Model visual , if it allows you to visualize the relationships and connections of the simulated system, especially in dynamics.

Example. The computer screen often uses visual model an object, such as a keyboard in a keyboard training simulator.

Model natural , if it is a material copy of the object modeling.

Example. Globe - natural geographical model the globe.

Model geometric , graphic, if it can be represented by geometric images and objects.

Example. The layout of the house is in kind geometric model house under construction. A polygon inscribed in a circle gives model circles. It is she who is used when depicting a circle on a computer screen. The straight line is model the numerical axis, and the plane is often depicted as a parallelogram.

Model cellular automaton 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; segments, straight lines, planes, etc. are built on its basis. An indivisible element of the cellular-automaton field is a cell, on the basis of which clusters of cells and various configurations of cellular structures are built. This is the "world" of some automaton, executor, structure. The 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 real-energy-informational. The laws of evolution are local, i.e. the dynamics of the system is determined by a fixed 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 mentioned, are set). The change of states in the cellular automaton field occurs simultaneously and in parallel, and time passes discretely. Despite the apparent simplicity of their construction, cellular automata can exhibit a variety 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 in a plane), three-dimensional (with cells in space), or multidimensional (with cells in multidimensional spaces).

Example. classical cellular automaton model- Game of Life by John Conway. It has been described in many books. We will consider another cellular automaton model environmental pollution, diffusion of a pollutant in some environment. 2D cellular automaton (on the plane) for modeling environmental pollution can be generated by the following rules:

• The plane is divided into identical cells: each cell can be in one of two states: state 1 - it has a diffusing pollutant particle, and state 0 - if it does not exist;
• The cell field is divided into 2×2 blocks in two ways, which we will call even and odd partitions (an even partition has an even number of points or field cells in a cluster or block, an odd block has an odd number of them);
• · at the next step of evolution, each block of an even partition is rotated (according to a given rule for the propagation of pollution or a generated distribution of random numbers) by a given angle (the direction of rotation is chosen by a random number generator);
• · a similar rule is defined for blocks of odd partition;
• The process continues until a certain moment or until the environment is cleared.

Let the unit of time be the step of the cellular automaton, the unit of length be the size of its cell. If we enumerate all possible combinations of rotations of blocks of even and odd partitions, we see that in one step the particle can move along each of the coordinate axes at a distance of 0, 1 or 2 (without taking into account the direction of displacement) with probabilities, respectively, p 0 =1/4 , p 1 \u003d 1/2, p 2 \u003d 1/4. The probability of a particle hitting a given point depends only on its position at the previous time, so we consider the motion of the particle along the x (y) axis as random.

On fig. 10.4 - fragments of the program cellular automaton model pollution of the cellular eco-environment (cell sizes are increased).

Rice. 10.4. The window on the right - the state of the cell field (in the upper - initial, slightly polluted, in the lower - after 120 cycles of pollution), in the upper left corner - "Microscope", increasing the cluster of the field, in the middle left - a graph of the pollution dynamics, in the lower left - 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. Since there are no cavities in it, we can assume that the density does not depend on the size. For example, when R is increased 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 - dimension of space. An object whose mass and size are related by this ratio is called "compact". Its density

If the 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 is the Cantor set. Consider . Divide it into 3 parts and discard the middle segment. The remaining 2 intervals will again be divided into three parts and we will throw out the middle intervals, etc. We get a set called the Cantor set. In the limit, we get 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 on any spatial scale, are scale invariant, fragments of the structure are repeated at certain spatial intervals. Therefore, they are very suitable for modeling irregularities, since they make it possible to describe (for example, by discrete models) the evolution of such systems for any moment of 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 is usually used when the real object cannot be represented in the form of a classical models when we are dealing with non-linearity (multivariance of development paths and the need to choose) and indeterminacy, chaoticity and irreversibility of evolutionary processes.

Type models depends on the information essence of the system being modeled, 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, learning a second foreign language, output 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 attribution models to one type or another are often very conditional. You 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= .

Main properties any models:

• goal-oriented model always displays some system, i.e. has a purpose;
• limb - model displays the original only in a finite number of its relations and, in addition, resources modeling finite;
• simplification - model displays only the essential aspects of the object and, in addition, should be easy to study or reproduce;
• approximation - reality is displayed model roughly or approximately;
• adequacy - model must successfully describe the system being modeled;
• visibility, visibility of its main properties and relationships;
• availability and manufacturability for research or reproduction;
• information content - model should contain sufficient information about the system (within the framework of the hypotheses adopted in the construction models) and should provide an opportunity to obtain new information;
• preservation of the information contained in the original (with the accuracy of those considered in the construction models hypotheses);
• completeness - in models all the main connections and relationships necessary to ensure the goal should be taken into account modeling;
• stability - model must describe and ensure the stable behavior of the system, even if it is initially unstable;
• integrity - model implements some system (i.e. the whole);
• closure - model takes into account and displays a closed system of necessary basic hypotheses, connections and relationships;
• adaptability - model can be adapted to various input parameters, environmental influences;
• controllability (simulation) - model must have at least one parameter, by changing which it is possible to simulate the behavior of the simulated system in various conditions;
• Evolvability - the possibility of development models(of the previous level).

Life cycle of the simulated system:

• collection of information about the object, hypotheses, pre-model analysis;
• Designing the structure and composition models(submodels);
• construction of specifications models, development and debugging of individual submodels, assembly models in general, identification (if needed) of parameters models;
• · study models- choice of research method and development of an algorithm (program) modeling;
• study of adequacy, stability, sensitivity models;
• valuation of funds modeling(resources expended);
• interpretation, analysis of results modeling and the establishment of some cause-and-effect relationships in the system under study;
• generation of reports and design (national economic) decisions;
• clarification, modification models, if necessary, and return to the system under study with new knowledge obtained using models And modeling.

Modeling- method of system analysis. But often in system analysis with a model approach of research, one methodological error can be made, namely, the construction of correct and adequate models(submodels) of subsystems of the system 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, stating that in a complex isolated system there can be truths and conclusions that are correct in this system and incorrect outside of it.

The science modeling is to separate the process modeling(systems, models) into stages (subsystems, submodels), a detailed study of each stage, relationships, connections, relations between them and then an effective description of them with the highest possible degree of formalization and adequacy. If these rules are violated, we get 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. The isomorphism of systems (original and model) is important here - the isomorphism of both the copy itself and the knowledge with which it was proposed.

Models And modeling applied in the main areas:

• education (as models, modeling, as well as themselves models);
• knowledge and development of the theory of the systems under study (with the help of any models, modeling, results modeling);
• Forecasting (output data, situations, system states);
• Management (of the system as a whole, individual subsystems of the system), development of management decisions and strategies;
• Automation (of a system or individual subsystems of a system).

Questions for self-control

• 1. What is model what is it for and how is it used? Which model called static (dynamic, discrete, etc.)?
• 2. What are the main properties models and how important are they?
• 3. What is the life cycle modeling(simulated system)?

Tasks and exercises

• 1. Recently, the most pressing problem in the economy has been the impact of the level of taxation on economic activity. Among other principles of levying taxes, an important place is occupied by the question of the marginal norm, the excess of which entails losses to society and the state, incommensurable with current budget revenues. Determining the total amount of tax collections in such a way that, on the one hand, it corresponds to government spending to the maximum, and, on the other hand, has a minimum negative impact on business activity, is one of the main tasks of government management. Describe what, in your opinion, parameters should be taken into account in models taxation of economic activities corresponding to the specified purpose. Compose a simple (for example, recurrent form) model collection of taxes, based on tax rates that vary within the specified ranges: income tax - 8-12%, value added tax - 3-5%, corporate property tax - 7-10%. Aggregate tax deductions should not exceed 30-35% of profit. Specify in this models control parameters. Define one control strategy using these options.
• 2. Numeric - x i , i=0, 1, ..., n and symbolic - y i , i=0, 1, ..., m arrays X and Y are given. Compose model stack calculator that allows you to perform operations:
• 1. cyclic shift to the right of the X or Y array and writing the given number to x 0 or the operation symbol - y 0 (to the "top of the stack" X (Y)) i.e. performing the operation "pushing into the stack";
• 2. reading the "top of the stack" and the subsequent circular shift to the left of the array X or Y - the operation of "popping from the stack";
• 3. swap x 0 and x 1 or y 0 and y 1 ;
• 4. "doubling the top of the stack", i.e. getting a copy of x 0 or y 0 into x 1 or y 1 ;
• 5. reading the "top of the stack" Y (sign +, -, * or /), then decoding this operation, reading the operands of the operations from the "top" X, performing this operation and placing the result at the "top" X.
• 3. Famous classical dynamic model V.Volterra of the "predator-prey" type system, which is model resource-consumption type. Consider cellular automaton model such a system. The behavioral algorithm of a cellular automaton simulating a "predator-prey" type system consists of the following steps:
• 1. the initial distributions of predators and prey are given, randomly or deterministically;
• 2. laws of "neighborhood" of individuals (rules of relationships) of cells are determined, for example, cells (i-1,j), (i,j+1), (i+1, j),(i,j-1);
• 3. The laws of birth and death of cells are set, for example, if a cell has less than two (more than three) neighbors, it dies "from loneliness" ("from overpopulation").

Target modeling: determination of the evolution of the next generation of predators and prey, i.e., using the given laws of neighborhood and the dynamics of discrete development (time changes discretely), the number of new individuals (cells) and the number of dead (dead) individuals are determined; if a given cell configuration is achieved or development has led to the extinction of the species (cyclicity), then modeling ends.

Topics of scientific research and abstracts, Internet sheets

• 1. Modeling as a method, methodology, technology.
• 2. Models in the microcosm and the macrocosm.
• 3. Linearity of models (our knowledge) and non-linearity of natural and social phenomena.

The theoretical level of scientific research is a rational (logical) stage of knowledge. At the theoretical level, with the help of thinking, there is a transition from a sensory-concrete idea of ​​the object of study to a logical-concrete one. The logically concrete is the theoretically reproduced in the thinking of the researcher a concrete idea of ​​the object in all the richness of its content. At the theoretical level, the following methods of cognition are used: abstraction, idealization, thought experiment, induction, deduction, analysis, synthesis, analogy, modeling.

Abstraction- this is a mental distraction from some less significant properties, aspects, features of the object or phenomenon being studied with the simultaneous selection, formation of one or more essential aspects, properties, features. The result obtained in the process of abstraction is called abstraction.

Idealization- this is a special kind of abstraction, the mental introduction of certain changes in the object under study in accordance with the objectives of the research. We give examples of idealization.

Material point- a body devoid of any dimensions. This is an abstract object, the dimensions of which are neglected, it is convenient in describing the movement.

Completely black body- is endowed with a property that does not exist in nature to absorb absolutely all the radiant energy that falls on it, reflecting nothing and not passing through itself. The emission spectrum of a blackbody is an ideal case, since it is not affected by the nature of the substance of the emitter or the state of its surface.

thought experiment is a method of theoretical knowledge, which involves operating with an ideal object. This is a mental selection of positions, situations that allow you to detect important features of the object under study. In this it resembles a real experiment. In addition, it precedes the real experiment in the form of a planning procedure.

Formalization- this is a method of theoretical knowledge, which consists in the use of special symbolism, which allows you to abstract from the study of real objects, from the content of the theoretical provisions that describe them, and instead operate with a certain set of symbols, signs.

To build any formal system, it is necessary:

1. setting the alphabet, i.e. a certain set of characters;

2. setting the rules by which "words", "formulas" can be obtained from the initial characters of this alphabet;

3. setting the rules by which one can move from one word, formula of a given system to other words and formulas.

As a result, a formal sign system is created in the form of a certain artificial language. An important advantage of this system is the possibility of carrying out within its framework the study of an object in a purely formal way (operating with signs) without directly referring to this object.

Another advantage of formalization is to ensure the brevity and clarity of the recording of scientific information, which opens up great opportunities for operating with it.

Induction- (from Latin induction - guidance, motivation) is a method of cognition based on a formal logical conclusion, which leads to a general conclusion based on particular premises. In other words, it is the movement of our thinking from the particular, the individual to the general. Finding similar features, properties in many objects of a certain class, the researcher concludes that these features, properties are inherent in all objects of this class.

The popularizer of the classical inductive method of cognition was Francis Bacon. But he interpreted induction too broadly, considered it the most important method of discovering new truths in science, the main means of scientific knowledge of nature. In fact, the above methods of scientific induction serve mainly to find empirical relationships between the experimentally observed properties of objects and phenomena. They systematize the simplest formal logical techniques that were spontaneously used by natural scientists in any empirical study.

Deduction- (from lat. deduction - derivation) is the receipt of private conclusions based on the knowledge of some general provisions. In other words, it is the movement of our thinking from the general to the particular.

However, despite the attempts that have taken place in the history of science and philosophy to separate induction from deduction, to oppose them, in the real process of scientific knowledge, both of these two methods are used at the corresponding stage of the cognitive process. Moreover, in the process of using the inductive method, deduction is often “hidden” as well. Generalizing the facts in accordance with some ideas, we indirectly derive the generalizations we receive from these ideas, and we are not always aware of this. It seems that our thought moves directly from facts to generalizations, that is, that there is pure induction here. In fact, in accordance with some ideas, implicitly guided by them in the process of generalizing facts, our thought indirectly goes from ideas to these generalizations, and, consequently, deduction also takes place here ... We can say that in all cases, when we generalize according to some philosophical propositions, our conclusions are not only induction, but also hidden deduction.

Analysis and synthesis. Under analysis understand the division of an object into constituent particles for the purpose of studying them separately. Such parts may be some material elements of the object or its properties, features, relationships, etc. Analysis is a necessary and important stage in the cognition of an object. But it is only the first stage of the process of cognition. To comprehend an object as a single whole, one cannot limit oneself to studying only its constituent parts. In the process of cognition, it is necessary to reveal the objectively existing connections between them, to consider them together, in unity. To carry out this second stage in the process of cognition - to move from the study of individual component parts of an object to the study of it as a single connected whole - is possible only if the method of analysis is supplemented by another method - synthesis. In progress synthesis the component parts of the object under study, dissected as a result of the analysis, are joined together. On this basis, further study of the object takes place, but already as a single whole. At the same time, synthesis does not mean a simple mechanical connection of disconnected elements into a single system. It reveals the place and role of each element in the system of the whole, establishes their interrelation and interdependence.

Analysis and synthesis are also successfully used in the sphere of human mental activity, that is, in theoretical knowledge. But here, as well as at the empirical level of cognition, analysis and synthesis are not two operations separated from each other. In essence, they are two sides of a single analytical-synthetic method of cognition.

Analogy and modeling. Under analogy similarity, the similarity of some properties, features or relationships of objects that are generally different is understood. Establishing similarities (or differences) between objects is carried out as a result of comparison. Thus, comparison underlies the method of analogy.

The analogy method is used in various fields of science: in mathematics, physics, chemistry, cybernetics, in the humanities, etc. There are various types of conclusions by analogy. But what they have in common is that in all cases one object is directly investigated, and a conclusion is made about another object. Therefore, inference by analogy in the most general sense can be defined as the transfer of information from one object to another. In this case, the first object, which is actually being studied, is called a model, and the other object, to which the information obtained as a result of the study of the first object (model) is transferred, is called the original (sometimes a prototype, sample, etc.). Thus, the model always acts as an analogy, i.e., the model and the object (original) displayed with its help are in a certain similarity (similarity).

The limits of the scientific method.

The limitations of the scientific method are mainly associated with the presence of a subjective element in cognition and are due to the following reasons.

Human experience, which is the source and means of cognition of the surrounding world, is limited. Man's senses allow him only limited orientation in the world around him. The possibilities of experiential knowledge of the surrounding world by a person are limited. The mental capabilities of man are great, but also limited.

The dominant paradigm, religion, philosophy, social conditions and other elements of culture inevitably influence the worldview of scientists, and hence the scientific result.

The Christian worldview proceeds from the fact that the fullness of knowledge is revealed by the Creator and man is given the opportunity to possess it, but the damaged state of human nature limits his ability to know. Nevertheless, a person is capable of knowing God, that is, he can know himself and the world around him, see the manifestation of the Creator's features in himself and in the world around him. It should not be forgotten that the scientific method is only an instrument of knowledge and, depending on whose hands it is in, it can be beneficial or harmful.

Learning about systems and using that knowledge to create and manage systems requires systems thinking, consisting in a combination of analytical and synthetic ways of thinking. essence analysis consists in dividing the whole into parts, in representing the complex as a set of simpler components. But in order to cognize the whole, the complex, the reverse process is also necessary - synthesis . The need to combine these types of cognition follows from the property of the emergence of systems: the integrity of the system is violated during analysis, when the system is divided, not only the essential properties of the system itself are lost, but also the properties of its parts that are separated from it. The result of the analysis is only the disclosure of the composition of the components, the knowledge of how the system works, but not the understanding of why and why it does this. Synthetic thinking explains the behavior of the system, why the system works the way it does. At the same time, the system should be considered as part of a larger whole.

Analysis and synthesis complement each other. So, when synthesizing an organizational structure, it is necessary to first analyze the activities of the organization being created, single out individual processes (functions), compare organizational units with them, and then combine them into a separate whole, i.e. carry out the synthesis. When choosing the method of functioning of an organization, the opposite often takes place: first, a synthetic approach is used - the activities of the organization as a whole are considered; a common goal and mode of functioning are selected, and then the selected mode is disaggregated into separate functions.

The main content of the "Systems Analysis" discipline is complex decision-making problems, in the study of which informal procedures for presenting common sense and ways of describing situations play no less a role than formal mathematical apparatus. System analysis is a synthetic discipline. It can be divided into three main directions. These three directions correspond to three stages that are always present in the study of complex systems:

1) building a model of the object under study;

2) setting the research problem;

3) solution of the set mathematical problem.

The knowledge of systems and the use of this knowledge to create systems and control them is carried out through modeling.

The ultimate goal of system analysis is to resolve the problem situation that has arisen before the object of the ongoing system research (usually it is a specific organization, team, enterprise, separate region, social structure, etc.). System analysis deals with the study of a problem situation, clarification of its causes, development of options for its elimination, decision-making and organization of the further functioning of the system, resolving the problem situation. The initial stage of any system research is the study of the object of the ongoing system analysis, followed by its formalization. At this stage, tasks arise that fundamentally distinguish the methodology of system research from the methodology of other disciplines, namely, a two-pronged task is solved in system analysis. On the one hand, it is necessary to formalize the object of system research, on the other hand, the process of studying the system, the process of formulating and solving the problem, is subject to formalization.

Let's take an example from systems design theory. The modern theory of designing complex systems can be considered as one of the parts of systems research. According to her, the problem of designing complex systems has two aspects. First, it is required to carry out a formalized description of the design object. Moreover, at this stage, the tasks of a formalized description of both the static component of the system (mainly its structural organization is subject to formalization) and its behavior in time (dynamic aspects that reflect its functioning) are solved. Secondly, it is required to formalize the design process. The components of the design process are the methods of forming various design solutions, methods of their engineering analysis and decision-making methods for choosing the best options for implementing the system.

We will try to outline the main procedures of the algorithm for conducting a system analysis, which are a generalization of the sequence of stages for conducting such an analysis, formulated by a number of authors, and reflect its general patterns. We list the main procedures for system analysis:

- study of the structure of the system, analysis of its components, identification of relationships between individual elements;

- collection of data on the functioning of the system, the study of information flows, observations and experiments on the analyzed system;

– building models;

– verification of the adequacy of models, analysis of uncertainty and sensitivity;

– study of resource opportunities;

– determination of the goals of system analysis;

– formation of criteria;

– generation of alternatives;

– implementation of choice and decision-making;

– implementation of the results of the analysis.

The concept of a model

Replacing one object with another in order to obtain information about the most important properties of the original object using the model object can be called modeling, i.e. modeling is the representation of an object by a model to obtain information about the object by conducting an experiment with its model.

From the point of view of philosophy, modeling should be considered as an effective means of understanding nature. At the same time, the modeling process assumes the presence of an object of study, a researcher-experimenter and a model.

In automated information processing and control systems, the object of modeling can be production and technological processes for obtaining final products; the processes of movement of documents, information flows in the implementation of the institutional activities of the organization; processes of functioning of a complex of technical means; processes of organization and functioning of information support of automated control systems; processes of functioning of the ACS software.

The advantages of modeling are that it becomes possible by relatively simple means to study the properties of the system, change its parameters, and introduce the target and resource characteristics of the external environment. As a rule, modeling is used in the following stages:

1) studies of the system before it is designed, in order to determine its main characteristics and rules for the interaction of elements among themselves and with the external environment;

2) designing a system for the analysis and synthesis of various types of structures and choosing the best implementation option, taking into account the formulated optimality criteria and limitations;

3) operation of the system to obtain optimal modes of operation and predictable estimates of its development.

At the same time, the same system can be described by different types of models. For example, the transport network of a certain area can be modeled by an electrical circuit, a hydraulic system, a mathematical model using the apparatus of graph theory.

The following types of models are widely used to study systems: physical (geometric similarity, electrical, mechanical, etc.) and symbolic (meaningful and mathematical). A mathematical model is understood as a set of mathematical expressions that describe the behavior (structure) of the system and the conditions (perturbations, restrictions) in which it operates. In turn, mathematical models, depending on the mathematical apparatus used, are divided, for example, into:

· static and dynamic;

deterministic and probabilistic;

discrete and continuous;

analytical and numerical.

Static models describe an object at any point in time, while dynamic models reflect the behavior of an object over time. Deterministic models describe processes in which there are no (not taken into account) random factors, and probabilistic models reflect random processes - events. Discrete models characterize the processes described by discrete variables, continuous - continuous. Analytical models describe the process in the form of certain functional relationships and/or logical conditions. Numerical models reflect the elementary stages of calculations and the sequence of their implementation. If natural language (the language of communication between people) is used to describe the system, then such a description is called a content model. Examples of meaningful models are: verbal problem statements, systems development programs and plans, organization goal trees, etc. Content models are of independent value in solving problems of research and systems management, and are also used as a preliminary step in the development of mathematical models. Therefore, the quality of the mathematical model depends on the quality of the corresponding mathematical model.

Natural language (the language of communication between people), diagrams, tables, flowcharts, graphs are used as language means for describing meaningful (verbal) models. Complex systems are called complex because they are difficult to formalize. For them, it is advisable to use meaningful models. Content models are indispensable in the early stages of complex system design, when the concept of the system is being formed. System analysis methods using decomposition approach, allow you to identify an ordered set of subsystems, elements, system properties and their relationships. The integrated content model of the system allows you to present the big picture, make a generalized description, in which the main entities are emphasized, and the details are hidden. The main thing in such a model is brevity and clarity. Such a model can serve as a basis for building more detailed models that describe individual aspects, subsystems. Thus, a meaningful model can serve as a framework for constructing other models, including mathematical ones. It also serves to structure information about an object.

The multiplicity of models of one object is due, in particular, to the fact that for different purposes it is required to build (use) different models. One of the bases for the classification of models can be the correlation of types of models with types of goals. For example, models can be divided into cognitive and pragmatic.

Cognitive models are a form of organization and presentation of knowledge, a means of connecting new knowledge with existing ones. Therefore, when a discrepancy between the model and reality is detected, the task is to eliminate this discrepancy by changing the model by bringing the model closer to reality.

Pragmatic models are a means of management, a means of organizing practical actions, a way of presenting exemplary correct actions or their results. Therefore, when a discrepancy is found between the model and reality, the task is to eliminate this discrepancy by changing reality in such a way as to bring it closer to the model.

Thus, pragmatic models are of a normative nature, they play the role of a standard, a model, under which both the activity itself and its result are “adjusted”. Examples of pragmatic models are plans, action programs, organizational charters, codes of laws, algorithms, working drawings and templates, selection parameters, technological tolerances, examination requirements, etc.

There are physical and abstract models.

Physical models are formed from a set of material objects. For their construction, various physical properties of objects are used, and the nature of the material elements used in the model is not necessarily the same as in the object under study. An example of a physical model is a layout.

Information (abstract) model is a description of the object of research in any language. The abstractness of the model is manifested in the fact that its components are concepts, and not physical elements (for example, verbal descriptions, drawings, diagrams, graphs, tables, algorithms or programs, mathematical descriptions).

Information Models describe the behavior of the original object, but do not copy it. An information model is a purposefully selected information about an object that reflects the most significant properties of this object for the researcher. Among the information (abstract) models, there are: - descriptive, visual and mixed; - epistemological, infological, cybernetic, sensual (sensual), conceptual, mathematical.

Gnoseological models aimed at studying the objective laws of nature (for example, models of the solar system, biosphere, world ocean, catastrophic natural phenomena).

infological model (narrow interpretation) is a parametric representation of the process of information circulation, subject to automated processing.

Sensual Models- models of some feelings, emotions, or models that affect human feelings (for example, music, painting, poetry).

conceptual model- this is an abstract model that reveals the cause-and-effect relationships inherent in the object under study and essential within the framework of a particular study. The main purpose of the conceptual model is to identify a set of cause-and-effect relationships that must be taken into account to obtain the required results. The same object can be represented by different conceptual models, which are built depending on the purpose of the study. So, one conceptual model can display the temporal aspects of the system functioning, another - the impact of failures on the system performance.

Mathematical model is an abstract model presented in the language of mathematical relations. It takes the form of functional dependencies between the parameters taken into account by the corresponding conceptual model. These dependencies specify the cause-and-effect relationships identified in the conceptual model and characterize them quantitatively.

In this way, model is a special object that in some respects replaces the original. Fundamentally, there is no model that would be a complete equivalent of the original. Any model reflects only some aspects of the original. Therefore, in order to obtain large gaps about the original, it is necessary to use a set of models. The complexity of modeling as a process lies in the appropriate choice of such a set of models that replace the real device or object in the required respects. For example, a system of differential equations that describes switching processes in the elements of a digital device can be used to evaluate their performance (switching time), but it is inappropriate to use to build tests or timing diagrams of the device. Obviously, in the latter cases it is necessary to use some other models, for example, logical equations

Methods of processing and systematization of knowledge of the empirical level are primarily synthesis and analysis. Analysis is the process of mental, and often real, dismemberment of an object, phenomenon into parts (features, properties, relationships). The reverse procedure of analysis is synthesis. Synthesis is a combination of the sides of the subject identified during the analysis into a single whole.

Induction is a way of reasoning or a method of obtaining knowledge, in which a general conclusion is made on the basis of a generalization of particular premises. Induction can be complete or incomplete.

Deduction is a way of reasoning or a method of moving knowledge from the particular, that is, the process of a logical transition from general premises to conclusions about particular cases.

Analogy is a method of cognition, in which the presence of similarity, the coincidence of features of non-identical objects allows us to suggest their similarity in other features. Analogy is an indispensable means of visualization, pictorial thinking.

The modeling method is based on the principle of similarity. Its essence lies in the fact that not the object itself is directly investigated, but its analogue, its substitute, its model, and then the results obtained during the study of the model are transferred to the object according to special rules. Modeling is used in cases where the object itself is difficult to access, or its direct study is economically unprofitable.

27. Empirical methods of scientific knowledge: observation and experiment. Types of experiments.

Observation is a deliberate and purposeful perception of phenomena and processes without direct intervention in their course, subject to the tasks of scientific research. The main requirements for scientific observation are as follows:

Unambiguity of purpose, intent

Consistency in observation methods

Objectivity

Possibility of control either by repeated observation or by experiment.

An important place in the process of observation is occupied by the operation of measurement. Measurement - is the definition of the ratio of one quantity to another, taken as a standard.

An experiment, unlike observation, is a method of cognition in which phenomena are studied under controlled and controlled conditions. The experiment is carried out on the basis of a theory or hypothesis that determines the formulation of the problem and the interpretation of the results. There are several types of experiment:

qualitative, establishing the presence or absence of the alleged theory of phenomena.

measuring or quantitative, setting the numerical parameters of any property of an object, process.

a special kind of experiment in the fundamental sciences is a thought experiment

a social experiment carried out in order to introduce new forms of social organization and optimize management. The scope of social experiment is limited by moral and legal norms.

Observation and experiment are the source of scientific facts. Facts are the foundation of the building of science, they form the empirical basis of science, the basis for putting forward hypotheses and creating theories.

Scientific methods of theoretical research.

1. Theoretical analysis and synthesis. elemental analysis. Analysis by units.

2. Methods of abstraction and concretization. Rising from the abstract to the concrete.

3. Modeling method.

4. Thought experiment as a kind of modeling.

5. Induction and deduction.

6. Formalization.

7. Hypothetical-deductive method, its essence.

8. Axiomatic method.

The theoretical level of scientific knowledge reflects the phenomena and processes from the side of their universal internal connections and regularities, this is achieved by rational processing of data of 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 the facts and reveal external connections between them, but also to explain why they exist, what caused them, to identify the possibilities for their transformation.

Theoretical methods (and this is their shortcoming) do not have a direct impact on the variety of observed facts, however, they make it possible to discover hidden patterns in facts, general, necessary, essential, 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 verified directly, not by empirical, practical means, but by proof. In substantiating theoretical truths, practice takes part indirectly, through truths that have already been verified before. This is due to the composition of this method.

The most important difference between theoretical knowledge and empirical knowledge is that it makes it possible to transfer conclusions obtained under certain conditions and on the basis of the analysis of certain objects to other conditions and objects, including those that do not yet exist, designed, created mentally, in the imagination. .

Let's move on to characterizing the methods of theoretical research (cognition).

Theoretical analysis and synthesis. elemental analysis. Analysis by units.

originality method of theoretical analysis and synthesis in its universal capabilities to consider the phenomena and processes of reality in their most complex combinations, to single out the most significant features and properties, connections and relationships, to establish the patterns of their development.

Analysis(Greek - decomposition, dismemberment) - the division of an object into its component parts for the purpose of their independent study.

Analysis task is to from various kinds of data reflecting individual phenomena and facts, to compile a general holistic picture of the process, to identify its inherent patterns, trends.

The characteristics of the analysis deserve special attention. from the standpoint of dialectics, where it is considered as a special technique for studying 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 regularity of the developing whole.

In social work, analysis acts as a method or way of knowing social reality.

Analysis is applied both in real (practice) and in mental activity. There are several types of analysis:

Mechanical dismemberment;

Definition of dynamic composition;

Identification of forms of interaction of 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 a mental selection of individual parts, connections based on decomposition, dismemberment of the whole. Say, when studying real social processes, phenomena, contradictions, aggregates that contain contradictions and give rise to a problem situation, it is possible to isolate separately their goals, content, external conditions, technology, organization, system of relations of its subjects for analysis.

Unit Analysis involves the dismemberment of the process while maintaining the integrity of its elementary structural elements, each of which holds the most important features of a holistic process. In the activity of the client of a social work specialist, this can be an act, in socio-pedagogical design - the social situation of personality development.

After performing the analytical work, there is a need for synthesis, integration of the results of the analysis in a common system.

Synthesis (Greek - connection, combination, composition) - the union, real or mental, of various sides, parts of an object into a single whole.

In the dictionary of the Russian language S.I. Ozhegov synthesis interpreted as method of studying a phenomenon in its unity and interconnection of parts, generalization, bringing together data obtained by analysis.

In this way, synthesis should be considered as the process of practical or mental reunification of the whole from parts or the combination of various elements, sides of an object into a single whole, a necessary stage of knowledge.

The result of synthesis is a completely new formation, the properties of which are not only an external connection of the properties of the components, but also the result of their internal interconnection and interdependence.

Analysis and synthesis are dialectically interconnected. They play an important role in the 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 (lat. - distraction)- mental abstraction of any property or attribute of an object from its other attributes, properties, connections ( concept for research in social work) .

This is done in order to study the subject more deeply, to isolate it from other subjects and from other properties, signs.

In order to penetrate into the essence of social phenomena, to reveal the invariant features of the process under study, it is necessary to isolate the subject of study in its “pure” form, to be able to dissociate itself 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, it is possible at the 1st stage to abstract from the conditions of the socio-economic crisis, political struggle, the pedagogical failure of many families and consider in a “pure” form (without interference, inhibitory influences) the educational opportunities of the family, school, cultural institutions, law enforcement agencies, government and commercial structures, public organizations.

There are different types of abstractions:

– identification abstraction, as a result of which the general properties and relations of the studied methods are singled out (the rest of the properties are disregarded). Here the classes corresponding to them are formed on the basis of establishing the equality of objects in given properties or relations, the identical in objects is taken into account and abstraction from all differences between them takes place;

– isolating abstraction- acts of the so-called "pure distraction" in which certain properties and relations are distinguished, which begin to be considered as independent individual objects ("abstract objects" - "kindness", "empathy", etc.);

– abstraction of actual infinity in mathematics– when infinite sets are considered as finite. Here the researcher is distracted from the fundamental impossibility of fixing and describing each element of an infinite set, accepting such a problem as solved;

– potential feasibility abstraction- 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, and so on. Philosophical categories are characterized by the highest level of abstraction.

The limiting case of abstraction is idealization . Idealization is the mental construction of concepts about objects that do not exist and are not feasible in reality, but those for which there are prototypes in the real world.

The basis of abstraction during idealization is taken from the connections and qualities of phenomena that exist in principle or are possible, but the abstraction is carried out so consistently, the subject is so completely isolated from the 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 formed concepts. As a result, a so-called “idealized object” is formed, which can be used by theoretical thinking when reflecting real objects.

However, it is precisely these idealized objects that serve as models that make it possible to reveal much deeper and more fully some of the connections and patterns that are manifested in many real objects.

Instantiation method in its logical nature is the opposite of abstraction. It consists in a mental reconstruction, a re-creation of an object on the basis of previously identified abstractions.

Concretization, aimed at reproducing the development of an object as an integral system, becomes a special research method. Thinking from selected individual abstractions concentrates the whole object. The result is concrete, but already mentally concrete (in contrast to the real concrete, which exists in reality).

The unity of diversity, the combination of many properties and qualities of an object, is called concrete here.

Abstract, on the contrary, is one-sided, isolated from other moments of development, the properties or characteristics of a given object.

A special method of theoretical knowledge is method of ascending from the abstract to the 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, which would most adequately reproduce 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 the study of the object itself is impossible, difficult, expensive, takes too long, etc.

Between the model and the original there must be a known similarity (similarity relation): physical characteristics, functions; the behavior of the object under study and its mathematical description; structures, etc. It is this similarity that allows you to transfer the information obtained as a result of the study of the model to the original.

Depending on the nature of the models used in scientific research, several types of modeling are distinguished.

1. Physical(material, subject): characterized by a physical similarity between the model and the original, its goal is to reproduce in the model the processes inherent in the original. According to the results of the study of certain physical properties of the model, the phenomena occurring in natural (“natural”) conditions are judged. Neglecting the results of such simulations can have serious consequences. An example is the story of the English battleship Captain, built in 1870. Shipbuilding scientist W. Reed examined the ship model and revealed 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, which resulted in the death of more than 500 sailors.

At present, physical modeling is widely used for the development and experimental study of various structures (power plant dams, irrigation systems, etc.), machines, etc. before they are actually built. For example, the aerodynamic qualities of aircraft are studied on models.

2. Perfect(mental): this type of M. includes a variety of mental representations in the form of certain 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 the solar system: electrons ("planets") revolve around the nucleus ("Sun"). The same model can be realized materially in the form of sensually perceived physical models.

Ideal modeling includes the so-called “mental modeling”, which is classified into (see table 1):

The complexity, inexhaustibility, infinity of the object of study 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). It opens up the possibility of transferring the information obtained when using the model, by analogy with the 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 the indispensability of modeling as a method of scientific knowledge.

4. A special kind of modeling based on abstraction is thought experiment.

In such an experiment, the researcher, on the basis of theoretical knowledge about the objective world and empirical data, creates ideal objects, correlates them in a certain dynamic model, mentally imitating the movement and those situations that could be 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 cognizer, to play the designed situations, to weed out ineffective or too risky options.

5. Induction (lat. - guidance) - a logical method (reception) of research associated with the generalization of the results of observations and experiments and the movement of thought from the singular to the general.

In I., the data of experience “lead” to the general, induce it. Since experience is always infinite and incomplete, inductive conclusions always have a problematic (probabilistic) character. Inductive generalizations are usually viewed as empirical truths or empirical laws.

In the dictionary of the Russian language, induction is understood as a way of reasoning from particular facts, provisions to general conclusions.

Valery Pavlovich Kokhanovsky highlights the following types of inductive generalizations:

1) popular induction, when regularly repeating properties observed in some representatives of the studied set (class) and fixed in the premises of inductive reasoning are transferred to all representatives of the studied set (class) - including its unexplored parts.

So, what is true in "n" observed cases is true in the next, or in all observed cases similar to them. However, the resulting conclusion often turns out to be false (for example, “all swans are white”) due to hasty generalization. Thus, this kind 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 case enumeration induction.

That is, when the number of cases is not limited, almost infinite, we are dealing with incomplete induction. This procedure of establishing a general proposition based on several separate cases in which a certain property was observed, which is characteristic of all possible cases similar to the observed one, is called induction by simple enumeration.

The main problem of complete induction is the question of how legitimate is such a transfer of knowledge from individual cases known to us, listed in separate sentences, to all possible and even cases still unknown to us.

2) Induction incomplete– where it is concluded that all representatives of the set under study have 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, which concludes that all representatives of the studied set have the property “n” on the basis of the information obtained during the experimental study that each representative of the studied set has the property “n”.

Those. the general sentence is established by enumerating in the form of singular sentences all the cases that are subsumed under it. If we have been able to enumerate all 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 give new knowledge and does not go beyond what is contained in its premises. The general conclusion obtained on the basis of the study of particular cases summarizes the information contained in them, allows you to generalize, systematize it.

4) Scientific induction, in which, in addition to the formal substantiation of the generalization obtained by induction, a substantive additional substantiation of its truth is given, including with the help of deduction (theories, laws). Scientific induction gives a reliable conclusion due to the fact that here the emphasis is on necessary, regular and causal relationships.

In any scientific research, it is often important to establish causal relationships between various objects and phenomena. For this, appropriate methods based on inductive reasoning are used.

Consider the main inductive methods for establishing causal relationships(Bacon–Mill rules of inductive research).

but) 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 the phenomenon occurs or does not occur differ only in one antecedent circumstance, and all other circumstances are identical, then this one circumstance is the cause of this phenomenon

in) Combined Similarity and Difference Method is formed as a confirmation of the result obtained using the single similarity method by applying the single difference method to it: this is a combination of the first two methods.

G) Accompanying 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, the rest of the previous phenomena remain unchanged.

The considered methods of establishing causal relationships are most often used not in isolation, but in interconnection, complementing each other.

Deduction (lat. - derivation):

- firstly, the transition in the process of cognition from the general to the individual (private), 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 some given sentences - premises to their consequences (conclusions). As one of the methods (techniques) of scientific knowledge is closely related to induction. These are, as it were, dialectically interconnected ways of thought movement. V.P. Kokhanovsky believes that great discoveries, 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 the establishment of new starting points by induction, to deduce consequences and compare conclusions with facts. D. provides a test of hypotheses and serve as a valuable antidote to the excess of fantasy.

The term "deduction" appeared in the Middle Ages and was introduced by Boethius. But the concept of deduction as a proof of a sentence by means of a syllogism appears already in Aristotle (First Analytics). An example of deduction as a syllogism would be the following conclusion.

The first premise: crucian is a fish;

second premise: crucian carp lives in water;

conclusion (conclusion): fish lives in water.

7. Formalization - a special approach in scientific knowledge, which consists in the use of special symbols that allow one to abstract from the study of real objects, from the content of the theoretical positions that describe them, and instead operate with a certain set of symbols (signs). Example F. - mathematical description. To build any formal system, it is necessary:

1) setting the alphabet, i.e. a certain set of characters;

2) setting the rules by which "words", "formulas" can be obtained from the initial characters of this alphabet;

3) setting the rules by which one can move from one word, formula of a given system to other words and formulas (the so-called inference rules).

Dignity F. - provides brevity and clarity of recording scientific information. A formalized language is not as rich and flexible as a natural one, but it is not polysemantic (polysemy), but has unambiguous semantics. Thus, a formalized language has the monosemic property.

The language of modern science differs significantly from natural human language. It contains many special terms, expressions, formalization tools are widely used in it, among which the central place belongs to mathematical formalization. Based on the needs of science, various artificial languages ​​\u200b\u200bare created to solve certain problems. The entire set of created and being created artificial formalized languages ​​is included in the language of science, forming a powerful means of scientific knowledge.

7 . In scientific knowledge hypothetical-deductive method was developed in the 17-18 centuries, when significant progress was made in the field of mechanics of terrestrial and celestial bodies. The first attempts to use this method in mechanics were made by Galileo and Newton. Newton's work "The Mathematical Principles of Natural Philosophy" can be considered as a hypothetical-deductive system of mechanics, the premises of which are the basic laws of motion. The method of principles created by Newton had a great influence on the development of exact natural science.

From a logical point of view, a hypothetical-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 have the greatest logical force. Hypotheses of a lower level are derived from them as premises. At the lowest level of the system are hypotheses that can be compared with empirical reality.

A variation of the hypothetical-deductive method can be considered a mathematical hypothesis, which is used as the most important heuristic tool for discovering patterns in natural science. Usually, hypotheses here are some equations that represent a modification of previously known and verified relationships. By changing these ratios, they make up a new equation expressing a hypothesis that refers 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 hypothetical-deductive method plays an auxiliary role in this process, since it does not put forward new hypotheses, but only checks the consequences arising from them, which thereby control the research process.

8. Close to the hypothetical-deductive method axiomatic method. This is a way of constructing a scientific theory, in which it is based on some initial provisions (judgments) - axioms, or postulates, from which all other statements of this theory must be derived in a purely logical way, through proof. The construction of science on the basis of the axiomatic method is usually called deductive. All concepts of the deductive theory (except for a fixed number of initial ones) are introduced by means of 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 also some branches of physics.

All the methods of cognition described above in real scientific research always work in interaction. Their specific systemic organization is determined by the characteristics of the object under study, as well as the specifics of a particular stage of the study.