A model is such a material or mentally represented object that, in the process of studying, replaces the original object, retaining some of its typical features that are important for this study. Formation of the basic concepts of the section "formalization and modeling

It was thanks to formalization that mathematical logic could be used in electronic computers that work according to its laws.

V. Pekelis

The whole life of a person constantly confronts him with acute and different tasks and problems. The emergence of such problems, difficulties, surprises means that in the reality around us there is a lot of unknown, hidden. Therefore, an ever wider knowledge of the world is needed, the discovery in it of more and more new processes, and the relationship of people and things.

The success of the student's intellectual development is achieved mainly in the classroom, where the degree of students' interest in learning, the level of knowledge, readiness for constant self-education, i.e., depends on the teacher's ability to organize systematic cognitive activity. their intellectual development.

The experience of teaching the subject of informatics shows that the types of students' activities in analyzing situations, forecasting, building information models, creating conditions for a variable choice of solutions, using heuristic techniques, and the ability to carry out design activities are especially highlighted as goals.

The specific tasks of studying computer science at school take the form:

to acquaint students with the concepts of system, information, model, algorithm and their role in the formation of a modern information picture of the world, teach them to define these concepts, highlight their features and explain them, distinguish between types of models, algorithms, etc.;
reveal the general patterns of information processes in nature, society, technical systems;
to acquaint students with the principles of formalization, structuring information and develop the ability to build information models of the studied objects and systems;
develop algorithmic and logical styles of thinking;
to form the ability to organize the search for information necessary to solve the problem;
to form the ability to plan actions to achieve the goal, using a fixed set of tools.

Formation is a process of education and training aimed at developing the personality of a person or his individual qualities. To form is to organize and conduct education and training in such a way, to influence the student in such a way as to develop one or another quality in him.

The mastering of the section “Formalization and Modeling” is proposed to be fundamental on this path.

per section “Modeling and Formalization” 8 hours are allotted. The section covers the following topics:

An object. Classification of objects. object models. 2h.
Classification of models. The main stages of modeling. 2h.
Formal and informal statement of the problem.
Basic principles of formalization. 2h.
The concept of information technology for solving problems.
Building an information model. 2h.

The main concepts that students should learn after studying the topic:

Object, model, modeling; formalization; information model; information technology for problem solving; computer experiment.

At the end of the unit, students should know:

about the existence of many models for the same object;
stages of information technology for solving problems using a computer.

students should be able to:

give examples of modeling and formalization;
give examples of a formalized description of objects and processes;
give examples of systems and their models.
build and explore the simplest information models on a computer.

The study of the section proceeds in a spiral: it begins with the concept An object. Classification of objects. For study, a slide film is used, which defines these concepts, clearly shows examples of objects, explains - what are the properties of an object, environment (see<Рисунок 1> , <Рисунок 2>) etc.

Using this slide<Приложение 1 >The student can independently understand these concepts. After the systematization of the concepts associated with the object, there is a smooth transition to the concepts model, classification of models ( look<Рисунок 3> , <Рисунок 4> ) . The student is given tasks of the type: Object - person. The phenomenon is a thunderstorm. List their models and classify them.

Man has long used modeling to study objects, processes, phenomena in various fields. The results of these studies serve to determine and improve the characteristics of real objects and processes; to understand the essence of phenomena and develop the ability to adapt or manage them; for the construction of new facilities or the modernization of old ones. Modeling helps a person to make informed and well-thought-out decisions, to foresee the consequences of their activities.

Thanks to computers, not only the areas of application of modeling are significantly expanded, but also a comprehensive analysis of the results obtained is provided.

By studying the section, students become familiar with basics of modeling and formalization. Students should understand what a model is and what types of models there are. This is necessary so that when conducting research, students would be able to choose and effectively use the software environment and tools suitable for each model. The beginning of any research is formulation of the problem, which is determined by the given goal. The type of model, the choice of software environment, and the results obtained depend on how the purpose of modeling is understood. The student learns about main stages of modeling which the researcher must pass in order to achieve his goal.

The content of training is formed by a list of different models available for understanding by students. A sufficient number of such models are already known for which the use of a computer is essential. On specific models from different school subjects, students learn simulation technologies, learning to build information models. To do this, you can use different software environments. The student determines the volume of content and opportunities for various types of information technologies, depending on his abilities.

An important point in teaching and mastering the acquired knowledge is the provision of all educational elements of the section with tests of the required level, which are taken from the methodological manual 5, 7 *, also from the Internet, author N. Ugrinovich.

This article presents one of the variants of the test concerning the main educational elements of the section "Modeling and Formalization". Also given is the text of the control work developed by S.Yu. Piskunova, and her solution, from the collection 9*

Test on the topic "Modeling and formalization"

1. What is called an attribute of an object?

Representation of a real world object with the help of a certain set of its characteristics that are essential for solving this information problem.
An abstraction of real-world objects that share common characteristics and behaviors.
Relationship between an object and its characteristics.
Each individual characteristic common to all possible instances

2. The choice of model type depends on:

The physical nature of the object.
Purpose of the object.
Objectives of the study of the object.
The information entity of the object.

3. What is an information model of an object?

A material or mentally represented object that replaces the original object in the process of research with the preservation of the most essential properties that are important for this research.
A formalized description of an object in the form of text in some coding language containing all the necessary information about the object.
A software tool that implements a mathematical model.
Description of the attributes of objects that are essential for the problem under consideration and the relationships between them.

4. Specify the classification of models in the narrow sense of the word:

Natural, abstract, verbal.
Abstract, mathematical, informational.
Mathematical, computer, information.
Verbal, mathematical, informational

5. The purpose of creating an information model is:

Processing data about a real world object, taking into account the relationship between objects.
The complication of the model, taking into account additional factors that were previously informed.
Investigation of objects based on computer experimentation with their mathematical models.
Representation of an object as text in some artificial language accessible to computer processing.

6. Information modeling is based on:

Designation and name of the object.
Replacing a real object with a corresponding model.
Finding an analytical solution that provides information about the object under study.
Description of the processes of origin, processing and transmission of information in the studied system of objects.

7. Formalization is

The stage of transition from a meaningful description of the links between the selected features of an object to a description using some coding language.
Replacing a real object with a sign or a set of signs.
The transition from fuzzy problems that arise in reality to formal information models.
Isolation of essential information about the object.

8. Information technology is called

A process determined by a combination of means and methods of processing, manufacturing, changing the state, properties, shape of a material.
Changing the initial state of an object.
A process that uses a set of means and methods for processing and transmitting primary information of a new quality about the state of an object, process or phenomenon.
A set of specific actions aimed at achieving the goal.

9. What is called simulation modeling?

Modern technology of object research.
The study of physical phenomena and processes with the help of computer models.
Implementation of the mathematical model in the form of a software tool.

10. What is a computer information model?

Representation of an object as a test in some artificial language accessible to computer processing.
A set of information that characterizes the properties and state of an object, as well as its relationship with the outside world.
A model in mental or conversational form, implemented on a computer.
Method of research related to computer technology.

11. A computer experiment consists of a sequence of steps:

The choice of a numerical method - the development of an algorithm - the execution of a program on a computer.
Building a mathematical model - choosing a numerical method - developing an algorithm - executing a program on a computer, analyzing a solution.
Model development - algorithm development - implementation of the algorithm in the form of a software tool.
Building a mathematical model - developing an algorithm - executing a program on a computer, analyzing a solution.

question number
Answer No.	4	3	2	1	4	3	1	3	3	3	2

Test work on the topic “Modeling and formalization”

Option number 1.

1. Make up an answer on the topic “Models and how to compose them”, answering the questions in sequence.

What is an object model?
What models do you meet in everyday life?
What is an information model?
Can one object be described using different information models? If yes, how will they differ?
Compose an information model of the “car” object in order to characterize it for passengers. How will this model change if the goal is to characterize the car as a technical device?
Can a strategic computer game be called a game model? If possible, why?

2. Compose a mathematical model of the problem:

Determine the time of the meeting of two pedestrians going to meet each other.

Option number 2.

1. Make up an answer on the topic “Classification of objects”, answering the questions in sequence.

What is object classification? Why is it necessary to classify objects?
Give an example of classifying objects according to common properties.
What is the principle of inheritance?
Explain with the example of the classification of objects with the general name “computer program”.
How can models be classified?
On what basis are models divided into static and dynamic?

2. Create a mathematical model of the problem:

- Determine the time when one pedestrian will catch up with another.

Option 1

1. Answers to questions

1.1. A model is an image that studies some essential aspects of an object, phenomenon or process.

1.2. In everyday life, a person encounters material and information models.

1.3. Information models describe objects in one of the coding languages (colloquial, graphic, scientific, etc.).

1.4. One and the same object can have many models, it all depends on what properties of the object are to be studied. For example, one and the same object a person in physics is considered as a material point, in biology - as a system striving for self-preservation, etc.

1.5. When compiling an information model of a car in order to describe amenities for passengers, it is necessary to indicate: is it a truck or passenger car, capacity (how many people), how many doors, the presence and size of the trunk, interior size, upholstery, shape, seat softness, air conditioning, music, etc. .d. If you characterize a car as a technical device, then weight, size, load capacity, maximum speed, fuel consumption, etc. are indicated.

1.6. A strategic computer game displays the information processes that take place in life. For example, military strategies describe the structure of the state system in general and its army in particular, financial strategies describe various economic and social laws. Therefore, a strategic computer game can be considered as an information model of the information process that it describes.

L - initial distance

Result: t - movement time

For: L, v 1 , v 2 > 0

Method: t = L / (v 1 + v 2)

Option 2

1. Answers to questions

1.1. Among the variety of objects in the surrounding world, we try to identify groups of objects that have common properties. A class is a group of objects that have common properties. The objects in a class are called instances of the class. Objects of the same class differ from each other in some special properties. Classification is the distribution of objects into classes and subclasses based on common properties.

1.2. An example of a classification according to common properties - the object of literature can be divided into three large classes according to content: scientific literature, fiction, journalistic literature.

1.3. In a hierarchical structure, objects are organized into levels where the lower level instance is called the child class and is part of the higher level instance called the parent class. The most important property of classes is inheritance - each child class inherits all the properties of the parent class.

1.4. Any computer program is an algorithm written in a language understandable to a computer. Programs are divided into system and application. They perform different functions, but all are written in a language understandable to a computer - this is the property inherited by each child class (system and application programs) from the parent class - a computer program.

1.5. Models can be classified according to any essential feature.

1.6. Models that describe a system at a certain point in time are referred to as statistical information models. Models describing the processes of change and development of the system are referred to as dynamic information models.

2. Mathematical model of the problem

Given: t 02 - start time of the second pedestrian

v 1 - the speed of the first pedestrian

v 2 - the speed of the second pedestrian

Result: t - meeting time of pedestrians

When: t 02 , v 1 , v 2 > 0; v1< v 2

L 2 \u003d (t - t 02) * v 2

t * v 1 \u003d (t - t 02) * v 2

t * v 1 - t * v 2 = - t 02 * v 2

t \u003d t 02 * v 2 / (v 2 - v 1)

Literature:

for students

Ivanova I.A. Informatics. Grade 9: Workshop. - Saratov: Lyceum, 2004
Informatics, Basic course, grades 7 - 9. – M.: Basic Knowledge Laboratory, 2001.
Informatics grade 7-8 / edited by N.V. Makarova. - St. Petersburg: Publishing house "Peter", 1999.
Informatics grade 9 / edited by N.V. Makarova. - St. Petersburg: Peter Kom, 1999.
N. Ugrinovich “Informatics and information technologies”
O. Efimova, V. Morozov, N. Ugrinovich. Course of computer technology with the basics of informatics. Textbook for senior classes. - M., ABF, 1999.

Methodology

Beshenkov S.A., Lyskova V.Yu., Matveeva N.V. Formalization and modeling // Informatics and education. - 1999. - No. 5. - S. * - *; No. 6. - P.21-27; No. 7. - P.25-29.
Boyarshinov V.G. Mathematical modeling in the school course of informatics // Informatics and education. - 1999. - No. 7. - P.13-17.
Vodovozov V.M. Information preparation in the environment of visual objects // Informatics and
education. - 2000. - No. 4. - P.87-90.
Obornev E.A., Oborneva I.V., Karpov V.A. Modeling in spreadsheets // Informatics and education. - 2000. - No. 5. - P. 47-52.
Informatics. Test tasks. – M.: Basic Knowledge Laboratory, 2002.
Makarenko A.E. etc. Preparing for the exam in computer science. - M .: Iris-Press, 2002
Molodtsov V.A., Ryzhikova N.B. How to pass the exam and centralized testing in computer science for 100 points. - Rostov n / a: Phoenix, 2003.
Petrosyan V.G., Perepecha I.R., Petrosyan L.V. Methods for solving physical problems on a computer // Informatics and Education. - 1996. - No. 5. - P. 94-99.
Planned learning outcomes in computer science and information technology and their assessment in the main and secondary (ponoy) general education schools: Instructive-methodical collection / Authors and compilers: N.E. Kostyleva, L.Z. Gumerova, R.I. Yarochkina, L.V. Lunina, S.Yu. Piskunova, E.V. Zhuravleva - Naberezhnye Chelny: CRO, 2004.
Ponomareva E.A. Lesson on studying the concept of a model // Informatics and education. - 1999. - No. 6. - S. 47-50.
Ostrovskaya E.M. Modeling on a computer // Informatics and education. - 1998. - No. 7. - P. 64-70; No. 8. - P.69-84.
Smolyaninov A.A. The first lessons on the topic "Modeling" // Informatics and education. - 1998. - No. 8. - P. 23-29.
Khenner E.K., Shestakov A.P. Course "Mathematical modeling" // Informatics and education. - 1996. - No. 4. - P.17-23.

What is an object model and why is it created;
- what role does information play when creating a model;
- what is an information model;
- what is the adequacy of the information model.

The role of the goal in the development of an information model of an object

Knowing the world around us, each of us forms our own idea of it. One of the ways of cognition is the creation and study of a model of a real object, process or natural phenomenon. When constructing and studying a model, it is customary to introduce a generalized concept of the object of study (original, prototype), meaning by this any material or intangible object (process), as well as a natural phenomenon.

A model is understood as a material or mentally represented object, which in the process of research replaces the original object so that its study provides new knowledge about the original object. The model acts as a kind of tool of knowledge, which the researcher puts between himself and the object of study and with the help of which he studies the object of interest to him. The modeling process is a cyclic process, as a result of which it is possible to repeatedly change the model itself, constantly improving and refining it.

When creating a model, an important stage is the collection of information about the object to the extent that the goal of building the model requires. Without such information, model development is impossible.

A model is an object that reflects the essential properties of a real object of study, which are selected in accordance with a given modeling goal.

There are no strict rules on how best to present the model. However, humanity has accumulated vast experience in this field of activity. Models can take on all sorts of shapes and forms. Regardless of this, the model can be attributed either to the class of material or to the class of non-material models.

Any model is created and changed due to the information that a person has about real objects or phenomena. The ability to create models, as well as, in general, the possibilities in the knowledge of the surrounding world, depends on the ability of a person to correctly understand and process information. In order to study a real object, we purposefully collect information about it.

This information can be stored in a person’s memory, but if it is presented in any form in one of the information coding languages, then in this case we can talk about the creation and use of an information model of the research object (original).

The study of some aspects of the original object is carried out at the cost of refusing to reflect other aspects. Therefore, any information model replaces a real-life object only in a strictly limited sense. It follows from this that several information models can be created for one object, focusing attention on certain aspects of the object under study and characterizing the object with varying degrees of detail.

As an illustration, consider the housing construction industry. It's about building a house. What should be the information model of this house? It turns out that there can be many. Their number is determined by the goal facing those who are related to this construction. It is obvious that the points of view of the apartment buyer, architect, investor and construction organization in determining the purpose of building an information model differ significantly from each other. Thus, for the house in question, several different information models can be created, depending on the goal that is set for those who create it. Let's consider some of them.

Suppose the buyer's goal is to purchase a comfortable home. To build an information model, the most significant information should be selected in accordance with a given goal. Although the concept of comfort is ambiguous - everyone understands it in their own way, let's try to express it in one of the possible interpretations. We list the main indicators that should determine comfort. The house should be located in a quiet green place, equipped with modern technical devices, it should have an underground garage, a concierge or a security guard should sit in the entrance. To build an information model, it is necessary to select information that reflects all of the above requirements and present it, for example, in the form of a table or list. The task of the buyer includes: search for companies that are engaged in the construction of such houses; construction for each variant of the corresponding information model; according to the results of the analysis - the choice of the best option in terms of the goal. The selected option will be the information model (Table 1.1).

Table 1.1. Information models of houses under construction from the point of view of the buyer.
The goal is to acquire comfortable housing

We will use a similar technique to build information models for other persons interested in construction, for example, an investor and an architect. It is clear that the goals in both cases will be completely different compared to the buyer, which means that the models will also differ.

From the investor's point of view, the main goal is to make a profit, which means that the indicators that contain the information of interest to him will mainly be of a financial nature (Table 1.2).

Table 1.2. Information models of houses under construction from the point of view of the investor.
The goal is to get maximum profit

From the point of view of an architect, the main goal is to develop a modern architectural project taking into account the environment: the surrounding area with the established style of nearby houses, existing infrastructure, ecology, etc. Several options for an information model corresponding to this goal are given in Table. 1.3.

Let's highlight the main thing that you should pay attention to when building an information model:

♦ first, the goal of building an information model should be clearly formulated;
♦ then select information relevant to this purpose for several similar objects of study;
♦ then present this information using one of the information coding languages, for example in the form of a list of parameters (indicators) and their values for each object in tabular form (as shown in Tables 1.1-1.3).

Table 1.3. Information models of houses under construction from the point of view of an architect.
The goal is to create an architectural design that matches the environment

An information model is a model containing purposefully selected and presented in some form the most essential information about an object.

Information models play a very important role in human life. The knowledge gained in the lessons at school allows you to create various information models that together reflect the information picture of the world around you.

The lessons of history make it possible to build a model for the development of society, and knowledge of this model allows you to create a history of your life, either repeating the mistakes of your ancestors, or taking them into account.

In astronomy classes, you are taught about the solar system in accessible ways.

In geography lessons, you get information about geographical objects: mountains, rivers, cities and countries. These are also information models.

In chemistry lessons, information about the chemical properties and laws of interaction of different substances is supported by experiments that are models of real chemical processes.

Before building a model, it is necessary to collect information about the subject or phenomenon under study and present it in an appropriate form. Forms of presentation of information models can be different. The most commonly used forms are:
♦ oral (verbal);
♦ sign: tabular, graphic, symbolic (text, numbers, special characters);
♦ in the form of gestures or signals.

The form of presentation of information usually depends on the tool with which it will be processed. Nowadays, computers are used in most cases to process information. This universal tool allows you to develop and explore models of various objects: molecules and atoms, bridges and architectural structures, aircraft and cars. The computer memory can store large amounts of information about the object under study. This allows you to consider an object from different angles, explore its shape, states, actions, using a specific model and appropriate modeling methods for each case.

One of the most convenient forms of information model representation is a table. It is this form that is chosen as the main one in the entire set of textbooks. This is also due to the fact that the modeling and study of the properties of the model will be carried out on a computer, where a strict formalization of the task is required. Such a table reflects the main characteristics of the object, selected in accordance with the goal of modeling. Table 1 can serve as examples of this form of presentation. 1.1-1.3.

The concept of information model adequacy

Any model should reflect the most significant, from the point of view of the goal, properties of the object of study (original or prototype). The object of research can be not only a material object that a person can touch (a house, a tree, a flower, a piece of furniture), but also an intangible object, process or phenomenon (a piece of music, an oral story, a natural phenomenon, a dance).

Compliance of the model with the original can be achieved in appearance, in structure, in behavior, both individually and in combination of these features, depending on the goal of the study. Compliance in appearance is achieved mainly by meeting structural, ergonomic and aesthetic requirements. Correspondence in structure is achieved with the help of a system analysis of the object of study, as a result of which the composition of its elements is determined - simple objects that make up the original, as well as the relationships connecting them. All this together determines the structure of the object under study, the most essential features of which should be reflected in the model. Behavioral compliance is achieved by analyzing the behavior of the prototype, that is, studying its dynamic properties, and creating a model that would reflect the most significant aspects of this behavior.

In all these cases, the problem of assessing the quality of the model arises. The quality of a model depends on its ability to reflect and reproduce objects and phenomena of the objective world, their structure and regular order. How much information needs to be collected in order for the resulting information model to fully reflect the essential properties of the original object? To answer this question, the concept of model adequacy is introduced in modeling.

The adequacy of the model is the correspondence of the model to the original object in terms of those properties that are considered essential for the study.

The adequacy of the information model is the correspondence of the information model to the original object in terms of those properties that are considered essential for the study.

The concept of adequacy is, to some extent, conditional, since a complete correspondence of a model to a real object cannot be achieved. Any model has differences from the original. The model loses its meaning both in the case of complete adequacy to the original, when it ceases to be a model and becomes an exact copy of the modeled object, and in case of insufficient adequacy, excessive difference from the original, when the properties essential for the study are not reflected in the model.

A special role in determining the degree of adequacy is played by the information model, which the researcher needs not only as an independent object, but also as the basis for creating a material model. Recall that the information model includes only those parameters (indicators) that reflect the most significant information from the point of view of the goal. This means that some information will not be included in the information model. How to find the golden mean: what to include and what to neglect? The answer to this question can be given by checking the adequacy of the information model to the original.

The adequacy of the information model is determined in several ways, but, as a rule, these are rigorous mathematical methods of analysis based on probability theory and mathematical statistics. The method of numerical experiment on a computer is widespread, where it is also necessary to apply mathematical methods as a tool for generalizing the results obtained.

For a rougher assessment of the adequacy of the model, you can use simpler methods: for example, observation of the state and behavior of the original object or comparison with similar real or ideal objects that exist only in the human imagination.

Let us turn to the previous example related to the construction of a house. What is the adequacy of the three models presented in Table. 1.1-1.3, a real object? Realizing that the real object has not yet been built, it is too early to talk about the presence of any adequacy. However, this is why models exist, in order to achieve the smallest possible differences between the model and the real object already at the preliminary stages. From the point of view of the buyer, a greater degree of adequacy can be achieved if the selected option lists the largest number of indicators whose values correspond to the stated goal - maximum comfort. If we analyze the presented four options for the values of the parameters in Table. 1.1, then preference should be given to Elita, but this will be the most expensive housing. If the buyer imposes restrictions on the cost of the apartment, then the adequacy of the information models of other companies is less. In this case, it is necessary to carry out additional work to comprehend your requirements, refine existing information models in order to clarify additional information aspects, and then re-evaluate the adequacy of all three model options. The same should be done for other information models, for the investor and the architect. Do it yourself.

Control questions and tasks

Tasks

1. Consider different options for information models for the example of a house under construction given in the topic. For each model, evaluate its adequacy.

2. As an object of study, select the object "school" and develop information models that reflect the point of view of the student, parent of the student, school director. For each model, evaluate its adequacy.

3. Select a river object as the object of study and develop information models that reflect the point of view of the fisherman and the artist. For each model, evaluate its adequacy.

4. As an object of study, select the object "store" and develop information models that reflect the point of view of the buyer, seller and store owner. For each model, evaluate its adequacy.

5. As an object of study, select the process of creating a school play. Develop several information models. For each model, evaluate its adequacy.

test questions

1. What is an object model?

2. What is meant by the object of research and what are the synonyms for this concept?

3. What kinds of models do you know?

4. What is an information model of an object?

5. What is the most important thing when building an information model?

6. What is the adequacy of the model and why is this concept introduced^

7. How to make sure that the information model is adequate; original?

Information object

After studying this topic, you will learn and repeat:

What is an information picture of the world;
- what is an information object;
- How do the information model and the information object relate to each other.

We live in the real world, surrounded by various material objects. The presence of information about the objects of the real world gives rise to another world, inseparable from the consciousness of specific people, where only information exists. We give this world a variety of names. One of these names is the information picture of the world.

Cognition of the real world occurs through the information picture of the world. A person forms his own idea of the real world, receiving and comprehending information about each real object, process or phenomenon. At the same time, each person has his own information picture of the world, which depends on many factors, both subjective and objective. Of course, the level of education of a person plays a big role here. The informational pictures of the world of a schoolchild, a student and a teacher will differ significantly. The more voluminous and diverse the information that a person can perceive, the more colorful this picture is. So, for example, a child's information picture of the world is not at all the same as his. parents.

One of the ways of knowing the real world is modeling, which is primarily associated with the selection of the necessary information and the construction of an information model. However, any information model reflects the real object only in a limited aspect - in accordance with the goal set by the person. This is where a certain "inferiority" of perception of the world arises, if a person studies it only from one side, determined by one goal. Comprehensive knowledge of the surrounding world is possible only when there are different information models corresponding to different goals.

Suppose we have created several information models for one real world object (Fig. 1.2). Their number is determined by the number of targets set. For example, the information models of our planet for a schoolchild, an astronomer, a meteorologist and a geodesist will differ significantly, since they have different goals, which means that the information they select and form the basis of the information model will be different.

During development, the model is constantly compared with the prototype object to assess its compliance with the original. The measure of compliance is the concept of adequacy, discussed in the previous topic.

Rice. 1.2. Relationship between real world objects and information models

What will happen if we deal only with information models, moving away from the real world? In this case, there is no need for the concept of adequacy, since by eliminating the object, we thereby break the virtual connection that establishes the object-model relationship. And this means that we will completely immerse ourselves in a virtual, non-existent world, where only information circulates. There will be nothing to compare the model with, which means that there will be no need for the modeling itself.

Thus, the model turns into a kind of independent object, which is a collection of information.

Remembering the concept of an object, which is defined as some part of the surrounding world, considered as a whole, we can suggest that an information model that has no connection with the original object can also be considered an object, but not material, but informational. Thus, the information object is obtained from the information model by "alienating" information from the original object.

An information object is a collection of logically related information.

Then the information world will be a set of various information objects (Fig. 1.3).

Rice. 1.3. After breaking the links with the objects of the real world, there remains a set of information objects

An information object "alienated" from the original object can be stored on various material media. The simplest material carrier of information is paper. There are also magnetic, electronic, laser and other storage media.

With information objects fixed on a material carrier, you can perform the same actions as with information when working on a computer: enter them, store, process, transfer. However, the technology of working with information objects will be somewhat different than with information models. Creating an information model, we determined the purpose of modeling and, in accordance with it, identified essential features, focusing on the study. In the case of an information object, we are dealing with a simpler technology, since no research is needed. Here, the traditional stages of information processing are quite enough: input, storage, processing, transmission.

When working with information objects, the computer plays an important role. Using the opportunities that office technologies provide to the user, you can create a variety of professional computer documents that will be varieties of information objects. Everything that is created in computer environments will be an information object.

A literary work, a newspaper article, an order are examples of information objects in the form of text documents. Pictures, drawings, schemes are information objects in the form of graphic documents. A payroll sheet, a table of the cost of purchases made in a wholesale store, an estimate for the performance of work, and other types of documents in tabular form, where automatic calculations are made using formulas that link table cells, are examples of information objects in the form of spreadsheets. The result of a selection from the database is also an information object.

Quite often we are dealing with compound documents in which information is presented in different forms. Such documents may contain text, figures, tables, formulas, and much more. School textbooks, magazines, newspapers are well-known examples of compound documents that are information objects of a complex structure. To create compound documents, software environments are used that provide the possibility of presenting information in various forms.

Computer-generated presentations and hypertext documents are other examples of complex information objects. The presentation is a set of computer slides that provide not only the presentation of information, but also its display according to a pre-created scenario. Hypertext can be a document that contains hyperlinks to other parts of the same document or to other documents containing additional information.

Control questions and tasks

Tasks

1. Give examples of information objects that exist outside the computer environment.

2. Give examples of information objects that exist in the computer environment.

test questions

1. What is meant by the information picture of the world?

2. What is the information picture of the world of a preschool child?

3. What is the information picture of the world of a high school student?

4. What way of knowing the real world do you know?

5. What is an information object?

6. Under what conditions can an information model be perceived as an information object?

7. What can be done with an information object?

A model is such a material or mentally represented object that, in the process of studying, replaces the original object, retaining some of its typical features that are important for this study. A model is a simplified representation of a real object, process or phenomenon. What is a model?

The model is necessary in order to: Understand how a particular object is arranged - what are its structure, basic properties, laws of development and interaction with the surrounding world; Learn to manage an object or process and determine the best methods of management for given goals and criteria (optimization); Predict the direct and indirect consequences of the implementation of the specified methods and forms of impact on the object; No model can replace the phenomenon itself, but when solving a problem, when we are interested in a certain property of the process or phenomenon being studied, the model turns out to be useful, and sometimes the only tool for research, knowledge.

The process of building a model is called modeling, in other words, modeling is the process of studying the structure and properties of the original with the help of a model. Modeling technology requires the researcher to be able to set problems and tasks, predict research results, make reasonable estimates, highlight the main and secondary factors for building models, choose analogies and mathematical formulations, solve problems using computer systems, and analyze computer experiments. Modeling

Material modeling It is customary to call material (physical) modeling, in which a real object is opposed to its enlarged or reduced copy, which allows research (as a rule, in laboratory conditions) with the help of subsequent transfer of the properties of the studied processes and phenomena from model to object based on the theory of similarity.

Types of modeling Ideal modeling is based not on the material analogy of the object and the model, but on the analogy of the ideal, conceivable. Signed modeling is modeling that uses sign transformations of any kind as models: diagrams, graphs, drawings, formulas, symbol sets. Mathematical modeling is a modeling in which the study of an object is carried out by means of a model formulated in the language of mathematics: a description and study of the laws of Newtonian mechanics by means of mathematical formulas.

Scope of use Educational: visual aids, training programs, various simulators; Experienced: a ship model is tested in the pool to determine the ship's stability when rolling; Scientific and technical: an electron accelerator, a device that simulates a lightning discharge, a stand for testing a TV; Gaming: military, economic, sports, business games; Simulation: the experiment is either repeated many times in order to study and evaluate the consequences of any actions on the real situation, or is carried out simultaneously with many other similar objects, but set in different conditions).

Types of Models Material models can be otherwise called subject, physical. They reproduce the geometric and physical properties of the original and always have a real embodiment. Information models are a set of information that characterizes the properties and states of an object, process, phenomenon, as well as the relationship with the outside world.

Types of models A sign model is an information model expressed by special signs, that is, by means of any formal language. A computer model is a model implemented by means of a software environment. Verbal (from the Latin "verbalis" - oral) model - an information model in a mental or conversational form.

Models according to their purpose A cognitive model is a form of organization and presentation of knowledge, a means of combining new and old knowledge. The cognitive model, as a rule, is adjusted to reality and is a theoretical model. The pragmatic model is a means of organizing practical actions, a working representation of the goals of the system for its management. Reality is adjusted to some pragmatic model. This is usually the applied model. An instrumental model is a means of constructing, exploring and/or using pragmatic and/or cognitive models. Cognitive models reflect existing, and pragmatic, though not existing, but desired and, possibly, feasible relationships and connections.

The main properties of any model are: the finiteness of the model reflects the original only in a finite number of its relations and, in addition, the modeling resources are finite; simplification of the model displays only the essential aspects of the object and, in addition, should be easy to study or reproduce; approximateness reality is displayed by the model roughly, or approximately; adequacy of the modeled system the model should successfully describe the modeled system; visibility, visibility of the main properties and relationships;

The main properties of any model are: accessibility and manufacturability for research or reproduction; informative model should contain sufficient information about the system (within the framework of the hypotheses adopted in the construction of the model) and provide an opportunity to obtain new information; preservation of the information contained in the original (with the accuracy of the hypotheses considered in the construction of the model); completeness in the model should take into account all the main connections and relationships necessary to ensure the purpose of modeling; the stability of the model should describe and ensure the stable behavior of the system, even if it is initially unstable; closure model takes into account and displays a closed system of necessary basic hypotheses, connections and relationships

The goals of modeling Knowledge of the surrounding world. Why does a person create models? To answer this question, we must look into the distant past. Several million years ago, at the dawn of mankind, primitive people studied the surrounding nature in order to learn how to resist natural elements, use natural benefits, and simply survive. The accumulated knowledge was passed from generation to generation orally, later in writing, and finally with the help of subject models. Thus was born, for example, a model of the globe globe, which allows you to get a visual representation of the shape of our planet, its rotation around its own axis and the location of the continents. Such models make it possible to understand how a particular object is arranged, to find out its basic properties, to establish the laws of its development and interaction with the surrounding world of models.

Modeling Goals Creation of objects with specified properties (a task like "How to make..."). Having accumulated enough knowledge, a person asked himself the question: “Is it possible to create an object with the given properties and capabilities in order to counteract the elements or put natural phenomena at its service?” Man began to build models of objects that did not yet exist. This is how the ideas of creating windmills, various mechanisms, even an ordinary umbrella were born. Many of these models have now become a reality. These are objects created by human hands.

Modeling objectives Determining the consequences of the impact on the object and making the right decision (a problem like “What will happen if ...”: what will happen if the fare in transport is increased, or what will happen if nuclear waste is buried in such and such an area?) For example, in order to save St. Petersburg from constant floods that cause enormous damage, it was decided to build a dam. During its design, many models were built, including full-scale ones, precisely in order to predict the consequences of interference with nature.

Modeling goals Efficiency of object (or process) control. Since the criteria for management are very contradictory, it will be effective only if "both the wolves are fed and the sheep are safe." For example, you need to arrange food in the school cafeteria. On the one hand, it must meet age requirements (high-calorie, containing vitamins and mineral salts), on the other hand, most children should like it and, moreover, be “affordable” for parents, and on the third, the cooking technology must correspond to the capabilities of school canteens. How to combine the incompatible? Building a model will help find an acceptable solution.

Object analysis At this stage, the modeled object, its main properties, its elements and the relationships between them are clearly distinguished. A simple example of subordinate object relationships is parsing a sentence. First, the main members (subject, predicate) are distinguished, then the secondary members related to the main ones, then the words related to the secondary ones, etc.

Stage 2. Model development At this stage, properties, states, actions and other characteristics of elementary objects are clarified in any form: orally, in the form of diagrams, tables. An idea is formed about the elementary objects that make up the original object, i.e., the information model. Models should reflect the most significant features, properties, states and relationships of objects of the objective world. They give complete information about the object.

Stage 3. Computer experiment Computer modeling is the basis for the representation of knowledge in a computer. Computer modeling for the birth of new information uses any information that can be updated with the help of a computer. The progress of modeling is associated with the development of computer modeling systems, and the progress in information technology is with updating the experience of modeling on a computer, with the creation of banks of models, methods and software systems that allow you to collect new models from bank models.

Stage 4. Analysis of simulation results The ultimate goal of simulation is to make a decision, which should be developed on the basis of a comprehensive analysis of the results obtained. This stage is decisive either you continue the study or finish. Perhaps you know the expected result, then you need to compare the received and expected results. In case of a match, you can make a decision.

Simulation has now received an unusually wide application in many fields of knowledge: from philosophical and other humanitarian branches of knowledge to nuclear physics and other branches of physics, from the problems of radio engineering and electrical engineering to the problems of mechanics and fluid mechanics, physiology and biology, etc. modeling is the main way of knowing the world.

Modeling issues were considered in the works of philosophers (V. A. Shtof, I. B. Novikov, N. A. Uemov and others), specialists in pedagogy and psychology (L. M. Fridman, V. V. Davydov, B. A. Glinsky, S. I. Arkhangelsky and others).

The term "model" is widely used in various spheres of human activity and has many semantic meanings. The modeled object is called the original, the modeling object is called the model.

The concept of "model" arose in the process of experimental study of the world, and the word "model" itself came from the Latin words "modus", "modulus", meaning measure, image, method. In almost all European languages, it was used to denote an image or prototype, or a thing similar in some respect to another thing.

There are different points of view on the definition of the concept of "model".

So, for example, V. A. Shtof understands a model as such a mentally represented or materially realized system that displays and reproduces an object in such a way that its study provides new information about this object.

A. I. Uemov defines a model as a system, the study of which serves as a means to obtain information about another system.

Charles Lave and James March define a model as follows: “A model is a simplified picture of the real world. It has some, but not all, properties of the real world. It is a set of interconnected assumptions about the world. A model is simpler than the phenomena it purports to represent or explain.

V. A. Polyakov believes that “a model is an ideal formalized representation of a system and the dynamics of its stage-by-stage formation. The model should simulate real tasks and situations in an integrated way, be compact, adequately convey state transitions, and should coincide with the task or situation under consideration.”

Most psychologists understand a “model” as a system of objects or signs that reproduces some of the essential properties of the original system. The presence of a partial similarity relation (“homomorphism”) allows the model to be used as a substitute or representative of the system under study.

Sometimes a model is understood as such a material or mentally represented object that, in the process of cognition (study), replaces the original object, retaining some typical features that are important for this study.

Here are some examples of models:

1) An architect is preparing to build a building of a type never seen before. But before erecting it, he constructs this building with cubes on the table to see how it will look. This is a model.

2) There is a painting on the wall depicting a raging sea. This is a model.

“Modeling is the process of using models (of the original) to study certain properties of the original (transforming the original) or replacing the original with models in the course of any activity” (for example, to transform an arithmetic expression, its components can be temporarily denoted by letters).

“Modeling is an indirect practical or theoretical study of an object, in which not the object of interest to us is directly studied, but some auxiliary artificial or natural system:

1) being in some objective correspondence with the cognizable object;

2) capable of replacing him in certain respects;

3) giving, during its study, ultimately, information about the modeled object itself "

(the three features listed are, in fact, the defining features of the model).

Based on the above, we can distinguish the following modeling goals:

1) understanding the device of a particular system, its structure, properties, laws of development and interaction with the outside world;

2) management system, determining the best methods of management for given goals and criteria;

3) forecasting direct and indirect consequences of the implementation of the specified methods and forms of impact on the system.

All three goals imply, to one degree or another, the presence of a feedback mechanism, that is, it is necessary not only to transfer the elements, properties and relationships of the modeled system to the modeling one, but vice versa.

The scientific basis of modeling is the theory of analogy, in which the main concept is - the concept of analogy - the similarity of objects in terms of their qualitative and quantitative characteristics. All these types are united by the concept of generalized analogy - abstraction. Analogy expresses a special kind of correspondence between the compared objects, between the model and the original.

In general, analogy is the middle, mediating link between the model and the object. The function of such a link is:

a) in comparison of various objects, detection and analysis of the objective similarity of certain properties, relations inherent in these objects;

b) in operations of reasoning and conclusions by analogy, that is, in inferences by analogy.

Although the literature notes the inextricable link between the model and analogy, but "analogy is not a model." Uncertainties are generated by fuzzy distinction:

a) analogy as a concept expressing the actual relationship of similarity between different things, processes, situations, problems;

b) analogy as a special logic of reasoning;

c) analogy as a heuristic method of cognition;

d) analogy as a way of perception and understanding of information;

e) analogy as a means of transferring proven methods and ideas from one branch of knowledge to another, as a means of building and developing a scientific theory.

Inference by analogy involves interpreting the information obtained from the study of the model. The peculiarity of the method of obtaining conclusions by analogy in the logical literature is called traduction- transfer of relations (properties, functions, etc.) from one object to another. The traductive method of reasoning is used when comparing various objects in terms of quantity, quality, spatial position, temporal characteristics, behavior, functional parameters of the structure, etc.

Modeling is multifunctional, that is, it is used in a variety of ways for different purposes at different levels (stages) of research or transformation. In this regard, the centuries-old practice of using models has given rise to an abundance of forms and types of models.

Models are classified based on the most significant features of objects. In the literature devoted to the philosophical aspects of modeling, various classification features are presented, according to which different types of models are distinguished. Let's consider some of them.

V. A. Shtof offers the following classification of models:

1) according to the method of their construction (the form of the model);

2) by qualitative specifics (content of the model).

According to the method of construction, they distinguish material and ideal models. Material models, despite the fact that these models are created by man, exist objectively. Their purpose is specific - to reproduce the structure, nature, flow, essence of the process under study - to reflect the spatial properties - to reflect the dynamics of the processes under study, dependencies and connections.

Material models are inextricably linked with imaginary ones (before you can build anything, you must have a theoretical understanding, justification). These models remain mental even if they are embodied in some material form. Most of these models do not claim to be a material embodiment.

In turn, material models are divided into:

· figurative (constructed from sensually visual elements);

· iconic (in these models, the elements of the relationship and the properties of the phenomena being modeled are expressed using certain signs);

· mixed (combining the properties of both figurative and iconic models).

The advantage of this classification is that it provides a good basis for analyzing the two main functions of the model:

Practical (as a tool and means of a scientific experiment);

Theoretical (as a specific image of reality, which contains elements of the logical and sensual, abstract and concrete, general and singular).

B. A. Glinsky has another classification in his book “Modeling as a method of scientific research”. Along with the usual division of models according to the method of their implementation, he also divides the models according to the nature of the reproduction of the sides of the original into:

· substantial ;

· structural;

· functional;

mixed.

Consider another classification proposed by L. M. Fridman. From the point of view of the degree of clarity, he divides all models into two classes:

· material (real, real);

· ideal.

Material models include those that are built from any material objects, from metal, wood, glass and other materials. They also include living beings used to study certain phenomena or processes. All these models can be directly perceived by the senses, because they exist really, objectively. They are the material product of human activity.

Material models, in turn, can be divided into static (fixed) and dynamic (active) .

The author of the classification refers to the first type models that are geometrically similar to the originals. These models convey only the spatial (geometric) features of the originals on a certain scale (for example, models of houses, buildings of cities or villages, various kinds of dummies, models of geometric shapes and bodies made of wood, wire, glass, spatial models of molecules and crystals in chemistry, models of aircraft, ships and other machines, etc.).

Dynamic (acting) models include those that reproduce some processes, phenomena. They can be physically similar to the originals and reproduce the simulated phenomena on some scale. For example, to calculate the projected hydroelectric power station, they build an operating model of the river and the future dam; the model of the future ship allows you to study some aspects of the behavior of the designed ship in the sea or on the river in an ordinary bath, etc.

The next type of operating models are all kinds analog and simulating , which reproduce this or that phenomenon with the help of another, in some sense more convenient. Such, for example, are electrical models of various kinds of mechanical, thermal, biological and other phenomena. Another example is the kidney model, which is widely used in medical practice. This model - an artificial kidney - functions in the same way as a natural (living) kidney, removing toxins and other metabolic products from the body, but, of course, it is arranged completely differently than a living kidney.

Ideal models are usually divided into three types:

· ob-different (iconic);

· iconic (sign-symbolic);

· mental (mental).

Figurative, or iconic (picture), models include various kinds of drawings, drawings, diagrams that convey in a figurative form the structure or other features of the simulated objects or phenomena. Geographic maps, plans, structural formulas in chemistry, the model of the atom in physics, etc., should also be attributed to this type of ideal models.

Sign-symbolic models are a record of the structure or some features of the modeled objects using signs-symbols of some artificial language. Examples of such models are mathematical equations, chemical formulas.

Finally, mental (mental, imaginary) models are ideas about any phenomenon, process or object that express the theoretical scheme of the object being modeled. A mental model is any scientific representation of a phenomenon in the form of its description in natural language.

As you can see, the concept of a model in science and technology has many different meanings, among scientists there is no single point of view on the classification of models, and therefore it is impossible to unambiguously classify the types of modeling. Classification can be carried out on various grounds:

1) by the nature of the models (that is, by modeling tools);

2) by the nature of the simulated objects;

3) by areas of application of modeling (modeling in engineering, in the physical sciences, in chemistry, modeling of living processes, modeling of the psyche, etc.)

4) by levels ("depth") of modeling, starting, for example, with the allocation in physics of modeling at the microlevel.

The most famous is the classification according to the nature of the models. According to it, the following types of modeling are distinguished:

1. Subject modeling, in which the model reproduces the geometric, physical, dynamic or functional characteristics of the object. For example, a model of a bridge, a dam, a model of an airplane wing, etc.

2. Analog modeling, in which the model and the original are described by a single mathematical relationship. An example is the electrical models used to study mechanical, hydrodynamic and acoustic phenomena.

3. Sign modeling, in which the models are sign formations of some kind: diagrams, graphs, drawings, formulas, graphs, words and sentences in some alphabet (natural or artificial language)

4. Mental modeling is closely connected with the sign, in which models acquire a mentally visual character. An example in this case is the model of the atom, proposed at the time by Bohr.

5. Finally, a special type of modeling is the inclusion in the experiment not of the object itself, but of its model, due to which the latter acquires the character of a model experiment. This type of modeling indicates that there is no hard line between the methods of empirical and theoretical knowledge.

Test on the topic "Modeling and formalization"

1. What is called an attribute of an object?

Representation of a real world object with the help of a certain set of its characteristics that are essential for solving this information problem.

An abstraction of real-world objects that share common characteristics and behaviors.

Relationship between an object and its characteristics.

Each individual characteristic common to all possible instances

2. The choice of model type depends on:

The physical nature of the object.

Purpose of the object.

Objectives of the study of the object.

The information entity of the object.

3. What is an information model of an object?

A material or mentally represented object that replaces the original object in the process of research with the preservation of the most essential properties that are important for this research.

A formalized description of an object in the form of text in some coding language containing all the necessary information about the object.

A software tool that implements a mathematical model.

Description of the attributes of objects that are essential for the problem under consideration and the relationships between them.

4. Specify the classification of models in the narrow sense of the word:

Natural, abstract, verbal.

Abstract, mathematical, informational.

Mathematical, computer, information.

Verbal, mathematical, informational

5. The purpose of creating an information model is:

Processing data about a real world object, taking into account the relationship between objects.

The complication of the model, taking into account additional factors that were previously informed.

Investigation of objects based on computer experimentation with their mathematical models.

Representation of an object as text in some artificial language accessible to computer processing.

6. What model is static (describing the state of an object)?

Formula of uniformly accelerated motion

Chemical reaction formula

Chemical compound formula

Newton's second law.

7. Formalization is

The stage of transition from a meaningful description of the links between the selected features of an object to a description using some coding language.

Replacing a real object with a sign or a set of signs.

The transition from fuzzy problems that arise in reality to formal information models.

Isolation of essential information about the object.

8. Information technology is called

A process determined by a combination of means and methods of processing, manufacturing, changing the state, properties, shape of a material.

Changing the initial state of an object.

A process that uses a set of means and methods for processing and transmitting primary information of a new quality about the state of an object, process or phenomenon.

A set of specific actions aimed at achieving the goal.

9. Material model is:

1. Anatomical model;

2. Technical description of the computer;

3. Drawing of a functional diagram of a computer;

4. Program in a programming language.

10. What is a computer information model?

Representation of an object as a test in some artificial language accessible to computer processing.

A set of information that characterizes the properties and state of an object, as well as its relationship with the outside world.

A model in mental or conversational form, implemented on a computer.

Method of research related to computer technology.

11. A computer experiment consists of a sequence of steps:

The choice of a numerical method - the development of an algorithm - the execution of a program on a computer.

Building a mathematical model - choosing a numerical method - developing an algorithm - executing a program on a computer, analyzing a solution.

Model development - algorithm development - implementation of the algorithm in the form of a software tool.

Building a mathematical model - developing an algorithm - executing a program on a computer, analyzing a solution.

№ question

№ response