Explanations of known facts which. Material models. What can be modeled

“Modeling and Formalization” Grade 11 - Make models. Testing. Race for knowledge. Envelopes with tasks. Code of conduct for students. Biological models. Material model numbers. Structure. Material models. Weather forecast. Chess. Relay of terms. The groups change places. Local map. Decipher the known terms.

“Stages of model development” - stage 3. The main stages of developing and researching models on a computer. Practical task. Stage 2. Model of the solar system. Stage 5. Stage 1. Descriptive information models are typically built using natural languages and pictures. Construction of a descriptive information model. Stage 4.

“System approach in modeling” - System approach in organizations. Basic definitions of the system approach: System approach to cost restructuring. Function - the operation of an element in the system. A systematic approach as the basis for introducing specialized training. Peter Ferdinand Drucker. A system is a set of interconnected elements that form integrity or unity.

“Modeling as a method of scientific knowledge” - Let’s build a table. Method of understanding the surrounding world. Hierarchical model. Type. Two classes of objects. Yura lives in Novgorod. Five guys. Modeling stages. Math modeling. Lilac. Table of the “objects-properties” type. Real items. Semantic network of government structure. Development of a computer model.

"Modeling" - Examples of modeling. Models of airplanes and ships. Computer model. Words to insert. Drawings. Modeling. Examples of modeling in various fields of activity. Computer experiment. System. Objects and processes. Visualization of formal models. Main stages of development. Give examples.

“Modeling, formalization, visualization” - System. Conducting a computer experiment. Main stages. Network structure. Computer device prices. Models. Computer classification. Subject models. Models are divided into two classes. Network information models. Visualization of models. Types information models. Two ways to build a computer model.

There are 18 presentations in total

>> Models of objects and their purpose

Chapter 2. "Information Modeling

§ 2.1. Models of objects and " their purpose

A person strives to understand the objects of the surrounding world; he interacts with existing objects and creates new objects.

One of the methods of cognition an object ov of the surrounding world is modeling, which consists of creating and researching “substitutes” of real objects. The “substitute object” is usually called a model, and the original object is called a prototype or original.

For example, in a conversation we replace real objects with their names, window decorators use a mannequin - a model of a human figure, designers build models of airplanes and cars, and architects build models of buildings, bridges and parks. A model is any visual aid used on lessons at school: globe, dummy, map, diagram, table and so on.

The model is important not in itself, but as a tool that facilitates cognition or visual representation of an object.

Models are resorted to when the object under study is too large (solar system model) or too small (atomic model), when the process proceeds very quickly (internal combustion engine model) or very slowly (geological model), when studying the object may be dangerous for others (model of an atomic explosion), lead to the destruction of itself (model of an airplane) or the creation of a real object is very expensive (architectural model of a city), etc.

What do all models have in common? What properties do they have?

Firstly, the model is not an exact copy of the original object: it reflects only part of its properties, relationships and behavioral features. For example, you can put a suit on a mannequin, but you cannot talk to it. A car model can be without a motor, and a house model can be without electrical wiring and plumbing.

Secondly, since any model always reflects only part sign ov the original, you can create and use different models the same object. For example: a ball can reproduce only one property of the Earth - its shape; an ordinary globe also reflects the location of the continents; and the globe, which is part of the current model of the Solar System, also shows the trajectory of the Earth around the Sun.

The more features of an object a model reflects, the more complete it is. However, it is impossible to reflect all the properties of the original object in the model, and most often it is not necessary. After all, when creating a model, a person, as a rule, pursues a very specific goal and strives to most fully reflect only those features of objects that seem important to him, essential for the realization of this goal. If, for example, a model of an airplane is created for a collection, then it reproduces the appearance of the airplane, and not its flight characteristics.

The requirements for the model depend on the purpose of modeling: exactly what features of the original object it should reflect.

The characteristics of the original can be reflected in the model in one of two ways.

Firstly, signs can be copied and reproduced. Such a model is called full-scale (material).

Examples of full-scale models are dummies and models - reduced or enlarged copies that reproduce the appearance of a modeling object (globe), its structure (model of the Solar system) or behavior (radio-controlled model of a car).

Secondly, the features of the original can be described in one of the languages - give a verbal description, give a formula, diagram or drawing. This model is called an information model.

Models are used by humans to:

Presentation of material objects (model of a residential area in an architect’s studio);
explanations of known facts (model of a human skeleton in the biology classroom);
testing hypotheses and obtaining new knowledge about the objects under study (flight model of a new aircraft design in a wind tunnel);
forecasting (photographs of the movement of air masses taken from space);
management (train schedule), etc.

Briefly about the main thing

A model is an object that is used as a "surrogate", a representative of another object (the original) for a specific purpose. A model is not an exact copy of the original object: it reflects only part of its properties, relationships and behavioral features. You can create and use different models of the same object. The process of creating and using a model is called modeling.

There are natural and information models. Full-scale models are real objects that, in a reduced or enlarged form, reproduce the appearance, structure or behavior of the modeled object. Information models are descriptions of the original object in information coding languages. Models are used by humans to: represent material objects, explain known facts, obtain new knowledge about objects under study, predict and control, etc.

Questions and tasks

1. What is a model?
2. Name the main properties of models.
3. What is modeling?
4. How can we call the relationship between the original object and its model?
5. What models are called full-scale? Give 2-3 examples of full-scale models.
6. What models are called information models? Give 2-3 examples of information models.
7. For each of the listed models, name the actions that a person can perform with both it and the original object:

radio-controlled model airplane;
verbal description of the jacket;
apartment plan
life-size plasticine teapot;
a mental image of a future trip. What actions can only be performed with the original?

8. In what situation can artificial flowers and dummies of fruit be used as “substitute” models for real flowers and fruits? Which properties and relationships of objects are reflected by these models and which are not?

9. Give examples of using models for:

a) presentation of material objects;
b) explanations of known facts;
c) testing hypotheses and obtaining new knowledge about the objects under study;
d) forecasting;
d) management.

Bosova L. L., Computer Science and ICT: textbook for grade 7 by L. L. Bosova. M.: BINOM. Knowledge Laboratory, 2010. 229 p. : ill.

Lesson content lesson notes supporting frame lesson presentation acceleration methods interactive technologies Practice tasks and exercises self-test workshops, trainings, cases, quests homework discussion questions rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures, graphics, tables, diagrams, humor, anecdotes, jokes, comics, parables, sayings, crosswords, quotes Add-ons abstracts articles tricks for the curious cribs textbooks basic and additional dictionary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in a textbook, elements of innovation in the lesson, replacing outdated knowledge with new ones Only for teachers perfect lessons calendar plan for the year; methodological recommendations; discussion program Integrated Lessons

If you have corrections or suggestions for this lesson,

4. Modeling and formalization(9 grades).

4.1 Models and simulation

A person strives to understand the objects of the surrounding world; he interacts with existing objects and creates new objects.

One of the methods of cognition of objects in the surrounding world is modeling, consisting in the creation and research of “substitutes” of real objects. A “replacement object” is usually called model, and the original object is prototype or original.

Model is an object that has some properties of another object ( original) and is used instead.

For example, in a conversation we replace real objects with their names, window decorators use a mannequin - a model of a human figure, designers build models of airplanes and cars, and architects use models of buildings, bridges and parks. A model is any visual aid used in school lessons: a globe, a dummy, a map, a diagram, a table, etc.

What can be modeled?

You can build models of objects. For example ,

Small copies of buildings, ships, airplanes, ...

Models of the atomic nucleus, crystal lattices

Blueprints

You can build process models. For example ,

Changes in the environmental situation

Economic models

Historical models

You can build models of phenomena. For example ,

Earthquake

Solar eclipse

Models are used by humans to:

Presentation of material objects (model of a residential area in an architect’s studio);

Explanations of known facts (model of a human skeleton in the biology classroom);

Testing hypotheses and obtaining new knowledge about the objects under study (flight model of a new aircraft design in a wind tunnel);

Forecasting (photographs of the movement of air masses taken from space);

management (train schedule), etc.

The model is important not in itself, but as a tool that facilitates cognition or visual representation of an object. Modeling is the process of creating and using models to study originals.

When to use modeling:

the original doesn't exist

Ancient Egypt

Consequences of nuclear war

researching the original is life-threatening or expensive:

Testing a new spacesuit for astronauts

Development of a new aircraft or ship

the original is difficult to examine directly:

Solar system, galaxy (large sizes)

Atom, neutron (small sizes)

Processes in an internal combustion engine (very fast)

Geological phenomena (very slow)

I'm only interested in some properties of the original

Airplane fuselage paint inspection

The more features of an object a model reflects, the more complete it is. It is impossible, and it is not necessary, to reflect in the model all the features of the object - the original. The features of the original object that must be reproduced in the model are determined the purpose of modeling– the purpose of the future model. These features are essential for this model from the point of view of the purpose of the modeling.

Modeling Goals

original research study of the essence of an object or phenomenon

analysis (“what will happen if ...”) learn to predict the consequences of various influences on the original

synthesis (“how to make it so that...”) learn to control the original by influencing it

optimization (“how to do better”) choosing the best solution under given conditions

What do all models have in common? What properties do they have?

Secondly, since any model always reflects only part of the characteristics of the original, it is possible to create and use different models of the same object. For example: a ball can reproduce only one property of the Earth - its shape; an ordinary globe also reflects the location of the continents; and the globe, which is part of the current model of the Solar System, also shows the trajectory of the Earth around the Sun. Several different models can correspond to the original and vice versa!

The more features of an object a model reflects, the more complete it is. However, it is impossible to reflect all the properties of the original object in the model, and most often it is not necessary. After all, when creating a model, a person, as a rule, pursues a very specific target and strives to most fully reflect only those features of objects that seem important to him, significant to realize this goal. If, for example, a model of an airplane is created for a collection, then it reproduces the appearance of the airplane, and not its flight characteristics.

The requirements for the model depend on the purpose of modeling: exactly what features of the original object it should reflect. The type of model is determined by the goals of the modeling.

The characteristics of the original can be reflected in the model in one of two ways. The nature of the models can be of two types. Firstly, material (full-scale, physical, object) models. They copy and reproduce the features of the original. Examples of full-scale models are dummies and models - reduced or enlarged copies that reproduce the appearance of a modeling object (globe), its structure (model of the Solar system) or behavior (radio-controlled model of a car).

Secondly, information models – description of the original features in one of the information coding languages (in the form of a verbal description, formulas, diagrams or drawings).

Computer science examines the construction of information models using computer technology. An informationally cultured person must be able to build various information models, both with the help of a computer and without it.

4.2 Classification of models

There are many options for classifying information models. Let's look at some of them.

If we take as a basis the classification subject area, then we can distinguish physical, environmental, economic, sociological and other models.

Depending on the account time factor There are dynamic (changing over time) and static (not changing over time) models.

Models by area of application There are educational ones (including simulators), experimental ones - when creating new technical means, and scientific and technical ones.

Depending on the presentation forms information about the modeling object, a distinction is made between iconic, figurative and mixed (figurative-sign) types of information models.

Models by structure there are

Tabular models (matching pairs)

Exist special types of models. These include:

- imitation- it is impossible to calculate or predict the behavior of the system in advance, but you can simulate its reaction to external influences. The challenge is to find the best solution method
trial and error(multiple experiments)

Examples : drug testing on mice, monkeys, ... models of the learning process

- gaming– taking into account the actions of the enemy. The task is to find the best option actions in
worst case scenario.

Examples : models of economic situations; models of military operations; sport games; staff trainings

4.3 Information models

The original object can be replaced by a set of its properties: names (values) and values. A set of properties containing all necessary information about the objects and processes under study are called information model.

For example, an information model of a country house is a card from a catalog from which the customer of a construction company can select a suitable project. Each card in the catalog contains a table with the names (values) of house properties and the values of these properties.

All names of properties in information models are always symbolic elements, because the name can only be expressed by signs. But the values of quantities can carry both symbolic and figurative information. For example, the value of the quantity “appearance” can be expressed by a figurative element (drawing), and the values of other quantities are expressed using signs (numbers, words, commas). The figurative element of the information model can be not only a drawing or photograph, but also a three-dimensional layout or video recording. However, it must be possible to associate this element with the characteristics of a specific object. For example, in the line " Appearance» the house catalog may indicate the layout code. And in order for the layouts themselves to be elements of the information model, and not decoration, they need to be provided with labels with codes.

Information models represent objects and processes in figurative or symbolic form. Based on the method of presentation, the following types of information models are distinguished:

Figurative models (drawings, photographs, etc.) are visual images of objects recorded on some information medium (paper, photo and film, etc.). Photographs of the Earth's surface obtained from satellites provide specialists with a lot of information.

Sign information models are built using various natural and formal languages (sign systems). A signed information model can be presented in the form of text in natural language or a program in a programming language, formula (for example, the area of a rectangle S = Ab) etc.

Mixed information models combine figurative and symbolic elements. Examples of mixed information models include geographic maps, graphs, diagrams, etc. All of these models use both graphic elements, and signs.

4.4 Stages of building an information model

Any model is built to solve a certain problem. The construction of an information model begins with an analysis of the conditions of this problem, expressed in natural language (Fig. 2.2).

As a result of analyzing the problem conditions, the object of modeling and the purpose of modeling are determined.

After determining the goal of modeling, the properties, main parts and connections between them that are significant from the point of view of this particular goal are identified in the modeling object. In this case, it must be clearly defined what is given (what initial data are known, what data is acceptable) and what needs to be found in the problem being solved. The relationships between the input data and the results should also be indicated.

The next stage of building an information model is formalization - presentation of the identified connections and identified essential features of the modeling object in some form (verbal description, table, picture, diagram, drawing, formula, algorithm, computer program etc.).

Formalization- this is the replacement of a real object with its formal description, i.e., its information model.

Information models exist separately from modeling objects and can be processed independently of them. Having built an information model, a person uses it instead of the original object to study this object and solve the problem.

4.5 Verbal models.

One type of information sign models is verbal models. Verbal models- these are descriptions of objects, phenomena, events, processes in natural languages. They are also called text models. For example, the heliocentric model of the world that Copernicus proposed was verbally described as follows:

· The Earth rotates around its axis and around the Sun:

· All planets orbit around the Sun.

The verbal model consists of individual elements - words, interconnected in meaning. In turn, words consist of elements - letters, interconnected by spelling rules. Words are subsystems for text and supersystems for letters. The text as a whole is a model - a description of the original. It can reflect various properties of the described object. The quality of the verbal information model depends on the correct spelling of words, the accuracy of their selection, the correctness of combining words into sentences and the order of words and sentences in the text.

Verbal models can describe situations, events, and processes. A bunch of verbal models contained in school textbooks and encyclopedias. We use verbal descriptions in communication (in letters, during conversations...) To build these models, we use the usual spoken language we are familiar with.

There are some features of spoken languages:

Polysemy, synonymy, homonymy - the same word can have several meanings, several words can have the same meaning, the same meaning.

Words can be used both literally and figuratively.

These features make human speech expressive, colorful, and emotional. But their presence makes it impossible to use spoken language in many sciences, when creating verbal (sign) information models for the exact sciences. Mathematics, chemistry, computer science and other sciences, based on spoken language, create their own formalized scientific language containing many terms (words unique to this science). Formalized means without ambiguity, synonyms, or homonyms. In a formalized language, each word is assigned exactly one meaning and sense.

Verbal descriptions are very diverse; they can be performed in different styles. First of all, a distinction is made between conversational and book styles. Book style has the following varieties: scientific, official business, journalistic, artistic.

Scientific style is used to convey accurate scientific information. The most important qualities of a scientific style are logic and clarity of presentation. Scientific texts contain a large number of professional words and terms.

Artistic style is a style works of art. Its main purpose is to influence the reader or listener using figurative language (comparisons, metaphors, epithets, etc.)

Official business style is used when preparing documents.

The journalistic style is used when writing articles, notes in magazines and newspapers.

Working with verbal information models (historical, biological, geographical, artistic and other descriptive texts) requires a thoughtful attitude to what you read. The better the text is, the better it is formatted, the easier it is to read and analyze.

Works of fiction are also models, since they fix the reader’s attention on certain aspects of human life. When analyzing a literary work, you identify objects in it and their properties, relationships between characters, connections between events, draw parallels with other works, etc. The literary genre such as a fable is most directly related to the concept of a model. The meaning of this genre is to transfer relationships between people to relationships between fictional characters, for example animals.

4.6 Mathematical models

The main language of information modeling in science is the language of mathematics. Information models built using mathematical concepts and formulas are called mathematical models.

Example 1. In Fig. 2.3 is given geometric model proof of the Pythagorean theorem. It is so simple that the proof of the equality c2 = a2 + b2 becomes obvious.

International competitions" href="/text/category/mezhdunarodnie_sorevnovaniya/" rel="bookmark">At the international diving competitions, the first five places were taken by athletes from Germany, Italy, China, Russia and Ukraine. Even before the start of the competition, experts expressed their assumptions about their results:

1) The first place will be taken by an athlete from China, and the athlete from Ukraine will be third.

2) Ukraine will be in last place, and Germany will be in second to last place.

3) Germany will definitely be fourth, and China will take first place.

4) Russia will be first, and Italy will be in second place.

5) No, Italy will be fifth, and Germany will win.

At the end of the competition, it turned out that each expert was correct in only one statement. What places did the participants take in the competition?

Material models can otherwise be called objective, physical. They always have a real embodiment. Such models may reflect:

External properties of source objects;

Internal organization source objects;

The essence of processes and phenomena occurring with original objects.

Material models are material copies of modeling objects.

The simplest examples of material models are children's toys. From them the child gets his first idea of the world around him. A two-year-old child plays with a teddy bear. When, years later, a child sees a real bear in a zoo, he will easily recognize it.

Processes in which a real object participates can be replaced in a material model by processes of a different physical nature. For example, in the same children's car, the movement process is ensured not by the operation of an internal combustion engine, but by a twisted spring or an inertial mechanism. But at the same time, the principle of converting the rotational motion of the wheels into the forward motion of the car is respected.

Material models may not resemble their prototypes. For example, a robot that replaces people in difficult and hazardous production is completely different from a person. This is a mechanical device, a manipulator.

Since material models help to learn the properties of real objects and understand the “mechanism” of complex phenomena, they are often used in the learning process. Material models are a human skeleton and a stuffed bird, a three-dimensional model of the solar system and a model of a multi-stage rocket, an inclined plane with balls in a physics classroom, etc.

Information models cannot be touched or seen with your own eyes, they have no material embodiment, because they are built only on information. This modeling method is based on an information approach to studying the surrounding reality.

An information model is a set of information that characterizes the properties and state of an object, process, phenomenon, as well as the relationship with the outside world.

A person strives to understand the objects of the surrounding world; he interacts with existing objects and creates new objects.

One of the methods of cognition of objects in the surrounding world is modeling, which consists of creating and researching “substitutes” of real objects. The “replacement object” is usually called a model, and the original object is called prototype or original.

For example, in a conversation we replace real objects with their names, window decorators use a mannequin - a model of a human figure, designers build models of airplanes and cars, and architects use models of buildings, bridges and parks. A model is any visual aid used in school lessons: a globe, a dummy, a map, a diagram, a table, etc.

The model is important not in itself, but as a tool that facilitates cognition or visual representation of an object.

What do all models have in common? What properties do they have?

The requirements for the model depend on the purpose of modeling: exactly what features of the original object it should reflect.

The characteristics of the original can be reflected in the model in one of two ways.

Firstly, signs can be copied and reproduced. This model is called natural (material). Examples of full-scale models are dummies and models - reduced or enlarged copies that reproduce the appearance of a modeling object (globe), its structure (model of the Solar system) or behavior (radio-controlled model of a car).

Secondly, the features of the original can be described in one of the information coding languages - give a verbal description, give a formula, diagram or drawing. This model is called an information model.

Models are used by humans to:

· presentation of material objects (model of the development of a residential area in the architect’s workshop);

· explanations of known facts (model of the human skeleton in the biology classroom);

· testing hypotheses and obtaining new knowledge about the objects under study (flight model of a new aircraft design in a wind tunnel);

· forecasting (photographs of the movement of air masses taken from space);

· management (train schedule), etc.

i Briefly about the main thing

Questions and tasks

1. What is a model?

2. Name the main properties of models.

3. What is modeling?

4. How can we call the relationship between the original object and its model?

5. What models are called full-scale? Give 2-3 examples of full-scale models.

6. What models are called information models? Give 2-3 examples of information models.

7. For each of the listed models, name the actions that a person can perform with both it and the original object:

· radio-controlled model airplane;

· verbal description of the jacket;

· apartment plan;

· life-size plasticine teapot;

· a mental image of a future trip.

What actions can only be performed with the original?

9. Give examples of using models for:

a) presentation of material objects;

b) explanations of known facts;

c) testing hypotheses and obtaining new knowledge about the objects under study;

d) forecasting;

d) management.

§ 2.2. Information models

The original object can be replaced by a set of its properties: names (values) and values. A set of properties containing all the necessary information about the objects and processes under study is called an information model.

In table Figure 2.1 shows an example of an information model of a country house - a card from a catalog, from which the customer of a construction company can select a suitable project. Each card in the catalog contains the names (values) of house properties (on the left) and the values of these properties (on the right).

Table 2.1

The figurative element of the information model can be not only a drawing or photograph, but also a three-dimensional layout or video recording. However, it must be possible to associate this element with the characteristics of a specific object. For example, the “Exterior” line in a house catalog may contain a layout code. And in order for the layouts themselves to be elements of the information model, and not decoration, they need to be provided with labels with codes.

Information models represent objects and processes in figurative or symbolic form. According to the method of presentation, the following types of information models are distinguished - Fig. 2.1.