In everyday life, in production, in research, engineering or any other activity, a person is constantly faced with solving problems. All tasks according to their purpose can be divided into two categories: computing tasks whose purpose is to determine a certain quantity, and functional tasks designed to create a certain apparatus that performs certain actions - functions.
For example, designing a new building requires solving the problem of calculating the strength of its foundation, supporting structures, calculating the financial costs of construction, determining the optimal number of employees, etc. To increase the productivity of builders, many functional machines have been created (functional tasks have been solved), such as an excavator, a bulldozer, a crane, etc.
Computers of the first and second generation were used mainly for solving computational problems: carrying out engineering, scientific, and financial calculations. Starting from the third generation, the field of application of computers also includes the solution of functional problems: this is database maintenance, management, and design. A modern computer can be used to solve almost any problem.
Human activity and, in particular, problem solving are inextricably linked with the construction, study and use of models of various objects, processes and phenomena. In his activity - in the practical sphere, artistic, scientific - a person always creates a certain cast, a substitute for the object, process or phenomenon with which he has to deal. It can be a painting, a drawing, a sculpture, a model, mathematical formula, verbal description and etc.
object(from lat. objectum - subject) is called everything that opposes the subject in his practical and cognitive activity, everything that this activity is aimed at. Objects are understood as objects and phenomena, both accessible and inaccessible to human sensory perception, but having a visible effect on other objects (for example, gravity, infrasound or electromagnetic waves). Objective reality, which exists independently of us, is an object for a person in any of his activities and interacts with him. Therefore, an object should always be considered in interaction with other objects, taking into account their mutual influence.
Human activity usually goes in two directions: study properties of the object for the purpose of their use (or neutralization); creation new objects with useful properties. The first direction relates to scientific research and has a great role in their conduct. hypothesis, i.e. prediction of the properties of an object with insufficient knowledge of it. The second direction relates to engineering design. Wherein important role plays concept analogies– a judgment about any similarity between a known and a projected object. The analogy may be complete or partial. This concept is relative and is determined by the level of abstraction and the purpose of constructing an analogy.
Model(from Latin modulus - sample) of any object, process or phenomenon is called a substitute (image, analogue, representative) used as an original. The model gives us a representation of a real object or phenomenon in some form different from the form of its real existence. For example, in a conversation we replace real objects with their names, words. And from the replacement name in this case the most basic thing is required - to designate the necessary object. Thus, from childhood we are faced with the concept of “model” (the very first model in our life is a nipple).
The model is a powerful tool of knowledge. The creation of models is resorted to when the object under study is either very large (model of the solar system) or very small (model of the atom), when the process proceeds very quickly (model of an internal combustion engine) or very slowly (geological models), the study of the object can lead to its destruction (training grenade) or the creation of a model is very expensive (architectural model of the city), etc.
Each object has a large number of different properties. In the process of building a model, the main, most significant, properties, those that interest the researcher. This is the main feature and the main purpose of the models. Thus, under model some object is understood that replaces the real object under study with the preservation of its most essential properties.
There is no such thing as just a model, “model” is a term that requires a qualifying word or phrase, for example: a model of an atom, a model of the Universe. In a sense, a picture of an artist or a theater performance can be considered a model (these are models that reflect one or another side of the human spiritual world).
The study of objects, processes or phenomena by constructing and studying their models to determine or refine the characteristics of the original is called modeling. Simulation can be defined as the representation of an object by a model in order to obtain information about this object by experimenting with its model. The theory of replacing original objects with a model object is called modeling theory. The whole variety of modeling methods considered by modeling theory can be divided into two groups: analytical and simulation modeling.
Analytical modeling consists in building a model based on describing the behavior of an object or system of objects in the form of analytical expressions - formulas. With such modeling, the object is described by a system of linear or non-linear algebraic or differential equations, the solution of which can give an idea of the properties of the object. Analytical or approximate numerical methods are applied to the obtained analytical model, taking into account the type and complexity of the formulas. The implementation of numerical methods is usually assigned to computers with high computing power. However, the application of analytical modeling is limited by the complexity of obtaining and analyzing expressions for large systems.
Simulation modeling involves the construction of a model with characteristics that are adequate to the original, based on any of its physical or information principles. This means that external influences on the model and the object cause identical changes in the properties of the original and the model. With such modeling, there is no general analytical model of large dimensions, and the object is represented by a system consisting of elements interacting with each other and with outside world. By setting external influences, it is possible to obtain the characteristics of the system and analyze them. Recently, simulation modeling has been increasingly associated with the modeling of objects on a computer, which allows you to interactively explore models of objects of various nature.
If the simulation results are confirmed and can serve as a basis for predicting the behavior of the objects under study, then the model is said to be adequate object. The degree of adequacy depends on the purpose and criteria of modeling.
The main goals of modeling:
7. Understand how a particular object works, what is its structure, basic properties, laws of development and interaction with the outside world (understanding).
8. Learn to manage an object (process) and determine best ways management under given goals and criteria (management).
9. Predict the direct and indirect consequences of the implementation of the specified methods and forms of impact on the object (forecasting).
Almost any modeling object can be represented by a set of elements and relationships between them, i.e. be a system interacting with the external environment. System(from the Greek. system - the whole) is a purposeful set of interconnected elements of any nature. External environment is a set of elements of any nature existing outside the system that influence the system or are under its influence. With a systematic approach to modeling, first of all, the purpose of modeling is clearly defined. Creating a model of a complete analogue of the original is a laborious and expensive task, so the model is created for a specific purpose.
Once again, we note that any model is not a copy of the object, but reflects only the most important, essential features and properties, neglecting the rest of the characteristics of the object, which are insignificant within the framework of the task. For example, a model of a person in biology can be a system striving for self-preservation; in chemistry, an object consisting of various substances; in mechanics, a point with mass. One and the same real object can be described by different models (in different aspects and for different purposes). And the same model can be considered as a model of completely different real objects (from a grain of sand to a planet).
No model can completely replace the object itself. But when solving specific problems, when we are interested in certain properties of the object under study, the model turns out to be useful, simple, and sometimes the only research tool.
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Modeling method.
At present, the modeling method is widely used in pedagogical research.
Modeling is a method of creating and examining models. The study of the model allows you to get new knowledge, new holistic information about the object.
The essential features of the model are: visibility, abstraction, an element of scientific fantasy and imagination, the use of analogy as a logical method of construction, an element of hypotheticality. In other words,the model is a hypothesis expressed in visual form.
An important property of the model is the presence of creative imagination in it. Concepts, paradigms, various scenarios, business and cognitive games, etc. can become forms of modeling, say, the educational process.
The process of creating a model is quite laborious, the researcher, as it were, goes through several stages.
First - a thorough study of the experience associated with the phenomenon of interest to the researcher, the analysis and generalization of this experience and the creation of a hypothesis underlying the future model.
Second - drawing up a research program, organizing practical activities in accordance with the developed program, making adjustments to it prompted by practice, clarifying the initial research hypothesis taken as the basis of the model.
The third - Creation of the final version of the model. If at the second stage the researcher, as it were, offers various options for the constructed phenomenon, then at the third stage, on the basis of these options, he creates the final sample of the process (or project) that he is going to implement.
In pedagogy, modeling is successfully used to solve important didactic problems. For example, an educator-researcher may develop models for: structure optimization educational process, activation of cognitive independence of students, student-centered approach to students in the educational process.
The modeling method opens up the possibility of mathematization for pedagogical science pedagogical processes. Mathematization of pedagogy has a huge epistemological potential. Application mathematical modeling is most closely connected with an ever deeper knowledge of the essence of educational phenomena and processes, a deepening theoretical foundations research.
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Modeling (in the broadest sense)- the main method of research in all fields of knowledge, in various fields of human activity.
Modeling in scientific research has been used since ancient times. Modeling elements have been used since the very beginning of the emergence of the exact sciences, and it is no coincidence that some mathematical methods are named after such great scientists as Newton and Euler, and the word "algorithm" comes from the name of the medieval Arab scientist Al-Khwarizmi.
Gradually, modeling captured all new areas of scientific knowledge: technical design, construction and architecture, astronomy, physics, chemistry, biology and, finally, social sciences. However, the modeling methodology has long been developed by individual sciences independently of each other. There was no unified system of concepts, a unified terminology. Only gradually the role of modeling as a universal method began to be realized. scientific knowledge. Great success and recognition in almost all industries modern science brought the twentieth century to the modeling method. In the late 1940s and early 1950s, the rapid development of modeling methods was due to the advent of computers (computers), which saved scientists and researchers from a huge amount of routine computational work. Computers of the first and second generations were used to solve computational problems, for engineering, scientific, financial calculations, for processing large amounts of data. Starting from the third generation, the field of application of computers also includes the solution of functional problems: it is database processing, management, and design. A modern computer is the main tool for solving any modeling problems.
Here are the basic concepts related to modeling ,,.
Object (from lat. objectum - subject) of research- everything that human activity is aimed at.
Model (object - original)(from Latin modus - "measure", "volume", "image") - an auxiliary object that reflects the patterns, essence, properties, features of the structure and functioning of the original object that are most essential for the study.
The original meaning of the word "model" was associated with the art of building, and in almost all European languages it was used to denote an image or prototype, or a thing similar in some respect to another thing.
Currently, the term "model" is widely used in various fields of human activity and has many semantic meanings. This tutorial deals only with models that are tools for gaining knowledge.
Modeling- a research method based on replacing the original object under study with its model and working with it (instead of the object).
Modeling theory- the theory of replacing the original object with its model and studying the properties of the object on its model.
As a rule, some system acts as an object of modeling.
System- a set of interrelated elements united to achieve a common goal, isolated from the environment and interacting with it as an integral whole, and at the same time showing the main system properties. 15 main system properties are singled out, among which are: emergence (emergence); wholeness; structuredness; integrity; subordination to the goal; hierarchy; Infinity; ergaticity.
System properties:
1. Emergence (emergence). This is a system property, according to which the result of the behavior of the system has an effect that is different from the “addition” (independent connection) in any way of the results of the behavior of all the “elements” included in the system. In other words, according to this feature of the system, its properties are not reduced to the totality of properties of the parts of which it consists, and are not derived from them.
2. The property of wholeness, purposefulness. The system is always considered as something whole, integral, relatively isolated from the environment.
3. structured property. The system has parts that are expediently connected to each other and to the environment.
4. Integrity property. In relation to other objects or with environment the system acts as something inseparable into interacting parts.
5. The property of subordination to the goal. The whole organization of the system is subordinated to some goal or several different goals.
6. property of hierarchy. A system can have several qualitatively different levels of structure that cannot be reduced to one another.
7. property of infinity. The impossibility of complete knowledge of the system and its comprehensive representation by any finite set of models, in particular, descriptions, qualitative and quantitative characteristics etc.
8. Ergatic property. A system having parts may include a person as one of its parts.
Essentially, under modeling the process of building, studying and applying models of an object (system) is understood. It is closely related to such categories as abstraction, analogy, hypothesis, etc. The modeling process necessarily includes the construction of abstractions, and inferences by analogy, and the construction of scientific hypotheses.
Hypothesis- a certain prediction (assumption) based on experimental data, observations of a limited scope, conjectures. The hypotheses put forward can be tested in the course of a specially designed experiment. When formulating and testing the correctness of hypotheses, analogy is of great importance as a method of judgment.
by analogy called a judgment about any particular similarity of two objects. A modern scientific hypothesis is created, as a rule, by analogy with scientific provisions tested in practice. Thus, the analogy connects the hypothesis with the experiment.
The main feature of modeling is that it is a method of indirect cognition with the help of auxiliary substitute objects. The model acts as a kind of tool of knowledge, which the researcher puts between himself and the object, and with the help of which he studies the object of interest to him.
In the most general case, when building a model, the researcher discards those characteristics, parameters of the original object that are not essential for studying the object. The choice of characteristics of the original object, which are preserved and included in the model, is determined by the goals of modeling. Usually, such a process of abstracting from non-essential parameters of an object is called formalization. More precisely, formalization is the replacement of a real object or process by its formal description.
The main requirement for models is their adequacy to real processes or objects that the model replaces.
In almost all sciences about nature, animate and inanimate, about society, the construction and use of models is a powerful tool of knowledge. Real objects and processes are so multifaceted and complex that the best (and sometimes the only) way to study them is often the construction and study of a model that reflects only some facet of reality and therefore many times simpler than this reality. Centuries-old experience in the development of science has proved in practice the fruitfulness of this approach. More specifically, the need to use the modeling method is determined by the fact that many objects (systems) are either impossible to directly study or completely impossible, or this study requires too much time and money.
Lecture 11_1. "Modeling as a method of cognition"
We are surrounded by an unusually interesting and complex world, which a person begins to learn from an early age.
Children's toys are similar to objects of the surrounding world: people, animals, cars, buildings, etc.
Playing various games, children reproduce the relationships that develop in society (“mother-daughters”, “cosmonauts”, “hospital”, etc.)
At school, various layouts, dummies, maps, diagrams, tables are used as visual aids in the classroom. All this serves to study those objects, phenomena and processes that are difficult or impossible to study directly.
In his professional activity- scientific, practical, artistic - a person also uses models, i.e. creates an image of the object (process or phenomenon) with which he has to deal.
The creation of models is resorted to when the object under study is either very large (model solar system), or very small (atomic model), when the process is very fast (internal combustion engine model) or very slow (geological models), the study of the object can lead to its destruction (aircraft model) or the creation of the object is very expensive (architectural model of the city) etc.
Thus, the creation and study of models is an integral element of any purposeful activity.
Models make it possible to represent visual form objects and processesinaccessible to direct perception.
It is impossible to formulate strict rules for building models, but mankind has accumulated rich experience in modeling various objects and processes.
What is a model?
In real life, this term has many meanings:
Model (fr. modele, it. model lo, lat. modulus - measure, pattern) - this :
some simplified version real object;
reproduction of an object in a reduced or enlarged form (layout);
diagram, picture or description any phenomenon or process in nature and society;
physical or informational analogue of an object , the functioning of which, according to certain parameters, is similar to the functioning of a real object;
new object (real, informational or imaginary), different from the original, which has properties that are essential for the purposes of modeling and, within the framework of these purposes, completely replaces the original object.
Visual models are often used in the process learning. For example, in a geography course, we get the first ideas about our planet Earth by studying its model - a globe.
Models play an extremely important role in design and the creation of various technical devices, machines and mechanisms, buildings, electrical circuits, etc. Without the preliminary creation of a drawing, it is impossible to make even a simple part, not to mention a complex mechanism.
In the process of designing buildings and structures, in addition to drawings, mock-ups are often made. During the development of aircraft, the behavior of their models in air flows is studied in a wind tunnel.
The development of science is impossible without the creation theoretical models(theories, laws, hypotheses), reflecting the structure, properties and behavior of real objects. The creation of new theoretical models sometimes radically changes the idea of mankind about the surrounding world (the heliocentric system of the Copernican world, the Rutherford-Bohr model of the atom, the model of the expanding Universe, the model of the human genome).
Everything artistic creativity is actually the process of creating models. For example, such literary genre, like a fable, transfers real relationships between people to relationships between animals and actually creates models of human relationships.
Swan, pike and cancer
When there is no agreement among comrades,
Their business will not go well,
And nothing will come out of it, only flour.
One Day, Swan, Cancer and Pike
Carried with luggage, they took it,
And together the three all harnessed themselves to it;
They are climbing out of their skin, but the cart is still not moving!
The luggage would have seemed easy for them:
Yes, the Swan breaks into the clouds,
Cancer moves back, and Pike pulls into the water.
Who is to blame among them, who is right, is not for us to judge;
Yes, only things are still there.
What kind of human relations did Krylov model by shifting relations between people to animals?
Almost any literary work can be seen as a model of the real human life. Paintings, sculptures, theatrical performances, etc. are also models that reflect reality in an artistic form.
Models can serve not only real objects, but also “abstract, ideal constructions. Mathematical models are a typical example. As a result of the activities of mathematicians, logicians and philosophers involved in the study of the foundations of mathematics, the theory of models was created.
Probably the first models that replaced real objects were linguistic signs. They arose during the development of mankind and gradually turned into a spoken language. The first rock paintings (petroglyphs), which are 200 thousand years old, were graphic models that depicted everyday scenes, animals and hunting scenes. The next stage in the development of modeling can be considered the emergence of number systems and numerical signs.
Modeling has been developed since Ancient Greece. In the V-III centuries. BC e Ptolemy created a geometric model of the solar system, and Hippocrates used the eye of a bull to study the structure of the human eye (as a physical model of the eye).
The purpose of the simulation
Consider a few examples of models created for different purposes:
· simulator for training in aircraft control;
· mannequin for trying on clothes;
· Moscow Kremlin plan
· Mendeleev table.
Try to determine for what purpose each of the listed models was created, and to whom it can be useful?
As can be seen from the examples, a person creates object models that allow solving a wide variety of tasks:
· creation of objects with specified properties;
· explanation known facts;
· building hypotheses;
· obtaining new knowledge about the objects under study;
· forecasting;
· management, etc.
Different sciences explore objects and processes from different angles of view and build different types of models. In physics, the processes of interaction and change of objects are studied, in chemistry - their chemical composition, in biology, the structure and behavior of living organisms, and so on.
Each object has a large number various properties. No model can replace the object itself. But when solving a specific problem, when we are interested in a certain property of the object under study, the model turns out to be useful, and sometimes the only research tool.
In the process of building a model, the main, most significant for ongoing property research.
For example: In the process of studying the aerodynamic qualities of an aircraft model in a wind tunnel, it is important that the model has a geometric similarity to the original, but not important, for example, its color.
Different sciences explore objects and processes from different angles of view and build different types of models. In physics, the processes of interaction and change of objects are studied, in chemistry - their chemical composition, in biology - the structure and behavior of living organisms, and so on.
Let's take a person as an example: in different sciences, he is studied within the framework of various models. In terms of mechanics, it can be considered as material point, in chemistry - as an object consisting of various chemicals, in biology - as a system striving for self-preservation.
Thus, it can be said that the main purpose of modeling- is the study and study of the object or phenomenon for which the model is built.
Virtues modeling methods are:
Versatility;
Small cost;
Shorter duration in time (for example, for economic models).
disadvantages are:
Difficulties in building an adequate model;
collection of a large amount of reliable information.
The term "adequacy" (derived from the Latin adaequatus - "equal, equal") means the correct reproduction in the model of connections and relations of the objective world. This term characterizes the quality of the created model.
Reliability is not required from the model - in this case, not a model, but a copy will be obtained. The degree of compliance is determined by the goals of modeling. Excessive resemblance to the original is just as useless as insufficient resemblance.
For example, children's toys are models of real objects. The level of compliance depends on the age of the child. Toys for young children usually only model the shape of an object. For example, a model car for a child of three or four years old is adequate if it has a body, a cabin, four rotating wheels and retains the proportions of a real car. In more complex toys, the interaction between the elements of the original object is modeled: the doors and hood open, the steering controls work.
Adequacy of theoretical models to laws real world tested through experimentation and experimentation.
On the other hand, different objects can be described by the same model. So, in mechanics, various material bodies (from a planet to a grain of sand) can be considered as material points.
Homework - abstract
Topic 1. Modeling as a method of knowledge
Plan:
1. Model, simulation
2. Classification of models. Material and Information Models
1.Model, simulation
The American science fiction writer Ray Bradbury wrote the short story "Thunder Came". It tells about a company that organizes travel 60 million years into the past. All visitors to the past should move only along a specially laid path, because one careless step is already capable of breaking the subsequent History. According to one of the employees of the company, it is described as follows:
“Let's say we accidentally killed a mouse here. This means that all future descendants of this mouse will not exist... You will destroy not one, but a million mice... But what about the foxes, for which these mice were needed to feed? If ten mice are not enough, one fox will die. Ten foxes less - a lion will die of hunger ... And here is the result: after 59 million years, a caveman, one of a dozen that inhabits the whole world, goes hunting for a wild boar or a saber-toothed tiger. But by crushing one mouse, you crushed all the tigers in these places. And the caveman is dying of hunger... This is the death of a billion of his descendants. Maybe Rome will not appear on its seven hills ... "
In vain, one of the heroes of the story begged to return him to 60 million years ago in order to revive the butterfly he accidentally crushed. He ended up in a completely different History and died.
This, of course, is just a fantasy, a fairy tale, a situation modeled by the author, but it contains a hint to all of us how careful we should be in our communication with nature. How often our decisions turn out to be ill-conceived: either we suddenly decide to destroy all the wolves that supposedly bring only harm, or we populate the entire mainland with rabbits (this happened in Australia) and then we don’t know how to get rid of them. Every time I want to return to that fatal moment and take a more correct, as it seems to us, step. But this, alas, is impossible - there is no such time machine that would take us to the past.
There is, however, a "time machine" that allows you to look into the future, analyze, simulate a process, a situation - this is science.
Consider an example from life. In 1870, the English Admiralty launched a new battleship, the Captain. The ship went to sea and capsized. The ship was lost, 523 people were killed.
It was completely unexpected for everyone. For all but one person. It was the English shipbuilding scientist W. Reid, who had previously conducted research on a model of an armadillo and found that the ship would capsize even with a slight wave. But the lords from the Admiralty did not believe the scientist, who was doing some "frivolous" experiments with the "toy". And the unthinkable happened.
We encounter various models in early childhood: a toy car, an airplane or a boat were favorite toys for many, as well as a teddy bear or a doll. Children often model (play with cubes, an ordinary stick replaces a horse, etc.).
In the development of a child, in the process of learning about the world around him, such toys, which are, in essence, models of real objects, play an important role. In adolescence, for many, the passion for aircraft modeling, ship modeling, hand-made creation of toys that look like real objects influences the choice life path. Models and modeling have been used by mankind for a long time. In fact, it was the models and model relationships that led to the emergence spoken languages, writing, graphics. Rock carvings of our ancestors, then paintings and books are model, informational forms of transferring knowledge about the surrounding world to subsequent generations.
Let's try to understand what a model is.
It would seem that what is in common between a toy boat and a drawing on a computer screen depicting a complex mathematical abstraction? And yet there is something in common: in both cases we have an image of a real object, which is a “substitute” for some original, reproducing the original with varying degrees of certainty or detail. In other words: a model is a representation of an object in some form different from the form of its actual existence.
In almost all sciences about nature (living and non-living) and society, the construction and use of models is a powerful tool of knowledge. Real objects and processes are so multifaceted and complex that the best way to study them is to build a model that reflects only some facet of reality and therefore is incomparably simpler than this reality, and explore this model first. Centuries-old experience in the development of science has proved in practice the fruitfulness of this approach. The model is an invaluable and indisputable assistant to engineers and scientists.
Here are a few examples explaining what a model is.
Architect getting ready to build building hitherto unknown type. But before he erects it, he constructs it cube building on the table, to see what it will look like. This building model.
To explain how it works circulatory system, lecturer demonstrates diagram poster, on which arrows show the direction of blood flow. This model of the functioning of the circulatory system.
Hanging on the wall painting, depicting apple orchard in bloom. This apple orchard model.
Literary genre such as fable or parable is directly related to the concept of a model, since the meaning of this genre is to transfer relations between people to relations between animals.
Let's try to understand what is the role of models in the given examples.
Of course, an architect could have built a building without first experimenting with cubes. But he's not sure the building will look good enough. If it turns out to be ugly, then for many years it will be a silent reproach to its creator. It's better to experiment with cubes.
Of course, the lecturer could use a detailed anatomical atlas for demonstration. But he does not need such a degree of detail when studying the circulatory system. Moreover, it interferes with the study, as it does not allow you to focus on the main thing. It is much more efficient to use a poster.
Naturally, walking in a fragrant apple orchard, you can get the richest emotional impressions. But if we live in the Far North and we do not have the opportunity to see the apple orchard in bloom, we can look at the picture and imagine this garden.
In all the above examples, there is a comparison of some object with another that replaces it: the real building is a building made of cubes; circulatory system - scheme on the poster; apple orchard - a picture depicting it.
So, let's give the following definition of the model:
Model - it is such a material or mentally represented object that, in the process of study, replaces the original object, retaining some of the typical features of this original that are important for this study.
Or you can say in other words: model - it is a simplified representation of a real object, process or phenomenon.
The model allows you to learn how to properly control an object by testing various control options on the model of this object. Experimenting with a real object for this purpose is at best inconvenient, and as a rule, simply harmful or even impossible for a number of reasons (long duration of the experiment in time, risk of bringing the object into an undesirable and irreversible state, etc.)
So, let's conclude: The model is needed in order to:
Understand how a particular object is arranged - what are its structure, basic properties, laws of development and interaction with the outside 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.
Modeling called both the process of building a model and the process of studying the structure and properties of the original using the built model.
Modeling technology requires the researcher to be able to identify problems and set 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 skills are very important for a person in his daily activities. They help to reasonably plan the daily routine, study, work, choose the best options if there is a choice, and successfully resolve various life problems.
Material (subject, physical) called modeling, in which a real object is compared with its enlarged or reduced copy, which allows research (as a rule, in laboratory conditions) with the help of the subsequent transfer of the properties of the studied processes and phenomena from a model to an object based on the theory of similarity.
Examples: in astronomy - a planetarium, in architecture - models of buildings, in aircraft construction - models of aircraft.
It is fundamentally different from material modeling perfect Modeling, which is not based on material object and model analogies, but on the ideal, thoughtful.
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