Abstraction and formalization

Abstraction - this is the method scientific research, based on the fact that when studying a certain object, they are distracted from its insignificant sides and signs in this situation. This allows us to simplify the picture of the phenomenon under study and consider it in a “pure” form. Abstraction is associated with the idea of ​​the relative independence of phenomena and their aspects, which makes it possible to separate the essential aspects from the non-essential ones. In this case, as a rule, the original subject of research is replaced by another - equivalent, based on the conditions of this task. For example, when studying the operation of a mechanism, a calculation scheme is analyzed that displays the main, essential properties of the mechanism.

There are the following types of abstraction:

- identification (the formation of concepts by combining objects related by their properties into a special class). That is, on the basis of the similarity of a certain set of objects that are similar in some respect, an abstract object is constructed. For example, as a result of generalization - the property of electronic, magnetic, electrical, relay, hydraulic, pneumatic devices to amplify input signals, such a generalized abstraction (abstract object) as an amplifier arose. He is a representative of the properties of objects of different quality that are equated in a certain respect.

- isolation (selection of properties that are inextricably linked with objects). Isolating abstraction is carried out to isolate and clearly fix the phenomenon under study. An example is the abstraction of the real total force acting on the boundary of a moving fluid element. The number of these forces, like the number of properties of the liquid element, is infinite. However, pressure and friction forces can be singled out from this variety by mentally identifying an element of the surface at the flow boundary through which the external medium acts on the flow with a certain force (the reasons for the occurrence of such a force are this case the researcher is not interested). Having mentally decomposed the force into two components, the pressure force can be defined as a normal component of the external influence, and the friction force as a tangential one.

- idealization corresponds to the goal of replacing the real situation with an idealized scheme to simplify the situation under study and more efficient use of research methods and tools. The process of idealization is the mental construction of concepts about non-existent and impracticable objects, but having prototypes in real world. For example, ideal gas, absolutely solid, material point, etc. As a result of idealization, real objects are deprived of some of their inherent properties and endowed with hypothetical properties.

A modern researcher often from the very beginning sets the task of simplifying the phenomenon under study and constructing its abstract idealized model. Idealization acts here as a starting point in the construction of a theory. The criterion for the fruitfulness of idealization is the satisfactory agreement in many cases between the theoretical and empirical results of the study.

Formalization- a method of studying certain areas of knowledge in formalized systems using artificial languages. Such, for example, are the formalized languages ​​of chemistry, mathematics, and logic. Formalized languages ​​allow concise and clear recording of knowledge, avoiding the ambiguity of terms natural language. Formalization, which is based on abstraction and idealization, can be considered as a kind of modeling (sign modeling).

The special methods of scientific knowledge include abstraction and idealization procedures, during which scientific concepts are formed.
Abstraction is a mental abstraction from all the properties, connections and relationships of the object under study, which seem to be insignificant for this theory.
The result of the abstraction process is called abstraction. An example of abstractions are such concepts as a point, a line, a set, etc.
Idealization is the operation of mentally highlighting any one property or relation that is important for a given theory (it is not necessary that this property really exists), and mentally constructing an object endowed with this property.
It is through idealization that such concepts as “absolutely black body”, “ideal gas”, “atom” in classical physics, etc. are formed. The ideal objects obtained in this way do not actually exist, since in nature there cannot be objects and phenomena that have only one property or quality. This is the main difference between ideal objects and abstract ones.
Formalization - the use of special symbols instead of real objects.
A striking example of formalization is the widespread use of mathematical symbols and mathematical methods in natural science. Formalization makes it possible to investigate an object without directly referring to it and to write down the results obtained in a concise and clear form.
Induction
Induction is a method of scientific knowledge, which is the formulation of a logical conclusion by summarizing the data of observation and experiment, obtaining a general conclusion based on particular premises, moving from the particular to the general.
Distinguish between complete and incomplete induction. Complete induction builds a general conclusion based on the study of all objects or phenomena of a given class. As a result of complete induction, the resulting conclusion has the character of a reliable conclusion. But in the world around us there are not so many similar objects of the same class, the number of which is so limited that the researcher can study each of them.
Therefore, much more often, scientists resort to incomplete induction, which builds a general conclusion based on the observation of a limited number of facts, if among them there are those that contradict the inductive reasoning. For example, if a scientist observes the same fact on a hundred or more occasions, he may conclude that the same effect will occur under other similar circumstances. Naturally, the truth obtained in this way is incomplete, the knowledge obtained is of a probabilistic nature and requires additional confirmation.
Deduction
Induction cannot exist apart from deduction.
Deduction is a method of scientific knowledge, which is the receipt of particular conclusions on the basis of general knowledge, the conclusion from the general to the particular.
Deductive reasoning is based on following scheme: all objects of class A have property B, object a belongs to class A; therefore, a has property B. For example: "All men are mortal"; "Ivan is a man"; hence, "Ivan is mortal".
Deduction as a method of cognition proceeds from already known laws and principles. Therefore, the method of deduction does not allow obtaining meaningful new knowledge. Deduction is only a method of logical deployment of a system of provisions based on initial knowledge, a method of identifying the specific content of generally accepted premises. Therefore, it cannot exist apart from induction. Both induction and deduction are indispensable in the process of scientific knowledge.
Hypothesis
The solution of any scientific problem includes the advancement of various conjectures, assumptions, and most often more or less substantiated hypotheses, with the help of which the researcher tries to explain facts that do not fit into the old theories.
A hypothesis is any assumption, conjecture, or prediction put forward to eliminate a situation of uncertainty in scientific research.
Therefore, a hypothesis is not reliable, but probable knowledge, the truth or falsity of which has not yet been established.

Methods of scientific knowledge -"a set of techniques and operations for the practical and theoretical development of reality"

It is customary to divide the methods of cognition into empirical and theoretical.

Abstraction, idealization, formalization, modeling refers to theoretical knowledge and is aimed at forming a holistic picture of the process, knowledge of the essence of the objects under study.

Idealization, abstraction – replacement individual properties of an object or the entire object symbol or sign, a mental distraction from something in order to isolate something else. Ideal objects in science reflect sustainable connections and properties of objects: mass, speed, force, etc. But ideal objects can and not have real prototypes in the objective world, i.e. as scientific knowledge develops, some abstractions can be formed from others without recourse to practice. Therefore, they distinguish empirical and ideal theoretical objects.

Idealization is the necessary preliminary condition theory building, since the system of idealized, abstract images determines the specifics of this theory. In the theory system, there are main and derivatives idealized concepts. For example, in classical mechanics the main idealized object is the mechanical system as interaction of material points.

Generally idealization allows accurately delineate signs of an object, to be distracted from unimportant and vague properties. This provides a huge capacity expressions of thoughts. As a result, there are formed special languages ​​of science, which contributes to the construction of complex abstract theories and the whole process of cognition.

Formalization - operating with signs reduced to generalized models, abstract mathematical formulas. The derivation of some formulas from others is carried out according to strict the rules of logic and mathematics, which is a formal study of the main structural characteristics of the object under study.

Modeling.Model- mental or material replacement of the most significant parties object under study. A model is an object or system specially created by a person, a device that, in a certain respect, imitates, reproduces real-life objects or systems that are the object of scientific research.

Modeling is based on the analogy of properties and relationships between the original and the model. Having studied the relationships that exist between the quantities that describe the model, they are then transferred to the original and thus make a plausible conclusion about the behavior of the latter.

Modeling like method of scientific knowledge based on human ability abstract studied traits or properties various items, phenomena and install certain ratios between them.

Although scientists have been using for a long time this method, only from the middle of the XIX century. modeling conquers lasting recognition from scientists and engineers. In connection with the development of electronics and cybernetics, modeling is turning into extremely effective research method.

Thanks to the use of modeling the patterns of reality, which could be studied in the original just by observing, they become available for experimental research. Opportunity arises multiple repetition in the model of phenomena corresponding to the unique processes of nature or social life.

If we consider the history of science and technology from the point of view of the application of certain models, then we can state that at the beginning of the development of science and technology, material, visual models were used. Subsequently, they gradually lost, one after another, the specific features of the original, their correspondence to the original became more and more abstract character. Everything is currently greater value acquires a search for models based on logical grounds. Exists many options model classifications. In our opinion, the most convincing is the following option:

a) natural models (existing in nature in its natural form). So far, none of the designs created by man, can't compete with natural structures according to the complexity of the tasks to be solved. There is a science bionics, the purpose of which is the study of unique natural models in order to further use the knowledge gained in the creation artificial devices. It is known, for example, that the creators of the submarine shape model took the shape of a dolphin's body as an analogue; when designing the first flying vehicles, the wingspan model of birds was used, etc.;

b) material and technical models (reduced or enlarged, fully reproducing the original). At the same time, experts distinguish between: a) models created in order to reproduce the spatial properties of the object under study (models of houses, building districts, etc.); b) models that reproduce the dynamics of the objects under study, regular relationships, quantities, parameters (models of aircraft, ships, platinum, etc.).

Finally, there is a third kind of models - c) iconic models, including mathematical ones. Iconic modeling allows simplify the subject under study, highlight in it those structural relationships that most interested researcher. Losing to real-technical models in visibility, iconic models win due to a deeper penetration into the structure of the studied fragment of objective reality.

Yes, with the help sign systems able to understand the essence such complex phenomena like the device of an atomic nucleus, elementary particles, Universe. Therefore, the use of iconic models especially important in those areas of science, technology, where they deal with the study extremely general connections, relationships, structures.

The possibilities of sign modeling were especially expanded in connection with the advent of computers. Options for constructing complex sign-mathematical models have appeared that make it possible to choose the most optimal values ​​for the values ​​of complex real processes under study and to carry out computational experiments on them.

In the course of research, it often becomes necessary to build various models of the processes under study, ranging from material to conceptual and mathematical models.

In general, "the construction of not only visual, but also conceptual, mathematical models accompanies the process of scientific research from its beginning to end, making it possible to cover the main features of the processes under study in a single system of visual and abstract images."

15. Levels of scientific knowledge: facts, idea, hypothesis, theory, scientific picture of the world.

The science - this is a form of spiritual activity of people aimed at producing knowledge about nature, society and knowledge itself, with the immediate goal of comprehending the truth and discovering objective laws based on the generalization of real facts in their interconnection, in order to anticipate trends in the development of reality and contribute to its change.

On the empirical level living contemplation (sensory cognition) prevails, the rational moment and its forms (judgments, concepts) are present here, but have a subordinate meaning. signs empirical knowledge: collection of facts, their generalization, description of observed and experimental data, their systematization.

Theoretical level of knowledge characterized by the predominance of concepts, theories, laws. Sense cognition is not eliminated, but becomes a subordinate aspect.

The elementary form of scientific knowledge is scientific fact. As a category of science, a fact can be considered as reliable knowledge about a single one. Scientific facts are genetically related to the practical activities of man, the selection of facts that form the foundation of science is also associated with everyday human experience. In science, not every result obtained is recognized as a fact, since in order to come to objective knowledge about the phenomenon, it is necessary to carry out many research procedures and their statistical processing.

Idea represents an inseparable unity of the subjective form of the concept and its objective form. Such unity is achieved in highly developed living organisms. Such an organism, on the one hand, is a real object, and on the other hand, it acts only on the basis of its subjective idea of ​​itself and the world around it.

Hypothesis - this is the intended solution to the problem. As a rule, a hypothesis is preliminary, conditional knowledge about a regularity in the studied subject area or about the existence of some object. The main condition that a hypothesis must satisfy in science is its validity; this property distinguishes a hypothesis from an opinion.

Theory - the highest, most developed form of organization of scientific knowledge, which gives a holistic display of the laws of a certain sphere of reality and is a symbolic model of this sphere. This model is built in such a way that the characteristics that have the most common nature, form the basis of the model, while others obey the main provisions or are derived from them according to logical laws.

Scientific picture of the world is a system of scientific theories describing reality. scientific theory- is a systematized knowledge in their totality. Scientific theories explain a lot of accumulated scientific facts and describe a certain fragment of reality (for example, electrical phenomena, mechanical movement, the transformation of substances, the evolution of species, etc.) through a system of laws. The main difference between a theory and a hypothesis is reliability, proof. The term theory itself has many meanings. A theory in a strictly scientific sense is a system of already confirmed knowledge that comprehensively reveals the structure, functioning and development of the object under study, the relationship of all its elements, aspects and theories.

The functions of science.

The science- this is a historically established form of human activity, aimed at the knowledge and transformation of objective reality, such spiritual production, which results in purposefully selected and systematized facts, logically verified hypotheses, generalizing theories, fundamental and particular laws, as well as research methods. Science is both a system of knowledge and its spiritual production, and practical activity based on it.

The functions of science are distinguished depending on the general purpose of its branches and their role in the development of the surrounding world with a constructive purpose.

The functions of science are distinguished according to the main activities of researchers, their main tasks, as well as the scope of the acquired knowledge. Thus, the main functions of science can be defined as cognitive, ideological, industrial, social and cultural.

Cognitive the function is fundamental, given by the very essence of science, the purpose of which lies in the knowledge of nature, man and society as a whole, as well as in the rational-theoretical comprehension of the world, the explanation of processes and phenomena, the discovery of patterns and laws, the implementation of forecasting, etc. This function is reduced to the production of new scientific knowledge.

worldview function is largely intertwined with cognitive. They are interrelated, since its goal is to develop a scientific picture of the world and the worldview corresponding to it. Also, this function implies the study of a rationalistic attitude of a person to the world, the development of a scientific worldview, which means that scientists (along with philosophers) must develop scientific worldview universals and corresponding value orientations.

Production a function, which can also be called a technical and technological function, is necessary for the introduction of innovations, new forms of organization of processes, technologies and scientific innovations in manufacturing industries. In this regard, science turns into a productive force working for the benefit of society, a kind of shop where new ideas and their implementation are developed and implemented. In this regard, scientists are even sometimes referred to as production workers, which most fully characterizes the production function of science.

Social function began to stand out especially significantly in recent times. This is due to the achievements of the scientific and technological revolution. In this regard, science turns into a social force. This is manifested in situations where the data of science are used in the development of programs for social and economic development. Since such plans and programs are complex in nature, their development involves close interaction various industries natural, social and technical sciences.

Cultural The function of science (or educational) boils down to the fact that science is a kind of cultural phenomenon, an important factor in the development of people, their education and upbringing. Achievements of science significantly influence the educational process, the content of educational programs, technologies, methods and form of education. This function is implemented through the education system, the media, journalistic and educational activities of scientists.

In addition to the listed functions, one should not forget the group   of traditional functions inherent in it. Among them:

Descriptive function - collection and accumulation of data, facts. Any science begins with this function (stage). it can only be based on in large numbers actual material. So, for example, scientific chemistry could appear only when its predecessors, the alchemists, had accumulated a huge amount of factual material about chemical properties various substances.

Explanatory function - aimed at identifying cause-and-effect relationships and dependencies, building the so-called "world lines" (explanation of phenomena and processes, their internal mechanisms)

epistemological function; is aimed at building a system of objective knowledge about the properties of relations and processes of objective reality. The epistemological function is organically inherent in science as a creative activity in obtaining new knowledge. The task of science is to explain - to reveal the essence of the object being explained, which can be carried out only through the knowledge of its relations and connections with other entities or its internal relations and connections. Cognition can also manifest itself in the form of worldly knowledge, artistic and even religious exploration of the world.

The generalizing function is the formulation of laws and patterns that systematize and absorb numerous disparate phenomena and facts. As classic examples we can cite the classification of biological species by K. Linnaeus, the theory of evolution by Ch. Darwin, the periodic law of D.I. Mendelev.

predictive function - scientific knowledge make it possible to foresee previously unknown new processes and phenomena. So, for example, the planets Uranus, Neptune, Pluto were discovered, astronomers can calculate the collision of the Earth with any comet with an accuracy of seconds, etc. The position of science in relation to practice, as a rule, is ahead. Science has always been the basis of engineering and technology. For example, the use of computers, lasers, electrochemical processing methods, composite materials, etc. made possible only through scientific research. At the same time, in the field of the humanities and social sciences, the leading function of science can by no means always be realized due to the extremely complex object of study. Or predictive the function is manifested in the creation, according to the criteria of scientific rationality, of promising models of the studied, any possible objects.

The discovery of stable connections and dependencies is only the first stage in the process of scientific knowledge of the phenomena of reality. It is necessary to explain their grounds and causes, to reveal the essence of phenomena and processes. And this is possible only at the theoretical level of scientific knowledge. The theoretical level includes all those forms of knowledge in which logical form laws and other general and necessary connections of the objective world are formulated, as well as conclusions obtained with the help of logical means, and consequences arising from theoretical premises. The theoretical level represents various forms, techniques and stages of mediated cognition of reality.

Methods and forms of knowledge of the theoretical level, depending on the functions they perform, can be divided into two groups. The first group - methods and forms of cognition, with the help of which an idealized object is created and studied, representing the basic, defining relationships and properties, as it were, in a "pure" form. The second group - methods for constructing and justifying theoretical knowledge, which is given in the form of a hypothesis, which as a result acquires the status of a theory.

The methods of constructing and studying an idealized object include: abstraction, idealization, formalization, thought experiment, mathematical modeling.

A) Abstraction and idealization. The concept of an idealized object

It is known that any scientific theory studies either a certain fragment of reality, a certain subject area, or a certain side, one of the aspects of real things and processes. At the same time, the theory is forced to digress from those aspects of the subjects it studies that do not interest it. In addition, the theory is often forced to abstract from certain differences in the subjects it studies in certain respects. From the point of view of psychology, the process of mental abstraction from certain aspects, properties of the objects being studied, from certain relations between them is called abstraction. Mentally selected properties and relationships are in the foreground, appear as necessary for solving problems, act as a subject of study.

The process of abstraction scientific knowledge is not arbitrary. He obeys certain rules. One of these rules is abstraction interval. The interval of abstractions is the limits of the rational validity of this or that abstraction, the conditions for its "objective truth" and the limits of applicability, established on the basis of information obtained by empirical or logical means. The interval of abstraction depends, firstly, on the assigned cognitive task; secondly, what is distracted from in the process of comprehending an object must be outsiders(according to a clearly defined criterion) for a specific object that is subject to abstraction; thirdly, the researcher must know to what extent a given distraction is valid.

The abstraction method involves, when studying complex objects, to produce a conceptual unfolding and conceptual assembly of objects. Conceptual development means displaying the same original object of study in different mental planes (projections) and, accordingly, finding a set of abstraction intervals for it. So, for example, in quantum mechanics, the same object (elementary particle) can be alternately represented within the framework of two projections: as a corpuscle (under certain experimental conditions), then as a wave (under other conditions). These projections are logically incompatible with each other, but only taken together they exhaust all the necessary information about the behavior of particles.

Concept assembly- representation of an object in a multidimensional cognitive space by establishing logical connections and transitions between different intervals that form a single semantic configuration. So, in classical mechanics, the same physical event can be displayed by an observer in different systems in the form of a corresponding set of experimental truths. These different projections, however, can form a conceptual whole thanks to the "Galilean transformation rules" that govern how one moves from one group of statements to another.

Abstraction as the most important method of human cognitive activity is widely used at all stages of scientific and cognitive activity, including at the level of empirical knowledge. Empirical objects are created on its basis. As V.S. Stepin noted, empirical objects are abstractions that fix the signs of real objects of experience. They are certain schematizations of fragments of the real world. Any sign, the "carrier" of which is an empirical object, can be found in the corresponding real objects (but not vice versa, since the empirical object does not represent all, but only some of the signs of real objects, abstracted from reality in accordance with the tasks of cognition and practice) . Empirical objects make up the meaning of such terms of the empirical language as "Earth", "wire with current", "distance between the Earth and the Moon", etc.

Theoretical objects, unlike empirical ones, are not just abstractions, but idealizations, "logical reconstructions of reality." They can be endowed not only with attributes that correspond to the properties and relationships of real objects, but also with attributes that none of such an object possesses. Theoretical objects form the meaning of such terms as "point", "ideal gas", "black body", etc.

In logical and methodological studies, theoretical objects are sometimes called theoretical constructs, as well as abstract objects. Objects of this kind serve as the most important means of knowing real objects and the relationships between them. They are called idealized objects, and the process of creating them is called idealization. Thus, idealization is the process of creating mental objects, conditions, situations that do not exist in reality by means of a mental abstraction from some properties of real objects and relations between them, or by endowing objects and situations with those properties that they do not actually possess or cannot possess, with the purpose of a deeper and more accurate knowledge of reality.

The creation of an idealized object necessarily includes abstraction - a distraction from a number of aspects and properties of the specific objects being studied. But if we limit ourselves to this, then we will not get any integral object yet, but simply destroy the real object or situation. After abstracting, we still need to highlight the properties of interest to us, strengthen or weaken them, combine and present them as properties of some independent object that exists, functions and develops according to its own laws. And this is achieved by using idealization method.

Idealization helps the researcher to single out in a pure form the aspects of reality that interest him. As a result of idealization, the object acquires properties that are not in demand in empirical experience. In contrast to ordinary abstraction, idealization focuses not on the operations of abstraction, but on the mechanism replenishment. Idealization gives an absolutely exact construct, mental construct, in which this or that property, state is represented in marginal, most expressed. Creative constructs, abstract objects act as ideal model.

Why is it necessary to use abstract objects (theoretical constructs) in cognition? The fact is that a real object is always complex, significant for a given researcher and secondary properties are intertwined in it, the necessary regular relations are obscured by random ones. Constructs, ideal models are objects endowed with a small number of specific and essential properties that have a relatively simple structure.

The researcher, relying on a relatively simple idealized object, to give a deeper and more complete description of these aspects. Cognition moves from concrete objects to their abstract, ideal models, which, becoming more and more precise, perfect and numerous, gradually give us a more and more adequate image of concrete objects. This widespread use of idealized objects is one of the most characteristic features of human knowledge.

It should be noted that idealization is used both on the empirical and on the theoretical levels. The objects to which scientific propositions refer are always idealized objects. Even in those cases when we use empirical methods of cognition - observation, measurement, experiment, the results of these procedures are directly related to idealized objects, and only due to the fact that idealized objects at this level are abstract models of real things, the data of empirical procedures can be attributed to actual items.

However, the role of idealization sharply increases in the transition from the empirical to the theoretical level of scientific knowledge. The modern hypothetical-deductive theory is based on some empirical basis - a set of facts that need explanation and make it necessary to create a theory. But theory is not a simple generalization of facts and cannot be deduced from them in a logical way. In order to make it possible to create a special system of concepts and statements called a theory, an idealized object is first introduced, which is an abstract model of reality, endowed with a small number of properties and having a relatively simple structure. This idealized object expresses the specificity and essential features of the studied field of phenomena. It is the idealized object that makes possible creation theories. Scientific theories, first of all, are distinguished by the idealized objects underlying them. In the special theory of relativity, an idealized object is an abstract pseudo-Euclidean four-dimensional set of coordinates and instants of time, provided that there is no gravitational field. For quantum mechanics an idealized object is characteristic, represented in the case of a set of n particles by a wave in an n-dimensional configuration space, the properties of which are related to the quantum of action.

The concepts and statements of a theory are introduced and formulated precisely as characteristics of its idealized object. The main properties of an idealized object are described by a system of fundamental equations of the theory. The difference between the idealized objects of theories leads to the fact that each hypothetical-deductive theory has its own specific system of fundamental equations. In classical mechanics we deal with Newton's equations, in electrodynamics - with Maxwell's equations, in the theory of relativity - with Einstein's equations, etc. The idealized object gives an interpretation of the concepts and equations of the theory. Refinement of the equations of the theory, their experimental confirmation and correction lead to a refinement of the idealized object or even to its change. Replacing the idealized object of the theory means reinterpreting the basic equations of the theory. No scientific theory can be guaranteed that its equations will not be reinterpreted sooner or later. In some cases, this happens relatively quickly, in others - after a long time. So, for example, in the doctrine of heat, the original idealized object - caloric - was replaced by another - a set of randomly moving material points. Sometimes a modification or replacement of an idealized object of a theory does not significantly change the form of its fundamental equations. In this case, it is often said that the theory is preserved, but its interpretation changes. It is clear that one can say this only with a formalistic understanding of scientific theory. If by theory we understand not only certain mathematical formulas, but also a certain interpretation of these formulas, then the change of the idealized object should be considered as a transition to a new theory.

Experiment

the most important integral part scientific research is an experiment. More than 2/3 of all labor resources science is spent on experiments. The basis of the experiment is a scientifically set experiment (experiments) with precisely taken into account and controlled conditions that make it possible to monitor its course, control it, and recreate it every time these conditions are repeated. The word experiment itself comes from the Latin. experimentum- test. Experience is understood as the reproduction of the phenomenon under study under certain conditions of the experiment, with the possibility of recording its results. Experience is a separate elementary part of the experiment.

The experiment differs from the usual, ordinary passive observation by the active influence of the researcher on the phenomenon under study.

in scientific language and research work the term "experiment" is usually used in the meaning common to a number of related concepts: experience, purposeful observation, reproduction of the object of knowledge, organization of special conditions for its existence. This concept includes the scientific setting of experiments and the observation of the phenomenon under study under precisely taken into account conditions that make it possible to follow the course of phenomena and recreate it every time these conditions are repeated.

Basic purpose experiment are the identification of the properties of the objects under study and the verification of the validity of hypotheses

When conducting experimental studies, it is possible to decide two main tasks:

1. Identification of quantitative patterns that establish the relationship between the variables that describe the object of study.

2. Finding the values ​​of variables that provide the optimal (according to a certain criterion) mode of operation of the object.

Distinguish natural and model experiment. If the first is placed directly with the object, then the second - with its deputy - the model. Currently, the most common types of models are mathematical, and experiments carried out on such models are called computational.

Before each experiment, its program is compiled, which includes:

- the purpose and objectives of the experiment; choice of variable factors (input variables);

- substantiation of the scope of the experiment, the number of experiments;

- determination of the sequence of changing factors;

– choice of the factor change step, setting intervals between future experimental points;

– substantiation of measuring instruments;

– description of the experiment;

- substantiation of methods for processing and analyzing the results of the experiment.

Before the experiment, it is necessary to choose variable factors, i.e. establish the main and secondary characteristics that affect the process under study, analyze the calculated (theoretical) schemes of the process. The main principle for establishing the degree of importance of a characteristic is its role in the process under study.

Often the experimenter's work is so chaotic and disorganized, and its effectiveness is so low, that the results obtained are not able to justify even the funds that were spent on the experiments. Therefore, the issues of organizing the experiment, reducing the cost of conducting it and processing the results obtained are quite relevant.

Modern methods of planning an experiment and processing its results, developed on the basis of probability theory and mathematical statistics, allow:

– significantly (often by several times) to reduce the number of experiments required for conducting;

– to make the work of the experimenter more purposeful and organized,

- significantly increase both the productivity of his work and the reliability of the results obtained.

The theory of experiment planning began with the work of the English scientist R. Fisher in the 30s of the XX century, who used it to solve agrobiological problems.

The planning of the experiment consists in choosing the number and conditions of the experiments, allowing to obtain the necessary knowledge about the object of study with the required accuracy. This is a purposeful control of the experiment, implemented in conditions of incomplete knowledge of the mechanism of the phenomenon under study.

The purpose of experiment planning is to find such conditions and rules for conducting experiments under which it is possible to obtain reliable and reliable information about the object with the least labor costs, and also to present this information in a compact and convenient form with a quantitative assessment of accuracy.

The general direction of the theory of experiment planning can be formulated as follows - " less experiences– more information – higher quality of results”.

Experiments are usually carried out in small series according to a predetermined algorithm. After each small series of experiments, the results of observations are processed and a strictly justified decision is made about what to do next. When choosing an algorithm for planning an experiment, of course, the purpose of the study is taken into account, as well as a priori information about the mechanism of the phenomenon under study. This information is always incomplete, with the possible exception of a trivial case - demonstration experiments.

As a rule, any object of study (the carrier of some unknown and subject to study properties or qualities) can be represented as a "black box" with a certain number of inputs and outputs (Fig. 2.2.).

Rice. 5.1. Structural scheme object of study

Input variables Х i , i = 1, 2,…k (where k is the number of variables) that determine the state of the object are called factors. The fixed value of the factor is called factor level. The main requirement for factors is sufficient controllability, which means the ability to set the desired level of the factor and stabilize it throughout the experiment.

The output variable Y g (usually g = 1) is the response of the object to input actions; she bears the name response, and the dependence

Y = f(X 1 , X 2 , …X i ,…X k) (2.1)

called response function or goals. Usually, there is only a general idea about the nature of this dependence. The choice of the response function is determined by the purpose of the study, which can be the optimization of the economic (cost, productivity), technological (accuracy, speed), design (dimensions, reliability) or other characteristics of the object.

The geometric representation of the response function in the factor space Х 1 , Х 2 , …, Х k is called response surface

The true form of the response function (2.1) before the experiment is most often unknown, and therefore, for the mathematical description of the response surface, a statistical model of the process is used

Y р = f(X 1 , X 2 , …X i ,…X k). (2.2)

Equation (2.2) is obtained as a result of the experiment and is called the approximating function or regression model of the process. Approximation is understood as the replacement of exact analytical expressions by approximate ones. A polynomial of some degree is usually used as a regression equation. Moreover, polynomials of the first and second order are most widely used in calculations, since the required accuracy of calculations is usually very low (on the order of 5–15%).

For example, for k = 1, the polynomial of the nth degree has the form

for k = 2 and n = 1, is usually written as

where a 0 , a 1 , a 2 ,…a n are unknown regression coefficients that are calculated based on the results of the experiment

In addition, due to the finite number of terms of the approximating polynomial, the discrepancy between the true and approximate values ​​of the response function outside the experimental points can be significant. In connection with the foregoing, the problem arises of finding such a type of polynomial and such a number of experiments that a certain criterion is satisfied. Usually, the sum of the squared deviations of the experimental values ​​Y j from their calculated value Y j р is taken as a criterion. The best approximation of the approximating function to the true one is the function that satisfies the minimum condition for this sum.

To determine the unknown coefficients of the regression model (5.2), the most universal is usually used least squares method (LSM).

Using the LSM, the values ​​a 0 , a 1 , a 2 , …, a n are found from the condition of minimizing the sum of squared deviations of the experimental response values ​​Y j from those obtained Y j p using a regression model, i.e. by minimizing the sum:

Minimization of the sum of squares is done in the usual way using differential calculus by equating to 0 the first partial derivatives with respect to a 0 , a 1 , a 2 ,…., a n . As a result, it turns out closed system algebraic equations, with unknowns a 0 , a 1 , a 2 ,…. ,a n .

When using the least squares method necessary condition obtaining statistical estimates is the fulfillment of the inequality N > d, i.e. the number of experiments N must be greater than the number of unknown coefficients d.

The main feature of the considered statistical (regression) model is that such a model cannot accurately describe the behavior of an object in any particular experiment. The researcher cannot predict exact value Y in each experiment, but with the help of an appropriate statistical model, can indicate around which center the values ​​of Y will be grouped for a given combination of values ​​of the factors X ij .

Induction and deduction

Induction - this is a kind of generalization, which consists in the transition from knowledge of individual facts and from less general knowledge to more general knowledge. With the inductive method of research on particular facts and phenomena, general principles and laws.

The induction process usually begins with a comparison and analysis of observational and experimental data. As this data set expands, a regular occurrence of a property or relationship may emerge. The multiple repetition observed in experiments in the absence of exceptions inspires confidence in the universality of the phenomenon and leads to inductive generalization - the assumption that this will be the case in all similar cases. A conclusion by induction is a conclusion about general properties of all objects belonging to a given class, based on the observation of a fairly wide set of single facts. So, for example, D.I. Mendeleev, using private facts about chemical elements, formulated the periodic law.

Usually inductive generalizations are considered as empirical truths, or empirical laws.

Deduction- this is an operation of thinking, which consists in the fact that new knowledge is derived on the basis of knowledge of a more general nature, previously obtained by generalizing observations, experiments, practical activities, that is, with the help of induction. When applied deductive method particular provisions are derived from general patterns, axioms, etc. The deductive conclusion is built according to the following scheme; all objects of class "A" have the property "B"; item "a" belongs to class "A"; so "a" has the property "B". In general, deduction as a method of cognition proceeds from already known laws and principles. Therefore, the method of deduction does not allow obtaining meaningful new knowledge. Deduction is only a method of logical deployment of a system of provisions based on initial knowledge, a method of identifying the specific content of generally accepted premises. So, for example, on the basis of the general laws of mechanics, the equations of motion of a car are obtained.

The disadvantage of the deductive method of research is the limitations arising from the general patterns on the basis of which the particular case is investigated. So, for example, in order to comprehensively investigate the movement of a car, it is not enough to know only the laws of mechanics, it is necessary to apply other principles arising from the analysis of the system: “driver - car - external environment».

Induction and deduction are closely related and complement each other. For example, a scientist, justifying the hypothesis of scientific research, establishes its compliance with the general laws of natural science (deduction). At the same time, the hypothesis is formulated on the basis of particular facts (induction).

Analysis and synthesis

Analysis(from the Greek analysis - decomposition): a method by which the researcher mentally separates the object under study into various components(both parts and elements), giving Special attention connections between them. Analysis is an integral part of any scientific research, which is usually its first stage, when the researcher moves from an undivided description of the object under study to the identification of its structure, composition, as well as its properties and features.

Synthesis(from the Greek synthesis - connection): using this method, the researcher mentally combines the various components (both parts and elements) of the object under study into a single system. In synthesis, not just a union occurs, but a generalization of the analytically distinguished and studied features of an object. The provisions obtained as a result of the synthesis are included in the theory of the object, which, being enriched and refined, determines the paths of a new scientific search.

Methods of analysis and synthesis are equally used in scientific research. So, highlighting individual elements (subsystems and mechanisms) in the study of the functioning of the engine, the analysis method is used, studying the engine as a system consisting of elements, the synthesis method is used. The synthesis method allows you to generalize the concepts of laws, theories. The operations of analysis and synthesis are inextricably linked with each other; each of them is carried out with the help and through the other.

Analogy

Analogy- a method of cognition in which there is a transfer of knowledge obtained in the course of consideration of any one object to another, less studied and in this moment studied. The analogy method is based on the similarity of objects in a number of any signs, which allows you to get quite reliable knowledge about the subject being studied. The use of the analogy method in scientific knowledge requires a certain amount of caution. Here it is extremely important to clearly identify the conditions under which it works most effectively. However, in those cases where it is possible to develop a system of clearly formulated rules for transferring knowledge from a model to a prototype, the results and conclusions by the analogy method become evidential.

Abstraction and formalization

Abstraction - This is a method of scientific research based on the fact that when studying a certain object, it is distracted from its sides and features that are not essential in a given situation. This allows us to simplify the picture of the phenomenon under study and consider it in a “pure” form. Abstraction is associated with the idea of ​​the relative independence of phenomena and their aspects, which makes it possible to separate the essential aspects from the non-essential ones. In this case, as a rule, the original subject of research is replaced by another - equivalent, based on the conditions of this task. For example, when studying the operation of a mechanism, a calculation scheme is analyzed that displays the main, essential properties of the mechanism.

There are the following types of abstraction:

- identification (the formation of concepts by combining objects related by their properties into a special class). That is, on the basis of the similarity of a certain set of objects that are similar in some respect, an abstract object is constructed. For example, as a result of generalization - the property of electronic, magnetic, electrical, relay, hydraulic, pneumatic devices to amplify input signals, such a generalized abstraction (abstract object) as an amplifier arose. He is a representative of the properties of objects of different quality that are equated in a certain respect.

- isolation (selection of properties that are inextricably linked with objects). Isolating abstraction is carried out to isolate and clearly fix the phenomenon under study. An example is the abstraction of the real total force acting on the boundary of a moving fluid element. The number of these forces, like the number of properties of the liquid element, is infinite. However, pressure and friction forces can be singled out from this variety by mentally separating a surface element at the flow boundary through which the external medium acts on the flow with a certain force (in this case, the researcher is not interested in the reasons for the occurrence of such a force). Having mentally decomposed the force into two components, the pressure force can be defined as a normal component of the external influence, and the friction force as a tangential one.

- idealization corresponds to the goal of replacing the real situation with an idealized scheme to simplify the situation under study and more efficient use of research methods and tools. The process of idealization is the mental construction of concepts about non-existent and impracticable objects, but having prototypes in the real world. For example, an ideal gas, an absolutely rigid body, a material point, etc. As a result of idealization, real objects are deprived of some of their inherent properties and endowed with hypothetical properties.

A modern researcher often from the very beginning sets the task of simplifying the phenomenon under study and constructing its abstract idealized model. Idealization acts here as a starting point in the construction of a theory. The criterion for the fruitfulness of idealization is the satisfactory agreement in many cases between the theoretical and empirical results of the study.

Formalization- a method of studying certain areas of knowledge in formalized systems using artificial languages. Such, for example, are the formalized languages ​​of chemistry, mathematics, and logic. Formalized languages ​​allow concise and clear recording of knowledge, avoiding the ambiguity of natural language terms. Formalization, which is based on abstraction and idealization, can be considered as a kind of modeling (sign modeling).

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