretical knowledge. But here, as at the empirical level of knowledge, analysis and synthesis are not two operations separated from each other.
Analogy– a method of cognition that allows, based on the similarity of objects according to one characteristics, to draw a conclusion about their similarity according to others. Analogy is called inference from individual to individual or from particular to particular.
Close to analogy is the method comparisons , allowing us to establish not only the similarity, but also the difference between objects and phenomena. Analogy and comparison do not have great explanatory resources, but they help to establish additional connections and relationships of the object. Analogy and comparison allow us to put forward new hypotheses and thereby contribute to the development of scientific knowledge.
Modeling– this is the operation of an object that is an analogue of another, for some reason inaccessible for manipulation. Thanks to modeling, it is possible to gain insight into the inaccessible properties of an object using its analogue. Based on the knowledge obtained using the model, a conclusion is made about the properties of the original. Modeling is based on analogy.
Ethical principles of scientific research:
The intrinsic value of truth
Initial criticism
Freedom of scientific creativity
Novelty of scientific knowledge
Equality of scientists in the face of truth
Public availability of truth
Bioethics is a direction on the border of science and the system of human values. Studies a complex of problems associated with any intervention in the life of living systems (transplantation, genetic engineering, resuscitation, new reproductive technologies, the status of the human embryo, the problem of human death, including euthanasia)
Pseudo-scientific activities(alchemy, astrology, etc.) preceded science and subsequently went alongside science. Modern pseudoscience, like real science, is very heterogeneous in composition. This includes various esoteric and mystical teachings, the practical activities of sorcerers, magicians, and psychics. These teachings, which can be called parascientific (from the Greek para- “about”), actually do not need scientific justification. The scientific status they strive for is needed
only to increase their rating and authority. Such pseudosciences include parapsychology, bioenergy, the doctrine of the biofield, astrology, etc. Pseudoscientific ideas also arise in the depths of real science, when scientists “forget” about scientific methods, scientific ethics, trying to accomplish scientific revolution on the empty place. The objects of study of such pseudoscientists are unidentified flying objects (ufology), torsion and information fields, laser-holographic properties of biological objects and other problems of the so-called deviant science.
For SRS, the stages of formation are the history of the development of KSE
How to divide a model into submodels, how to build a hierarchy of models for studying elements (decomposition) and how to then combine them to study the system as a whole in order to explain the whole through particulars is the main problem of modeling.
The general methodology is based on a combination of analysis and synthesis methods. Synthesis is to create a description of an object, analysis is to determine the properties of an object from its description, i.e. during synthesis, projects of objects are formed, and during analysis, projects of objects are evaluated.
The unity of analysis and synthesis applies to all branches of knowledge, incl. to modeling. As is known, there are no algorithms for “analysis-synthesis” - only the general methodology is defined (how the operations of analysis and synthesis are performed).
The interaction of system elements is characterized by direct and feedback connections. The essence of system analysis is to identify these connections and establish their influence on the behavior of the entire system as a whole.
Analysis (from the gr. analysis - decomposition, dismemberment) involves the study of the behavior and properties of a system of a given structure when interacting with the external environment (the object exists, it is necessary to study its properties - system analysis, spectral analysis, blood test, etc.).
The purpose of the research is a qualitative and quantitative assessment of the properties of the system, various process control strategies, characteristics of elements and their combinations. The main analysis procedure is the construction of a generalized model that adequately reflects the properties of a real system and its relationships that interest the researcher. Process characteristics are determined as functions of system parameters.
To understand a system, study it, explore it (the task of analysis), it is necessary to describe the system, record its properties, behavior, structure and parameters, that is, build one or more models.
To do this you need to answer three main questions:
- what does the system do(find out the behavior, function of the system);
- how it works system (find out the structure of the system);
- what is the quality of the system(how well it performs its functions).
Description of the object as a system
There is some dependence between different types of parameters: the output parameters of an object (and, therefore, its quality) depend on input influences, parameters of the external environment and on the quality of the elements that make up the object ( X-parameters).
This dependence is presented in analytical form and is called global(integrative) function of the object.
The existence of a global function does not mean that it is known to the researcher or designer of the object - it is necessary to find this function.
If the global function cannot be represented in analytical form, for complex objects an algorithmic description of the object is provided (in the form of a behavioral simulation model).
Basic analysis operation (informal) – decomposition(dividing a whole into parts). In relation to building the structure of the model - determining the composition of the model (components).
Component is any part of the subject area that can be isolated as some independent entity. This is the system (model) as a whole, and any part of the system (model) - a subsystem, an element.
Main complexity of decomposition– determination of basic (indivisible) models of components, the relationship between micro- and macro-approach models. Decomposition is based on achieving a compromise between the completeness of the set of formal models of the system under consideration and simplicity; it can be achieved if the model includes only models of components that are significant in relation to the modeling goal.
Examples of analysis methods are analytical methods often used in mathematics: expansion of functions into series, spectral analysis, differential and integral calculus, etc.; in physics – molecular dynamics methods; in production - conveyor manufacturing technology.
Basic principles of analysis technology
In system analysis, one of the most important criteria for the effectiveness of decomposition are the criteria for the completeness of the decomposition and its simplicity, which are directly related to the completeness of the system model taken as the initial one for decomposition and the goals of its construction.
The main operation in analysis is dividing the whole into parts, i.e. decomposition is a method of decomposing a system into individual elements, which can be performed sequentially several times.
When decomposing, a certain compromise between completeness and simplicity must be accepted, achieved if only elements that are significant in relation to the purpose of the analysis are included in the structural model.
Enlarged decomposition algorithm
The number of decomposition levels (tree structure levels) is determined as follows.
Decomposition along each branch of the tree structure is carried out until it leads to the receipt of system elements that do not require further decomposition. Such components are called elementary.
To determine elementaryity, both formalized and non-formalized (expert) criteria are used.
The part of the system that cannot be considered elementary based on the selected criteria is subject to further decomposition. If the researcher has not achieved elementaryity on any branch of the tree structure, then new elements are introduced into the model taken as the basis, and the decomposition continues along them.
The process of model synthesis based on a systems approach includes the following steps:
1. Formation of requirements for the system model based on the purpose of the research (determined by the questions to which the researcher wants to get answers using the model) based on initial data, including the purpose of the model, operating conditions of the system, external environment for the system and imposed restrictions.
2. Definition of model subsystems based on the system actions necessary to fulfill the purpose of the system.
3. Selection of elements of model subsystems based on data for their implementation.
4.Selection of the constituent elements of the future model.
The resulting model is an integrated whole.
Synthesis involves creating the structure and characteristics of a system that ensure its specified properties.
System synthesis includes:
Determination of all necessary functions to solve the problem;
Finding ways to perform each function (formation of subsystems);
Determining a scheme of interaction between subsystems that would allow the tasks to be completed in the best possible way.
Alternative options for structural and functional diagrams compiled as a result of synthesis are examined in the process of analysis - the properties of pre-developed project options and the effectiveness of each option are examined.
The output parameters of an object (and, therefore, its quality) depend on input influences, parameters of the external environment and on the quality of the elements that make up the object.
Basic principles of synthesis technology
The variety of areas of application of complex systems, possible structures and process control strategies gives rise to a huge variety of options for their construction, which leads to the impossibility of solving the synthesis problem in a general formulation.
The resulting set of elements obtained as a result of decomposition (analysis), in addition to external integrity (i.e., a certain isolation from environment, well described by the “black box” model) must have internal integrity.
Internal integrity is related to the system structure model, i.e. establishing relationships between elements, the implementation of which is called an aggregation operation - combining several elements into a single whole. The result of aggregation (synthesis) is a system called an aggregate.
The properties of a component are not just a collection of properties of its individual elements. A component may have properties that none of its elements, taken separately, have, i.e. the component acquires a new quality that could not have appeared without this unification.
Examples of complex systems
The Earth observation space system as a complex technical system
Objectives of the Earth Observation Space System
Problems on a global scale are now intensifying: the reduction of reserves of critically important natural resources, increasing pollution and habitat degradation, increasing number of natural and man-made disasters, global warming climate change, the growth of terrorism and drug trafficking. Information Support of these problems - based on the rapid collection, processing and provision of necessary information to users - is provided by the space-based global Earth monitoring system.
Today in the world there are dozens of countries participating in the implementation of space observation programs - the level of informatization is becoming an increasingly important criterion for assessing the power and security of any state and an important means of developing internal and external strategies.
Modern problems solved by the Earth observation space system:
Weather observations and analysis of climate change on the planet;
Search for minerals, oil and gas fields;
Analysis of large-scale vegetation dynamics;
Monitoring of aquatic biological resources, observation and control of the activities of fishing vessels;
Ice situation analysis;
Monitoring the technical condition of industrial complexes;
Accounting and monitoring of city development (control over land resources and real estate);
Operational forecast and control of natural and man-made emergencies (monitoring of earthquake precursors, ecological situation, forest fires).
These tasks determine the requirements for satellite surveillance equipment: operational observation, increasing image resolution, increasing the survey bandwidth, mastering all informative ranges of the electromagnetic radiation spectrum.
Main modern development trends satellite observation – transition to digital data for the presentation of spatial information, as well as to digital spatial data bases as the basis for analytical work related to the modeling of objects or processes.
The importance of the military aspect is increasing - more and more countries want to have digital maps of increasing resolution (solving reconnaissance and target designation problems) and constantly update them.
Spatial data, linked to terrain using modern navigation systems, acts as the basis for various information, and the process of updating it is endless.
The joint European and American satellite navigation system (Galileo and GPS) will make it possible to determine coordinates with an accuracy of up to 2-3 m in normal mode and up to millimeters in differential mode - using a differential station ( a navigation signal receiver precisely tied to the terrain, which in a certain area issues corrections to other satellite navigation receivers).
New opportunities have emerged - small receiving stations and software products, which allow you to independently receive raw survey data in real time and immediately process them (which is much cheaper than purchasing processed images). This is especially important for some operational tasks, for example, in emergency situations, during environmental monitoring or operational monitoring of production (technical condition monitoring).
Small spacecraft (weighing up to 150 kg) are being widely developed, on the basis of which in the future independent, cost-effective multi-satellite systems can be formed for super-operative global observation of the most rapidly developing natural and man-made emergency situations. Orbital systems based on small spacecraft will be able to provide a combination of high information characteristics with high efficiency. This will stimulate an increase in demand for space information, which will ensure high investment potential for such projects.
The Earth observation system is a complex multifunctional technical system - a combination of a large number of different types of elements and heterogeneous connections between them, combined to perform complex tasks.
The system has a goal, interconnected components form a multi-level structure and perform functions aimed at achieving the goal, and has control, thanks to which all components function in a coordinated and purposeful manner.
Composition and structure of the Earth observation space system
A space-based Earth observation system may be part of a larger system for studying natural resources (depending on the system’s objectives), including space, airborne, ground-based, and marine observation systems.
Isolation of a specific system from the external environment is a subjective factor and is determined by design goals.
The quality of problem solving is determined by the system parameters and the characteristics of the components included in the space system.
The Earth observation space system is a set of functionally interconnected spacecraft and ground-based technical means, designed to solve target problems. The structure of the system is presented in Figure 1.1, information flows - in Figure 1.2.
The main functional element of the Earth observation space system is the spacecraft (SV).
Spacecraft as a complex technical system has a purpose of operation (observation of the Earth and transmission of information about the results of observation to Earth), consists of interconnected elements that ensure the fulfillment of the purpose of the system, and is an element of a higher level system (space system for Earth observation).
The external environment of the spacecraft is the natural environment (outer space) and other components of the Earth observation system.
Structurally, the spacecraft consists of two main subsystems - payload - target equipment (hardware and software necessary to obtain the required information) and a platform that ensures the operation of the payload and the transmission of the received information to Earth (service subsystem).
The composition of the target equipment is determined by the tasks assigned to the Earth observation space system and the characteristics of the observation object (external environment).
To obtain data on various natural and economic objects, both passive (photographic, optical-mechanical and optical-electronic, radiometric, spectrometric) and active (radar) systems in ultraviolet (UV), visible (V), infrared (IR) are used. and microwave (microwave, i.e. ultra-high frequency) regions of the spectrum.
Spacecraft platform provides conditions for the normal functioning of the payload: maintaining the specified parameters of the orbit and orientation of the spacecraft, ensuring the required operating conditions for the equipment (power supply, thermal conditions), issuing control commands to the payload, collecting target and telemetric information and transmitting it to Earth, ensuring structural integrity and rigidity.
Main platform subsystems:
Control system;
Orientation and stabilization system;
Power supply system;
Command-measuring system;
Satellite navigation equipment;
Solar panel orientation system;
Corrective propulsion system;
Design (including on-board cabling, antennas, separation and thermal management systems).
General requirements to the design:
Minimum dead weight;
Ensuring the required viewing angles of information equipment sensors and orientation systems;
The solar panel deployment system must meet safety and reliability requirements, and the layout of these panels must ensure the minimum possible moment of inertia on the SOSB drive shaft to reduce the weight and energy consumption of the latter;
Ensuring minimal disturbing moments from light and aerodynamic pressure;
The design should ensure ease of installation, testing and debugging of ground-based work, without complicating access to devices and cable network;
When placing equipment, the condition of minimizing the length of cable connections must be taken into account to reduce energy losses in wires and ensure electromagnetic compatibility of the equipment.
Ground system (ground segment) provides tracking and control of the spacecraft, transmission of commands for receiving and processing payload information and telemetry information, issuing information to consumers. Typical components of the ground segment: a control complex, a complex for receiving, processing and distributing information, a center for planning surveys and their archiving.
If the observation system includes more than one spacecraft, then their combination forms a separate subsystem - an orbital constellation. In this case, the spacecraft is created on the basis of a unified space platform.
The Earth observation space system may also include rocket and space complexes to create and maintain the system’s orbital constellation.
Figure 1 Structure of the space-based Earth observation system
Figure 2 Information flows of the Earth observation space system
The space system is a single complex multicomponent multifunctional system distributed in a three-dimensional space that is practically unlimited in volume. Individual components of space systems can simultaneously be components of other systems.
As a cybernetic system, the space system has the following specific features:
Is distributed;
has a high degree of automation, has a high proportion of information component, technical and technological diversity;
has high operational stability;
subsystems operate under conditions of uncertainty regarding the external environment;
is a permanently developing system;
has a pronounced innovative character.
From the point of view of systems theory, an orbital constellation is precisely a system, and not just a collection of spacecraft: the tasks of a spacecraft and an orbital constellation are fundamentally different. One spacecraft is not capable of ensuring the fulfillment of the target task - the fulfillment of the target task by the space system can only be achieved as a result of the overall functioning of the spacecraft.
The arrangement of elements in space is not random, tasks between spacecraft are strictly distributed, the functioning of an individual spacecraft at a given time depends on the functioning of other spacecraft and the state of the entire system, target information from each individual spacecraft is included in the general flow.
Spacecraft in an orbital constellation are in different relationships with each other: by location in space, by functional tasks, etc. An orbital constellation is an artificial multi-component space object distributed in space. This object serves as a large space station in the space system.
Complex socio-economic system.
Under economic system refers to any system in which cost or natural commodity variables operate.
An individual firm can act as an economic system; a technical or technological system that takes into account the cost of technical means or products; industry; state economy.
An economic system in which social factors operate is called socio-economic. In particular, any macroeconomic system of a state or region cannot but include the social sector and is therefore socio-economic 1.
The international standard ISO 9000:2000 defines an organization as a group of workers and necessary facilities with a distribution of responsibilities, powers and relationships.
Another definition can be given: an organization is a systematized, conscious association of the actions of people pursuing specific goals.
The concept of “organization” is revealed in Fig. 1 model of technical terms.
Rice. 1. Types of organizations represented using a model of technical terms
Rice. 2. Connections of the system-organization with the external environment.
The created model should answer the following questions:
Who in the organization should perform specific functions?
Under what conditions should the function be executed?
What should an employee do as part of this function?
How should it be done?
What resources are needed?
What are the results of executing the function?
What information tools are needed?
How can all this be reconciled?
How can all this be accomplished most effectively?
How can you change or build a business process?
How to reduce risk and increase the effectiveness of change?
2 CONSTRUCTION OF MATHEMATICAL MODELS
2.1 Mathematical model, mathematical modeling – basic concepts, terms and definitions
No definition can fully cover the actual activity of mathematical modeling. Despite this, definitions are useful in that they attempt to highlight the most essential features.
It is desirable to find a definition of a mathematical model that would make it possible to classify (cover) all existing and newly created models. Let us dwell on the formulation of the mathematical model, which reflects its target essence based on the concept of mathematical modeling as the process of constructing a model and research with its help.
The term “mathematical modeling” covers the methodologically unrelated development of a model and its use. Sometimes modeling refers to each of these two stages separately.
Mathematical modeling is a way of research various processes by studying phenomena that have different physical contents, but are described by the same mathematical relationships.
One of the aspects of mathematical modeling as a way of cognition is the study of a system or phenomenon using a computational experiment (in this understanding, the term “computational experiment” can be synonymous with the term “mathematical modeling”).
Many problems in systems research are difficult to formalize well enough and reduce to mathematical models that allow setting and solving the problems. Misunderstanding (or the inability to clearly state the problem) often leads to the “victory of mathematics over reason.” A systems researcher must be able to formalize a specific research problem in mathematical terms - to develop a mathematical model.
In practice, mathematical modeling as a research method has no limitations, since:
The modeling system can simultaneously contain descriptions of continuous and discrete action elements,
Be subject to the influence of numerous random factors of a complex nature;
It is acceptable to describe a high-dimensional relation system; ease of transition from one problem to another is ensured by introducing variable parameters, disturbances and various initial conditions.
Mathematical model as a means of cognition and research real world is formed on the basis general methodology for systems research.
Among the many approaches to building systems, two main ones can be distinguished (approaches “from below” and “from above”) - the desire to really study existing systems and based on this, draw conclusions about the observed patterns (L. Bertalanffy’s approach), and consider the set of all conceivable systems, reducing it to rational limits (W. Ashby’s approach).
Math modeling as one of the types of sign modeling, it is a formal description of an object in the language of mathematics, and the study of a model using mathematical methods.
Math modeling- the process of establishing a correspondence between a given real object and a certain mathematical object, called a mathematical model, and the study of this model, which allows one to obtain the characteristics of the real object in question.
Mathematical models are symbolic models.
Mathematical model– description in the form of mathematical relationships (for example, formulas, equations, inequalities, logical conditions, operators) of the state, changes, processes in a system or phenomenon (including the functioning of the system), depending on system parameters, input signals, initial conditions and time.
Mathematical model- this is the “equivalent” of an object, reflecting in mathematical form its most important properties - the laws to which it obeys, the connections inherent in its constituent parts.
Mathematical model- an abstract mathematical representation of a process, device or theoretical idea; it uses a set of variables to represent inputs, outputs, and internal states, and a set of equations and inequalities to describe their interactions. (The definition is based on the “input-output-state” idealization borrowed from automata theory).
Finally, the most succinct definition of a mathematical model: an equation that expresses an idea.
The type of mathematical model depends both on the nature of the real object and on the tasks of studying the object, the required reliability and accuracy of solving this problem. The mathematical model reflects exactly those features that need to be studied to solve the problem.
Typically, a mathematical model only approximately describes the behavior of a real system, being its abstraction, since knowledge about a real system is never absolute, and hypotheses are often forced or intentionally not taken into account some factors.
To support mathematical modeling, developed computer simulation systems, for example, Matlab, Matcad, etc. They allow you to create formal and block models of both simple and complex processes and devices and easily change model parameters during modeling. Block models are represented by blocks (most often graphic), the set and connection of which are specified by the model diagram.
The main quality of mathematical models is " variation". One symbolic description encodes physically different systems and phenomena. On the same model they can be studied big number options for its behavior (by changing parameters).
Versatility of models: Fundamentally different real phenomena can be described by the same mathematical model. For example, oscillatory processes of completely different nature are described by the same mathematical model - we immediately study a whole class of phenomena described by it.
The main task of mathematical modeling: using given input parameters, find the values of the system’s output parameters (map some given set X of values of input parameters x to a set Y of values of output parameters y).
A model is a pattern that transforms input values into output values: Y = M(X). By this we can mean a table, a graph, an expression from formulas, a law (equation), etc. This is a question of how to write a pattern. Y- some indicator of interest to the researcher.
On this basis, when defining the concept of “mathematical model”, the broad concept of an operator is used - a function, an algorithm, a set of rules that ensure the establishment of output parameters based on given input parameters.
A mathematical model can be considered as a certain mathematical operator and the concept of a mathematical model can be formulated as follows.
Mathematical model – any operator (rule) A, which allows, based on the values of input parameters x, to set the corresponding output values of parameters y of the system:
A: x → y, xÎ X, yÎ Y.
Such a broad definition includes not only the whole variety of mathematical models, but also information models - the procedure for searching data in a database can be represented as a certain operator. In this context, an information model is a specific form of a mathematical model.
Basic concepts in system modeling are determined from correspondence with similar system concepts: system element, connection, external environment.
Modeling as a research method has the following structure: problem statement, creation of a model, study of the model, transfer of knowledge from the model to the original.
Mathematics is a science that studies patterns of models regardless of their specific implementation and methods (ways) of using models to solve specific problems. The requirements for ensuring mathematical rigor in systems research are unrealistic (claims to absolute truth); the basis of system research is an informal simplification of the problem that is adequate to the goals set.
Therefore multiple models of one object: for each purpose, its own model of the same object is required (multiple models of one object, for example - aircraft models for research on aerodynamics and strength).
The model can focus on the functions of the system (functional model) or on its objects (data models).
Functional models allocate events in the system, represent with the required degree of detail a system of functions, which in turn reflect their relationships through system objects.
Data Models allocate objects systems that connect functions with each other and with their environment and represent detailed description system objects connected by system functions.
Scientific methods of theoretical research.
1. Theoretical analysis and synthesis. Elemental analysis. Analysis by units.
2. Methods of abstraction and concretization. Ascent from the abstract to the concrete.
3. Modeling method.
4. Thought experiment as a type of modeling.
5. Induction and deduction.
6. Formalization.
7. Hypothetico-deductive method, its essence.
8. Axiomatic method.
The theoretical level of scientific knowledge reflects phenomena and processes from their universal internal connections and patterns; this is achieved through rational processing of data from the empirical level of knowledge. Therefore, it involves all forms of thinking - concepts, judgments, inferences, general logical methods, as well as methods associated with mental operations: abstraction, idealization, formalization, etc.
The purpose of the theoretical level is not only to establish facts and reveal external connections between them, but also to explain why they exist, what caused them, and to identify possibilities for their transformation.
Theoretical methods (and this is their drawback) do not directly influence the variety of observed facts, but they make it possible to discover hidden patterns in facts, general, necessary, essential ones, and to understand the mutual influence of factors determining development.
The truths that are revealed by the methods of theoretical research are theoretical truths that are directly verified not by experimental, practical means, but by proof. Practice takes part in the substantiation of theoretical truths indirectly, through truths that have already been verified. This is due to the composition of this method.
The most important difference The difference between theoretical knowledge and empirical knowledge is that it makes it possible to transfer conclusions obtained in some conditions and on the basis of the analysis of some objects to other conditions and objects, including those that do not yet exist, those that are being projected, those that are still being created mentally, in the imagination.
Let us move on to characterize the methods of theoretical research (cognition).
Theoretical analysis and synthesis. Elemental analysis. Analysis by units.
Originality method theoretical analysis and synthesis in its universal capabilities to consider the phenomena and processes of reality in their most complex combinations, to highlight the most essential features and properties, connections and relationships, to establish patterns of their development.
Analysis(Greek – decomposition, dismemberment) – division of an object into its component parts for the purpose of their independent study.
Analysis task is to from various types of data reflecting individual phenomena and facts, create an overall holistic picture of the process, identify its inherent patterns and trends.
Special attention deserves characteristic analysis from the point of view of dialectics, where it is seen as special reception researching phenomena and developing theoretical knowledge about these phenomena. The main cognitive task of dialectical analysis is to isolate its essence from the variety of aspects of the subject being studied, not by mechanically dividing the whole into parts, but by isolating and studying the sides of the main contradiction in the subject, to discover the basis that connects all its sides into a single integrity, and to derive on this basis the pattern of the developing whole.
IN social work analysis acts as a method or way of understanding social reality.
Analysis is used both in real (practice) and in mental activity. There are several types of analysis:
Mechanical dismemberment;
Determination of dynamic composition;
Identification of forms of interaction between elements of the whole;
Finding the causes of phenomena;
Identification of levels of knowledge and its structure;
Analysis by elements (elementary) and analysis by units.
Elementary analysis- this is the mental selection of individual parts, connections based on decomposition, dismemberment of the whole. For example, when studying real social processes, phenomena, contradictions, aggregates that contain contradictions and give rise to a problematic situation, it is possible for analysis to isolate separately their goals, content, external conditions, technology, organization, system of relationships of its subjects.
Unit analysis involves the dismemberment of a process while maintaining the integrity of its elementary structural elements, each of which retains the most important features of the entire process. In the activities of a client of a social work specialist, this can be an act; in socio-pedagogical design, it can be a social situation of personality development.
After completing the analytical work, the need arises for synthesis and integration of the analysis results in a common system.
Synthesis (Greek - connection, combination, composition) - real or mental unification of various aspects, parts of an object into a single whole.
In the Russian language dictionary S.I. Ozhegova synthesis is interpreted as a method of studying a phenomenon in its unity and interconnection of parts, generalization, bringing together data obtained by analysis into a single whole.
Thus, synthesis should be considered as the process of practical or mental reunification of a whole from parts or the connection of various elements, sides of an object into a single whole, a necessary stage of cognition.
The result of the synthesis is a completely new formation, the properties of which are not only an external combination of the properties of the components, but also the result of their internal relationship and interdependence.
Analysis and synthesis are dialectically interconnected. They play an important role in cognitive process and are carried out at all its stages.
The methods of abstraction and concretization are closely related to the methods of analysis and synthesis.
2. Abstraction (Latin – distraction)- mental abstraction of any property or feature of an object from its other features, properties, connections ( concept for research in social work) .
This is done in order to study the object more deeply, to isolate it from other objects and from other properties and characteristics.
To get to the core social phenomena, to identify the invariant features of the process under study, it is necessary to isolate the subject of study in a “pure” form, to be able to dissociate ourselves from all side influences, to abstract from all the numerous connections and relationships that prevent us from seeing the most significant connections and characteristics that interest us as researchers.
For example, in order to identify the educational potential of society, at the 1st stage it is possible to abstract from the conditions of the socio-economic crisis, political struggle, pedagogical failure of many families and consider in a “pure” form (without interference or inhibitory influences) the educational capabilities of the family, school, cultural institutions, law enforcement agencies, government and commercial structures, public organizations.
Exist different kinds abstractions:
– abstraction of identification, as a result of which general properties and the relationships of the methods being studied (other properties are ignored). Here, corresponding classes are formed on the basis of establishing the equality of objects in given properties or relationships, taking into account what is identical in objects and abstracting from all the differences between them;
– isolating abstraction– acts of so-called “pure abstraction” in which certain properties and relationships are highlighted, which begin to be considered as independent individual objects (“abstract objects” - “kindness”, “empathy”, etc.);
– abstraction of actual infinity in mathematics– when infinite sets are treated as finite. Here the researcher is distracted from the fundamental impossibility of recording and describing every element of an infinite set, accepting such a problem as solved;
– abstraction of potential feasibility– is based on the fact that any but a finite number of operations can be carried out in the process of mathematical activity.
Abstractions also differ in levels (orders). Abstractions from real objects are called first-order abstractions. Abstractions from first-level abstractions are called second-order abstractions, etc. The most high level abstractions are characterized by philosophical categories.
The limiting case of abstraction is idealization . Idealization is the mental construction of concepts about objects that do not exist and cannot be realized in reality, but those for which there are prototypes in the real world.
Abstraction during idealization is based on connections and qualities of phenomena that are fundamentally existing or possible, but abstraction is carried out so consistently, the subject is so completely isolated from accompanying conditions that objects are created that do not exist in the real world.
That is, in the process of idealization, there is an extreme abstraction from all the real properties of the object and, at the same time, features that are not realized in reality are introduced into the content of the concepts being formed. As a result, a so-called “idealized object” is formed, with which theoretical thinking can operate when reflecting real objects.
However, it is precisely these idealized objects that serve as models that make it possible to identify much deeper and more fully some connections and patterns that appear in many real objects.
Concretization method in its logical nature it is the opposite of abstraction. It consists in mental reconstruction, recreating an object on the basis of previously isolated abstractions.
Concretization, aimed at reproducing the development of a subject as an integral system, becomes a special method of research. Thinking from isolated individual abstractions concentrates a whole object. The result is concrete, but already mentally concrete (as opposed to real concrete, existing in reality).
What is called concrete here is the unity of diversity, the combination of many properties and qualities of an object.
Abstract, on the contrary, are one-sided properties or characteristics of a given object, isolated from other moments of development.
A special method of theoretical knowledge is method of ascent from abstract to concrete, aimed at reproducing development and its sources.
It is necessary both for the knowledge of complex processes, and for such a presentation of the results of knowledge that would allow the most adequate reproduction of the development and functioning of complex objects.
3. Simulation– a method of studying objects of knowledge on their models. It involves the construction and study of models of real-life objects and phenomena.
The need for modeling arises when researching the object itself is impossible, difficult, expensive, takes too long, etc.
There must be a certain similarity (relationship of similarity) between the model and the original: physical characteristics, functions; behavior of the object being studied and its mathematical description; structures, etc. It is this similarity that allows the information obtained as a result of studying the model to be transferred to the original.
Depending on the nature of the models used in scientific research, several types of modeling are distinguished.
1. Physical(material, objective): characterized by physical similarity between the model and the original, its goal is to reproduce in the model the processes characteristic of the original. Based on the results of studying certain physical properties of the model, they judge phenomena occurring in natural (“natural”) conditions. Neglecting the results of such modeling can have dire consequences. An example is the story of the English battleship Captain, built in 1870. The shipbuilding scientist V. Reed conducted a study of the ship model and identified serious defects in its design. He reported this to the Admiralty, but his opinion was not taken into account. As a result, the ship capsized when going to sea, resulting in the death of more than 500 sailors.
Currently, physical modeling is widely used for the development and experimental research various structures (power dams, irrigation systems, etc.), machines, etc. before they are actually built. For example, the aerodynamic qualities of aircraft are studied using models.
2. Perfect(mental): this type of mental representation includes a variety of mental representations in the form of various imaginary models. Models appear in the form of diagrams, graphs, drawings, formulas, systems of equations, etc.
For example, Rutherford's model of the atom resembled solar system: electrons (“planets”) revolve around the core (“Sun”). The same model can be realized materially in the form of sensory-perceptible physical models.
Ideal modeling includes the so-called “mental modeling,” which is classified into (see Table 1):
| 1) visual modeling is carried out on the basis of the researcher’s ideas about a real object by creating a visual model that displays the phenomena and processes occurring in the object | |||
| Hypothetical- a hypothesis is laid about the patterns of processes in a real object, which reflects the level of knowledge of the researcher about the object and is based on cause-and-effect relationships between the input and output of the object being studied | Analog is based on the use of analogies at various levels, the analog model reflects several or only one aspect of the functioning of the object | Layout associated with creating a model of a real object on a certain scale and studying it | |
| 2) symbolic modeling is an artificial process of creating a logical object that replaces the real one and expresses its basic properties using a certain system signs and symbols. Depending on the semantic units used, it is divided into | |||
| linguistic (descriptive) | iconic (graphic) | ||
| 3) mathematical modeling based on a description of a real object using a mathematical apparatus | |||
The complexity, inexhaustibility, and infinity of the object of research in social work forces us to look for simpler analogues for research in order to penetrate into its essence, into its internal structure and dynamics. An object that is simpler in structure and accessible to study becomes a model of a more complex object called a prototype (original). This opens up the possibility of transferring information obtained when using the model, by analogy, to a prototype. This is the essence of one of the specific methods of the theoretical level - the modeling method.
The modeling method is constantly evolving; some types of models are being replaced by others as science progresses. At the same time, one thing remains unchanged: the importance, relevance, and sometimes irreplaceability of modeling as a method of scientific knowledge.
4. A special type of modeling based on abstraction is thought experiment.
In such an experiment, the researcher, based on theoretical knowledge about the objective world and empirical data, creates ideal objects, correlates them in a certain dynamic model, mentally simulating the movement and situations that could exist in real experimentation. At the same time, ideal models and objects help in a “pure” form to identify the most important, essential connections and relationships for the knower, to play out projected situations, and to weed out ineffective or too risky options.
5. Induction (Latin - guidance) - a logical method (technique) of research associated with generalizing the results of observations and experiments and the movement of thought from the individual to the general.
In I., the data of experience “point” to the general, induce it. Since experience is always infinite and incomplete, inductive conclusions always have a problematic (probabilistic) nature. Inductive generalizations are usually regarded as empirical truths or empirical laws.
In the Russian language dictionary, induction is understood as a method of reasoning from particular facts and provisions to general conclusions.
Valery Pavlovich Kokhanovsky highlights the following types of inductive generalizations:
1) Induction is popular, when regularly repeating properties observed in some representatives of the set (class) under study and fixed in the premises of inductive inference are transferred to all representatives of the set (class) being studied - including its unstudied parts.
So, what is true in “n” observed cases is true in the next or all observed cases similar to them. However, the resulting conclusion often turns out to be false (for example, “all swans are white”) due to a hasty generalization. Thus, this type of inductive generalization exists until a case is encountered that contradicts it (for example, the fact that there are black swans). Popular induction is often called induction by enumeration of cases.
That is, when the number of cases is not limited, almost infinite, we are dealing with incomplete induction. This is a procedure for establishing a general proposal based on several individual cases, in which it was observed specific property, characteristic of all possible cases similar to the observed one, is called induction through simple enumeration.
The main problem of complete induction is the question of how legitimate such a transfer of knowledge is from individual cases known to us, listed in separate sentences, to all possible and even cases still unknown to us.
2) Induction is incomplete– where the conclusion is made that all representatives of the set under study belong to the property “n” on the basis that “n” belongs to some representatives of this set.
For example, Some metals have the property of electrical conductivity, which means that all metals are electrically conductive.
3) Full induction, in which the conclusion is made that all representatives of the set under study have the property “n” based on the result obtained with pilot study information that each representative of the set under study belongs to the property “n”.
Those. a general proposition is established by listing in the form of single propositions all the cases that fall under it. If we were able to list all the cases, and this is the case when the number of cases is limited, then we are dealing with complete induction.
When considering complete induction, it must be borne in mind that it does not provide new knowledge and does not go beyond what is contained in its premises. The general conclusion, obtained on the basis of a study of particular cases, summarizes the information contained in them, allows you to generalize and systematize it.
4) Scientific induction, in which, in addition to the formal justification of the generalization obtained inductively, a meaningful additional justification for its truth is given, including with the help of deduction (theories, laws). Scientific induction provides a reliable conclusion due to the fact that the emphasis is on necessary, natural and causal relationships.
In any scientific research it is often important to establish cause-and-effect relationships between various objects and phenomena. For this purpose, appropriate methods based on inductive inferences are used.
Let's look at the main inductive methods for establishing causal relationships(Bacon–Mill rules of inductive research).
A) Single similarity method: if the observed cases of a phenomenon have only one circumstance in common, then, obviously (probably), it is the cause of this phenomenon.
b) Single difference method: if the cases in which a phenomenon occurs or does not occur differ only in one preceding circumstance, and all other circumstances are identical, then this one circumstance is the cause of this phenomenon
V) Combined method of similarities and differences is formed as confirmation of the result obtained using the method of single similarity by applying the method of single difference to it: this is a combination of the first two methods.
G) Concomitant Change Method: if a change in one circumstance always causes a change in another, then the first circumstance is the cause of the second. At the same time, other previous phenomena remain unchanged.
The considered methods for establishing causal relationships are most often used not in isolation, but in conjunction, complementing each other.
Deduction (Latin – excretion):
– firstly, the transition in the process of cognition from the general to the individual (particular), the derivation of the individual from the general;
- secondly, the process of logical inference, i.e., the transition, according to certain rules of logic, from certain given sentences - premises to their consequences (conclusions). As one of the methods (techniques) of scientific knowledge, it is closely related to induction. These are, as it were, dialectically interconnected ways of moving thought. V.P. Kokhanovsky believes that great discoveries and leaps forward in scientific thought are created by induction, a risky but truly creative method. D. prevents the imagination from falling into error; it allows, after establishing new starting points by induction, to derive consequences and compare conclusions with facts. D. provides testing of hypotheses and serves as a valuable antidote to overextended imagination.
The term "deduction" appeared in the Middle Ages and was introduced by Boethius. But the concept of deduction as proof of a proposition through a syllogism already appears in Aristotle (“First Analytics”). An example of deduction as a syllogism would be the following conclusion.
The first premise: crucian carp is a fish;
second premise: crucian carp lives in water;
conclusion (inference): fish live in water.
7. Formalization - special approach to scientific knowledge, which consists in the use of special symbolism, which allows one to escape from the study of real objects, from the content of the theoretical positions describing them, and to operate instead with a certain set of symbols (signs). Example F. - mathematical description. To build any formal system you need:
1) specifying an alphabet, i.e., a specific set of characters;
2) setting the rules by which “words” and “formulas” can be obtained from the initial characters of this alphabet;
3) setting rules according to which one can move from some words and formulas of a given system to other words and formulas (the so-called rules of inference).
The advantage of F. is that it ensures brevity and clarity in recording scientific information. Formalized language is not as rich and flexible as natural language, but it is not ambiguous (polysemy), but has unambiguous semantics. Thus, a formalized language has the property of being monosemic.
The language of modern science differs significantly from natural human language. It contains many special terms and expressions; it widely uses means of formalization, among which the central place belongs to mathematical formalization. Based on the needs of science, various artificial languages are created to solve certain problems. The entire set of artificial formalized languages created and being created is included in the language of science, forming a powerful means of scientific knowledge.
7 . In scientific knowledge hypothetico-deductive method developed in the 17th and 18th centuries, when significant advances were achieved in the field of mechanics of earth and celestial bodies. The first attempts to use this method in mechanics were made by Galileo and Newton. Newton's work “Mathematical Principles of Natural Philosophy” can be considered as a hypothetico-deductive system of mechanics, the premises of which are the basic laws of motion. The method of principles created by Newton had a huge influence on the development of exact natural science.
From a logical point of view, the hypothetico-deductive system is a hierarchy of hypotheses, the degree of abstraction and generality of which increases as they move away from the empirical basis. At the very top are the hypotheses that have the most general character and therefore having the greatest logical power. From these, as premises, lower-level hypotheses are derived. At the lowest level of the system there are hypotheses that can be compared with empirical reality.
A mathematical hypothesis can be considered a type of hypothetico-deductive method, which is used as the most important heuristic tool for discovering patterns in natural science. Usually, some equations representing a modification of previously known and tested relationships act as hypotheses here. By changing these relationships, a new equation is created that expresses a hypothesis that relates to unexplored phenomena. In the process of scientific research, the most difficult task is to discover and formulate those principles and hypotheses that serve as the basis for all further conclusions. The hypothetico-deductive method plays an auxiliary role in this process, since with its help new hypotheses are not put forward, but only the consequences arising from them are tested, which thereby control the research process.
8. Close to the hypothetico-deductive method axiomatic method. This is a way of constructing a scientific theory, in which it is based on certain starting points(judgments) - axioms, or postulates, from which all other statements of this theory must be deduced in a purely logical way, through proof. The construction of science based on the axiomatic method is usually called deductive. All concepts of a deductive theory (except for a fixed number of initial ones) are introduced through definitions formed from a number of previously introduced concepts. To one degree or another, deductive proofs characteristic of the axiomatic method are accepted in many sciences, but the main area of its application is mathematics, logic, and some branches of physics.
All the methods of cognition described above in real scientific research always work in interaction. Their specific system organization is determined by the characteristics of the object being studied, as well as the specifics of a particular stage of the study.
The basic concepts of system modeling, system types and properties of models are considered, life cycle modeling (of the simulated system).
The purpose of the lecture: introduction to the conceptual foundations of system modeling.
Model And modeling - universal concepts, attributes of one of the most powerful methods of cognition in any professional field, cognition of a system, process, phenomenon.
Models And modeling bring together specialists from various fields working to solve interdisciplinary problems, regardless of where they are model and results modeling will be applied. View models and the methods of its research are more dependent on the information-logical connections of the elements and subsystems of the modeled system, resources, connections with the environment used in modeling, and not from the specific nature, specific filling of the system.
U models, especially mathematical ones, there are also didactic aspects - the development of a model style of thinking, which allows one to delve into the structure and internal logic of the modeled system.
Construction models- a system task that requires analysis and synthesis of initial data, hypotheses, theories, and specialist knowledge. Systems approach allows not only to build model real system, but also use this model to evaluate (for example, management efficiency, operation) of the system.
Model - an object or description of an object, a system for replacing (under certain conditions, proposals, hypotheses) one system (i.e. the original) with another system for better study the original or reproduction of any of its properties. Model- the result of mapping one structure (studied) onto another (little studied). Mapping a physical system (object) onto a mathematical system (for example, the mathematical apparatus of equations), we obtain a physical and mathematical model systems or mathematical model physical system. Any model is constructed and studied under certain assumptions and hypotheses.
Example. Consider a physical system: a body of mass m sliding down inclined plane with acceleration a, which is affected by force F. By studying such systems, Newton obtained the mathematical relation: F=ma. This is a physical and mathematical model systems or mathematical model physical system. When describing this system (building this models) the following hypotheses are accepted: 1) the surface is ideal (i.e. the friction coefficient equal to zero); 2) the body is in a vacuum (i.e. air resistance is zero); 3) body weight is unchanged; 4) the body moves with the same constant acceleration at any point.
Example. The physiological system - the human circulatory system - obeys certain laws of thermodynamics. Describing this system in the physical (thermodynamic) language of balance laws, we obtain a physical, thermodynamic model physiological system. If we write these laws in mathematical language, for example, write down the corresponding thermodynamic equations, then we will obtain a mathematical model circulatory system. Let's call it physiological-physical-mathematical model or physical and mathematical model.
Example. A set of enterprises operates on the market, exchanging goods, raw materials, services, and information. If we describe economic laws, the rules of their interaction in the market using mathematical relationships, for example, the system algebraic equations, where the unknowns will be the amounts of profit received from the interaction of enterprises, and the coefficients of the equation will be the values of the intensities of such interactions, then we obtain the mathematical model economic system, i.e. economic-mathematical model systems of enterprises on the market.
Example. If the bank has developed a lending strategy, it could describe it using economic and mathematical models and predicts its lending tactics, then it has greater stability and viability.
Word " model" (Latin modelium) means "measure", "way", "resemblance to some thing."
Modeling based on mathematical theory similarity, according to which absolute similarity can only occur when one object is replaced by another exactly the same. At modeling most systems (with the possible exception of modeling some mathematical structures by others) absolute similarity is impossible, and the main goal modeling - model should reflect the functioning of the simulated system quite well.
Models, if we ignore the areas, areas of their application, there are three types: educational, pragmatic And instrumental.
Cognitive model - a form of organization and presentation of knowledge, a means of connecting new and old knowledge. Cognitive model, as a rule, is adjusted to reality and is theoretical model.
Pragmatic model - a means of organizing practical actions, a working representation of the goals of the system for its management. The reality in them is adjusted to some pragmatic model. These are usually applied models.
Instrumental model - a means of construction, research and/or use pragmatic and/or educational models.
Cognitive reflect existing ones, and pragmatic- although non-existent, but desirable and possibly feasible relationships and connections.
By level, "depth" modeling models there are:
- · empirical - based on empirical facts, dependencies;
- · theoretical - based on mathematical descriptions;
- · mixed, semi-empirical - based on empirical dependencies and mathematical descriptions.
Problem modeling consists of three tasks:
- · construction models(this task is less formalizable and constructive, in the sense that there is no algorithm for constructing models);
- · study models(this task is more formalizable; there are methods for studying various classes models);
- · usage models(constructive and specific task).
Model M, describing the system S(x 1, x 2, ..., x n; R), has the form: M=(z 1, z 2, ..., z m; Q), where z i Z, i=1, 2, ..., n, Q, R - sets of relations over X - the set of input, output signals and states of the system, Z - the set of descriptions, representations of elements and subsets of X.
Construction scheme models M of system S with input signals X and output signals Y is shown in Fig. 10.1.
Rice. 10.1.
If signals from X are received at the input M and signals Y appear at the input, then a law, a rule f of operation, is given models, systems.
Modeling is a universal method of obtaining, describing and using knowledge. It is used in any professional activity. IN modern science and technology role and significance modeling is intensified and updated by problems and successes of other sciences. Modeling real and nonlinear systems alive and inanimate nature allows us to build bridges between our knowledge and real systems, processes, including mental ones.
Classification models carried out according to various criteria. We will use the simplest and most practically significant.
Model called static , if among the parameters involved in its description there is no temporary parameter. Static model at each moment of time it gives only a “photograph” of the system, its slice.
Example. Newton's law F=am is static model a material point of mass m moving with acceleration a. This model does not take into account the change in acceleration from one point to another.
Model dynamic , if among its parameters there is a time parameter, i.e. it displays the system (processes in the system) over time.
Example. Model S=gt 2 /2 - dynamic model paths at free fall bodies. Dynamic model like Newton's law: F(t)=a(t)m(t). An even better form of dynamic models Newton is F(t)=s?(t)m(t).
Model discrete , if it describes the behavior of the system only at discrete moments in time.
Example. If we consider only t=0, 1, 2, :, 10 (sec), then model S t =gt 2 /2 or number sequence S 0 =0, S 1 =g/2, S 2 =2g, S 3 =9g/2, :, S 10 =50g can serve discrete model motion of a freely falling body.
Model continuous , if it describes the behavior of the system for all points in time from a certain period of time.
Example. Model S=gt 2 /2, 0 Model imitation
, if it is intended to test or study possible paths of development and behavior of an object by varying some or all parameters models. Example. Let model economic system for the production of goods of two types 1 and 2, respectively, in quantities x 1 and x 2 units and the cost of each unit of goods a 1 and a 2 at the enterprise is described as the ratio: a 1 x 1 +a 2 x 2 =S, where S is the total cost of all products produced by the enterprise (types 1 and 2). It can be used as simulation model, by which it is possible to determine (vary) the total cost S depending on certain values of the volumes of goods produced. Model deterministic
, if each input set of parameters corresponds to a completely definite and uniquely defined set of output parameters; otherwise - model non-deterministic, stochastic
(probabilistic). Example. The above physical models- deterministic. If in models S=gt 2 /2, 0 Model functional
, if it can be represented in the form of a system of any functional relationships. Example. Newton's continuous, deterministic law and model production of goods (see above) - functional. Model set-theoretic
, if it is representable using certain sets and relations of membership to them and between them. Example. Let the set X = (Nikolai, Peter, Nikolaev, Petrov, Elena, Ekaterina, Mikhail, Tatiana) and the relations be given: Nikolai is the husband of Elena, Ekaterina is the wife of Peter, Tatiana is the daughter of Nikolai and Elena, Mikhail is the son of Peter and Ekaterina, families Mikhail and Petra are friends with each other. Then the set X and the set of listed relations Y can serve set-theoretic model two friendly families. Model logical
, if it is representable by predicates, logical functions. Example. A combination of two logical functions of the form: z=xyxy, p=xy can serve as a mathematical model of a one-bit adder. Model gaming
, if it describes, implements some game situation between the participants of the game (individuals, coalitions). Example. Let player 1 be a conscientious tax inspector, and player 2 be an unscrupulous taxpayer. There is a process (game) of tax evasion (on the one hand) and of revealing tax evasion (on the other hand). Players choose natural numbers i and j (i,jn), which can be identified, respectively, with the fine of player 2 for non-payment of taxes when the fact of non-payment by player 1 is discovered and with the temporary benefit of player 2 from hiding taxes (in the medium and long term, the penalty for the concealment may be much more noticeable). Consider a matrix game with a payoff matrix of order n. Each element of this matrix A is determined by the rule a ij =|i-j|. Model The game is described by this matrix and the strategy of evasion and capture. This game is antagonistic, non-cooperative (for now we will understand the concepts formalized in mathematical game theory in a meaningful, intuitive way). Model algorithmic
, if it is described by some algorithm or set of algorithms that determines its functioning and development. The introduction of this, at first glance, unusual type models(indeed, it seems that any model can be represented by an algorithm for its research), in our opinion, is quite justified, since not all models can be explored or implemented algorithmically. Example. A model for calculating the sum of an infinite decreasing series of numbers can be an algorithm for calculating the finite sum of a series to a certain specified degree of accuracy. Algorithmic model The square root of a number x can be an algorithm for calculating its approximate, arbitrarily accurate value using a well-known recurrent formula. Model structural
, if it is representable by a data structure or data structures and the relationships between them. Example. Structural model may serve as a description (tabular, graph, functional or other) of the trophic structure of the ecosystem. Build one like this model(one of them was given above). Model graph, if it can be represented by a graph or graphs and the relations between them. Model hierarchical
(tree-like), if representable by some hierarchical structure (tree). Example. To solve the problem of finding a route in a search tree, you can build, for example, a tree-like model(Fig. 10.2): Rice. 10.2. Model network
, if it is representable by some network structure. Example. Construction of a new home includes the operations shown in the table below. Table of work during house construction Operation Lead time (days) Previous operations Arcs of the graph Site clearing Laying the foundation Site clearing (1) Walling Laying the foundation (2) Electrical wiring installation Construction of walls (3) Plastering works Electrical wiring installation (4) Landscaping Construction of walls (3) Finishing work Plastering works (5) Roof deck Construction of walls (3) Network model(network diagram) of house construction is given in Fig. 10.3. Rice. 10.3. Two jobs corresponding to arc 4-5 are parallel, they can either be replaced by one representing a joint operation (installation of electrical wiring and roofing) with a new duration of 3+5=8, or introduce a fictitious event on one arc, then arc 4-5 will take view. Model linguistic, linguistic
, if it is represented by some linguistic object, formalized language system or structure. Sometimes like this models are called verbal, syntactic, etc. Example. Traffic rules - language, structural model movement of vehicles and pedestrians on the roads. Let B be the set of generating stems of nouns, C be the set of suffixes, P be adjectives, “+” be the concatenation operation of words, “:=" be the assignment operation, “=>” be the inference operation (derivability of new words), Z be the set of values (semantic) adjectives. Language model M word formation: :=+ Model visual
, if it allows you to visualize the relationships and connections of the modeled system, especially in dynamics. Example. The computer screen often uses visual model of one or another object, for example, a keyboard in a simulator program for teaching how to use the keyboard. Model full-scale
, if it is a material copy of the object modeling. Example. Globe - full-scale geographical model globe. Model geometric
, graphic, if it can be represented by geometric images and objects. Example. The model of the house is full-scale geometric model house under construction. A polygon inscribed in a circle gives model circles. This is what is used to depict a circle on a computer screen. A straight line is model number axis, and the plane is often depicted as a parallelogram. Model cellular automata
, if it represents the system using a cellular automaton or a system of cellular automata. A cellular automaton is a discrete dynamic system, an analogue of a physical (continuous) field. Cellular automata geometry is an analogue of Euclidean geometry. An indivisible element of Euclidean geometry is a point; on its basis segments, straight lines, planes, etc. are constructed. An indivisible element of a cellular automata field is a cell; on its basis, clusters of cells and various configurations of cellular structures are built. This is the “world” of some automaton, performer, structure. A cellular automaton is represented by a uniform network of cells (“cells”) of this field. The evolution of a cellular automaton unfolds in a discrete space - a cellular field. Such cellular fields can be material-energy-informational. The laws of evolution are local, i.e. the dynamics of the system is determined by a given unchanging set of laws or rules, according to which the calculation of a new cell of evolution and its material-energy-informational characteristics is carried out depending on the state of its neighbors (neighborhood rules, as already said, are specified). The change of states in a cellular automata field occurs simultaneously and in parallel, and time passes discretely. Despite the apparent simplicity of their construction, cellular automata can exhibit varied and complex behavior. Recently, they have been widely used in modeling not only physical, but also socio-economic processes. Cellular automata (fields) can be one-dimensional, two-dimensional (with cells on a plane), three-dimensional (with cells in space) or multidimensional (with cells in multidimensional spaces). Example. Classical cellular automata model- Game "Life" by John Conway. It is described in many books. We'll look at another cellular automata model environmental pollution, diffusion of a pollutant in a certain environment. 2D cellular automaton (on the plane) for modeling environmental pollution can be generated by the following rules: Let the unit of time be the step of a cellular automaton, and the unit of length be the size of its cell. If we go through all possible combinations of rotations of blocks of even and odd partitions, we see that in one step a particle can move along each of the coordinate axes to a distance of 0, 1 or 2 (without taking into account the direction of displacement) with probabilities, respectively, p 0 = 1/4 , p 1 =1/2, p 2 =1/4. The probability of a particle hitting a given point depends only on its position at the previous moment in time, therefore we consider the movement of the particle along the x (y) axis as random. In Fig. 10.4 - fragments of the program cellular automata model pollution of the cellular eco-environment (cell sizes are increased). Rice. 10.4. The window on the right is the state of the cell field (in the top - initial, slightly contaminated, in the bottom - after 120 cycles of contamination), in the upper left corner is a “Microscope” that magnifies the field cluster, in the middle left is a graph of pollution dynamics, in the bottom left are pollution indicators Model fractal
, if it describes the evolution of the modeled system by the evolution of fractal objects. If the physical object is homogeneous (solid), i.e. there are no cavities in it, we can assume that the density does not depend on size. For example, when R increases to 2R, the mass will increase by R 2 times (circle) and R 3 times (ball), i.e. M(R)~R n (relationship between mass and length), n is the dimension of space. An object whose mass and size are related by this relationship is called "compact". Its density If an object (system) satisfies the relation M(R)~R f(n) , where f(n) Since f(n)-n<0, то плотность фрактального объекта уменьшается с увеличением размера, а с(R) является количественной мерой разряженности, ветвистости (структурированности) объекта. Example. Example fractal model- Cantor set. Let's consider. Divide it into 3 parts and discard the middle section. We again divide the remaining 2 gaps into three parts and discard the middle gaps, etc. We obtain a set called the Cantor set. In the limit, we obtain an uncountable set of isolated points (Fig. 10.5) Rice. 10.5. It can be shown that if n is the dimension of the Cantor set, then n=ln2/ln3?0.63, i.e. this object (fractal) does not yet consist only of isolated points, although it no longer consists of a segment. Fractal objects self-similar
, if they look the same at any spatial scale, are scale invariant, fragments of the structure are repeated at certain spatial intervals. Therefore they are very well suited for modeling irregularities, since they make it possible to describe (for example, by discrete models) the evolution of such systems for any moment in time and on any spatial scale. Self-similarity found in a variety of objects and phenomena. Example. Self-similar tree branches, snowflakes, economic systems (Kondratieff waves), mountain systems. Fractal model usually used when a real object cannot be represented in the form of a classical models, when we are dealing with nonlinearity (multivariate development paths and the need for choice) and indeterminism, chaoticity and irreversibility of evolutionary processes. Type models depends on the information essence of the modeled system, on the connections and relationships of its subsystems and elements, and not on its physical nature. Example. Mathematical descriptions ( models) the dynamics of an epidemic of an infectious disease, radioactive decay, the acquisition of a second foreign language, the release of products of a manufacturing enterprise, etc. are the same in terms of their description, although the processes are different. Boundaries between models of different types or assignment models to one type or another are often very conditional. We can talk about different modes of use models- simulation, stochastic, etc. Model includes: object O, subject (optional) A, task Z, resources B, environment modeling S: M= Basic properties any models: Life cycle of the simulated system: Modeling- method of system analysis. But often in system analysis with a model approach to research, one methodological mistake can be made, namely, the construction of correct and adequate models(submodels) of the system subsystems and their logically correct linking does not guarantee the correctness of the system constructed in this way models the entire system. Model, constructed without taking into account the connections of the system with the environment and its behavior in relation to this environment, can often only serve as another confirmation of Gödel’s theorem, or rather, its corollary, which states that in a complex isolated system there can be truths and conclusions that are correct in this system and incorrect ones outside of it. The science modeling consists of dividing the process modeling(systems, models) into stages (subsystems, submodels), a detailed study of each stage, relationships, connections, relationships between them and then effectively describing them with the highest possible degree of formalization and adequacy. If these rules are violated, we will not receive model systems, and model"own and incomplete knowledge." Modeling(in the meaning of “method”, “model experiment”) is considered as a special form of experiment, an experiment not on the original itself (this is called a simple or ordinary experiment), but on a copy (substitute) of the original. What is important here is the isomorphism of systems (original and model) - isomorphism of both the copy itself and the knowledge with the help of which it was proposed. Models And modeling are applied in the main areas: Questions for self-control Tasks and exercises Target modeling: determination of the evolution of the next generation of predators and prey, i.e., using the given laws of neighborhood and dynamics of discrete development (time changes discretely), the number of new individuals (cells) and the number of deceased (dead) individuals are determined; if a given cell configuration has been achieved or development has led to the extinction of a species (cyclicity), then modeling ends. Topics of scientific research and abstracts, Internet sheets Analysis is decomposition into parts, consideration of all sides and methods of functioning, synthesis is consideration of the method of connections and relationships of parts. give rise to special methods in each area. Abstraction and idealization. General scientific reception. This is a temporary mental isolation from the many properties and aspects of a phenomenon that interest us, abstraction from other properties and the construction of an ideal object such as a point or line. The difficult question is whether and in what way this method gives a correct idea of reality? How can it even work? Here the general concept of a class of objects arises. In the course of idealization, in addition to abstraction, there is also a technique for introducing new properties into an object. Induction, deduction, analogy. Induction is characteristic of experimental sciences, it makes it possible to construct hypotheses, but does not provide reliable knowledge, but is suggestive. At the same time, there are also separate strict forms of induction, such as mathematical induction. Deduction derives special conclusions from their general theorems. Gives reliable knowledge if the premise is true. Analogy - putting forward hypotheses about the property of an object based on its similarity to something already studied. Requires further justification. One object is replaced by another with similar properties, but not completely similar. Allows you to draw conclusions about the original based on studying the model. In this case, subject, physical, mathematical, symbolic, computer modeling is possible, depending on the type of model. Observation of experiment, measurement during them. In all forms of organization of scientific knowledge, a generalized description of reality is carried out, on the basis of which the essence of the phenomenon is revealed more deeply and thereby a gradual reduction is carried out in the direction from the least generalized to more and more generalized forms of description of reality. Despite the fact that in scientific knowledge there is a constant movement towards greater generalization, at the same time we have a huge variety of different fields of science and in no field of science has this movement led to the disappearance and elimination of the diversity of scientific theories and their reduction to a single theoretical scheme . Today science represents a colossal variety of different methods of cognition and a significant number of methodological research programs. for example, different approaches are applied to the study of the same phenomenon, in some cases certain aspects are considered, in others - others. In this case, it may be that the same aspects are considered, but are characterized by different quantities or different methods are used. Thus, the differentiation of science occurs on the basis of the emergence of new theories, which is associated with a deeper penetration into the essence of the object under study. What was previously one science, over time, buds into theories that develop into a separate science. An example is mathematics and physics, where some specialists no longer understand the field where others work. In addition to the division as a result of the concretization of the classical sciences, there is also a division in the method of study, in the aspect of study. In addition, as development progresses, new phenomena arise, primarily in social life, which leads to the emergence of an even greater number of sciences, the sources of which no longer have to be sought in the past. An example is various systems theory. Further, new sciences arise at the junction of traditional ones, for example, biophysics, biochemistry, structural analysis, mathematical linguistics. The interpenetration of sciences leads to their differentiation, while a new look at a phenomenon or subject of study is realized, which allows for more effective use of science data. Integration in science is associated primarily with the unification of various methods of scientific research. The development of scientific methodology has led to a unified scientific standard; of course, these methods are a level of abstraction and in each specific area they have their own object and fication. In addition, there are general scientific methods such as the use of mathematical methods for studying objects in all sciences without exception. Integration also occurs in terms of unifying theories and seeing their internal relationships based on the discovery of the fundamental principles of being. this does not mean the abolition of these sciences, but this is only a deeper level of penetration into the essence of the phenomena under study - the creation of general theories, metatheories and general methods of proof. There is a unification of sciences on the principle of a new level of abstraction, an example of which can again be systems theory. General characteristics of the functions of philosophy: speaking in everyday language, the functions of philosophy are those duties that are prescribed to philosophy by the very subject of philosophical knowledge. Otherwise, the functions of philosophy are the responsibilities of philosophy to a person if he relies on philosophy for knowledge: as a kind of algorithm for knowledge, philosophy must provide a certain result of cognitive activity, for example, give reliable ideas about the world and the place of man in it. More strictly, we can define the concept of “function” as follows: it is a method of action, a way of manifesting the activity of a system of philosophical knowledge. In this sense, Goethe (1749-1832) defined the concept of “function” as “the existence that we think of in action.” The functions of philosophy are divided into two groups: ideological and methodological. This division follows from the very definition of philosophy as a worldview. Worldview functions of philosophy: The methodological functions of philosophy express the purpose of philosophy as the general methodological foundation of science: 1. Heuristic function: involves promoting the growth of scientific knowledge, creating prerequisites for scientific discoveries in the context of the interaction of philosophical and formal logical methods, which leads to intensive and extensive changes in philosophical categories and, as a consequence, to the birth of new knowledge in the form of a forecast (hypothesis) ). It is necessary, in this sense, to note that there is not a single natural science theory, the creation of which would have been possible without the use of general philosophical concepts of causality, space, time, etc. It has been proven that theories in the natural sciences are created on a dual basis - on the unity of the empirical and the extra-empirical. The role of extra-empirical foundation is played by philosophy. In other words, philosophical ideas play a constructive role. General philosophical concepts and principles penetrate natural science through such philosophical branches as ontology, epistemology, as well as through the regulatory principles of the particular sciences themselves (for example, in physics, these are the principles of observability, simplicity, and correspondence). Thus, the epistemological principles of philosophy play an important role not only in the formation of a theory, but also serve as regulators that determine the process of its further functioning. It is interesting that philosophy influences scientific theories not as a whole, but only locally - with individual ideas, concepts, principles. Moreover, in the acts of mutual determination of philosophy and science, the position of a natural scientist is much more complicated than the position of a philosopher. A scientist, at the stage of theory formation, must accept points of view that are not compatible in one system. A philosopher, on the contrary, having discovered a system-creating principle, can then use it, interpreting the data of natural sciences in the interests of his own system (A. Einstein). Thus, the heuristic function of philosophy, which involves the use of dialectics as a general scientific method (dialectics as logic) of research, has a significant impact on the state of the natural scientific picture of the world; 2. Coordinating function: involves the coordination of research methods in the process of scientific research. Until the 20th century, the dominance of the analytical method was noted in science. Which led to the need to strictly observe the ratio: one subject - one method. However, in the 20th century this ratio was violated. In the research of one subject, several methods are already used and, on the contrary, in the study of several subjects - one method. The need to coordinate research methods is caused not only by the complication of the “method-subject” picture traditional for the analytical method, but also by the emergence of a number of negative factors, associated in particular with the growing specialization of scientists. In this regard, it should be noted that the specialization also affected philosophical knowledge. We can consider that the time of philosophical systems has passed. That is, philosophy as a system built from beginning to end by one philosopher is a non-renewable fact. Modern philosophers hardly have enough time, physical strength and philosophical technique to develop one particular problem related to the local field of philosophical research. In the context of coordinating scientific research methods, the task of determining the principle of compliance of the methods used with each other and the general purpose of the research becomes relevant. The fact is that each method has its own fixed theoretical-cognitive and logical capabilities, but the creation of a set of methods allows you to expand the capabilities of specific methods. At the same time, taking into account the fact that all methods have different effectiveness, their hierarchy is established in the context of scientific research. In conclusion, it should be noted that the philosophical method as a way to successfully solve scientific problems should not be used in isolation from the own methodology of science, in isolation from general scientific and special methods; 3. Integrating function: involves the implementation of the unifying role of philosophical knowledge, the identification and elimination of disintegrating factors, and the identification of missing links in scientific knowledge. The process of formation of individual scientific disciplines occurred by limiting the subject of a particular science from the subjects of other sciences. However, this led to the destruction of the ancient scientific paradigm, the main dimension of which was the unity of scientific knowledge. Isolationism as the basis for the crisis in the unity of science persisted until the 19th century. This problem could only be solved through philosophical principles - the actual scientific principles of organizing knowledge were not enough here. The integration of sciences was carried out using the philosophical principle of the unity of the world, according to which the integrity of nature determines the integrity of knowledge about nature. The application of the philosophical principle of the unity of the world for the purpose of integrating natural science knowledge led to the formation of three types of integrator sciences that carry out “integration by method”: these are “transitional” sciences, which have the properties of several scientific disciplines at once and connect only related scientific disciplines; “synthesizing” sciences, combining a number of substantively distant sciences and “problem” sciences that arise to solve a specific problem and represent a synthesis of a number of sciences. It should be noted that “integration by method” includes mathematical and philosophical methods, the use of which in the context of scientific research produces phenomena defined by the concepts of “mathematization of science” and “philosophization of science.” Integrating factors (particular; general; the most general) that unite scientific knowledge, the most general of which is philosophy, can be arranged in the following series: law-method-principle-theory-idea-metatheory-specific science-metascience-related science complex science scientific picture of the world philosophy. In this series, each subsequent factor is integrating for each previous one; 4. Logical-epistemological function: involves the development of the philosophical method itself, its normative principles; as well as the logical and epistemological justification of the conceptual and theoretical structures of scientific knowledge, for example, general scientific methods: thus, philosophy is used to develop a systems approach.
. For b i - “fish(a)”, s i - “n(th)”, we obtain from this models p i - “fishy”, z i - “cooked from fish”.
Modeling.