What are the research methods of natural science?

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Modern natural science research methods

The methodology of natural science is essentially the application of philosophical methodology principles in various specific natural sciences. As a science, it constitutes a soft science itself, and it is the most general science that provides methods, principles, means and ways for various specific natural sciences. As an advanced and complicated form of knowledge and cognition, natural science is obtained by using correct thinking methods, research methods and certain practical activities on the basis of existing human knowledge. It is the crystallization of human wisdom and creative labor. Therefore, in the process of scientific research, scientific invention and scientific discovery, whether you have the correct scientific research methods is the key to making contributions to the scientific cause. The correct scientific method can enable researchers to determine the correct research direction according to the objective law of scientific development; Can provide specific research methods for researchers; It can provide enlightenment and reference for new scientific discoveries and inventions. Therefore, in modern scientific research, it is especially necessary to pay attention to the research and application of scientific methodology, which is also a problem we should emphasize.

First, scientific experimental methods.

Scientific experiment, production practice and social practice are called the three practical activities of human beings. Practice is not only the source of theory, but also the only criterion to test the correctness of theory. Scientific experiment is the source and test standard of natural science theory. Especially in modern natural science research, any new discovery, invention and theory must be based on reproducible experimental results, otherwise it will not be accepted by others, and even the possibility of publishing academic papers will be banned. Even pure theoretical researchers must have a deep understanding of the experimental results and even the experimental process they are concerned about. Therefore, it can be said that scientific experiment is an extremely important activity and research method in the development of natural science.

(A) the types of scientific experiments

Scientific experiments have two meanings: first, exploratory experiments, that is, experiments to explore natural laws and create inventions or discover new things, which are often experiments that predecessors or others have never done or have not completed their research work; Second, it refers to experiments conducted by people in order to learn, master or teach others' existing scientific and technological knowledge, such as experiments conducted in experimental classes arranged by schools. In fact, there is no strict boundary between the two types of experiments, because sometimes repeating other people's experiments may also find new problems, so as to realize scientific and technological innovation by solving new problems. The innovative purpose of exploratory experiments is clear, so scientific and technological innovation is mainly obtained through such experiments.

From another perspective, scientific experiments can be divided into the following categories.

Qualitative experiment: to determine whether the research object has a certain composition, property or performance; Whether the structure exists; Whether its curative effect and technical and economic level have reached a certain level. Generally speaking, qualitative experiments should judge "yes" or "no", "yes" or "no", and give some preliminary understanding about the general nature of the research object and the relationship between other things from the experiments. Qualitative experiments are mostly used in the initial stage of an exploratory experiment, focusing on understanding the essential characteristics of things, which is the basis and prelude of quantitative experiments.

Quantitative experiment: an experiment to study the quantitative relationship between things. This kind of experiment focuses on the numerical value of things, finds out the quantitative relationship between some factors, and even gives the corresponding calculation formula. This kind of experiment is mainly carried out by physical measurement, so it can be said that measurement is an important part of quantitative experiment. Quantitative experiment is generally the follow-up of qualitative experiment, and it is a means to deeply study the essence of things. The change of things is always accompanied by the change from quantitative change to qualitative change, and quantitative experiments are often used to find the joint point from quantitative change to qualitative change, that is, to find the degree.

Confirmatory experiment: an experiment that repeats the corresponding experiment or verifies a theoretical hypothesis in order to master or test the achievements of predecessors or others. This kind of experiment is also an important exploration link to develop the specific problems studied to a deeper or broader level.

Structure and composition analysis experiment: it is an experiment to determine the chemical composition of substances or the spatial structure of atoms or atomic groups of compounds. In fact, component analysis experiments are often used in medicine, such as routine analysis and special analysis of blood, urine and stool. Structural analysis is often used to analyze the isomerism of organic compounds.

Comparative experiment: it refers to dividing the research object into two or more similar groups. One group is something whose result has been determined. As a standard of comparison, it is called "control group" and let it develop naturally. The other group is mysterious and unknown things. As the experimental research object, it is called the experimental group. Through certain experimental steps, it is determined whether the research object has certain properties. This kind of experiment is often used in biological and medical research, such as testing a new medical scheme or the role of drugs and nutritional crystals.

Comparative experiment: an experiment aimed at discovering similarities and differences, characteristics, etc. Between two or more subjects. That is, two or more experimental units are carried out at the same time and compared relatively. This method is often used in crop cross breeding, and excellent varieties are selected by comparison.

Factorial experiment: refers to the experiment designed and carried out in order to find the cause of the result from the known results. The purpose of this experiment is to determine the cause of fruit. If there may be multiple causes, the exclusion method is generally used to deal with, exclude or determine a factor. If it may be a double cause, it can be determined by comparative experiments. This is similar to the detection of a murder case. After the suspects were eliminated one by one, the scope of suspects gradually narrowed, and finally the murderer or principal offender was found, which was the real reason or main reason for the result.

Decisive experiment: refers to the experiment designed to verify the correctness of scientific hypothesis, scientific theory and design scheme, and its purpose is to make a final judgment. For example, the experiment of free falling in vacuum is a decisive experiment on Aristotle's wrong principle of falling (heavy objects fall faster than light objects).

In addition, the classification of scientific experiments includes intermediate experiments, production experiments, process experiments and model experiments, which are mainly related to industrial production.

(B) the significance and role of scientific experiments

1. General function of scientific experiment in natural science

The deepening process of human understanding of nature is actually composed of the long river of human scientific and technological innovation (or knowledge innovation). Scientific experiment is an important and powerful means to obtain new first-hand scientific research data. A large number of new, accurate and systematic scientific and technological information materials are often obtained through scientific experiments. For example, Edison, the "king of invention", conducted more than 2,000 experiments in 13 months and tried more than 600 materials before he found that platinum was more suitable. However, because platinum is expensive, it is not suitable for popularization, so he experimented with more than 6 000 materials and finally found that carbonized bamboo filament is the best filament. This shows that scientific experiments are the only way to explore the mysteries of nature and create inventions.

Scientific experiment is the only criterion to test the correctness of scientific theories and hypotheses. For example, science has discovered that there are four kinds of interactions in the universe. Is there any internal connection between them? Einstein put forward the "unified field theory", which was studied from 1925 to 1955, but there was no result, so many experts doubted the existence of the "unified field". However, American physicist Weinberg and Pakistani physicist Salam gave a unified field of weak interaction and electromagnetic interaction from gauge field theory, which was proved and recognized by experiments. This shows that the standard of theoretical correctness is the verification of experimental results, not the authority.

Scientific experiment is the life of natural science and technology and a powerful means to promote the development of natural science and technology. The mystery of nature is constantly revealed by scientific experiments, and this process will never end.

2. The special role of scientific experiments in natural science.

Things and natural phenomena in nature are varied, varied and inextricably linked, which constitutes a complex nature. Therefore, when exploring the laws of nature, it is often difficult to distinguish because of various factors intertwined. One of the special functions of scientific experiment is to control the research object artificially, so that the research object can be simplified and purified. For example, in the experiment of free falling in vacuum, feathers and iron fall at the same time, which eliminates the interference of air resistance, thus greatly simplifying the research object.

Scientific experiments can create various extreme conditions that do not exist in the natural conditions of the earth with the help of various technical means that human beings have mastered, such as experiments under ultra-high temperature, ultra-high pressure, ultra-low temperature, strong magnetic field and ultra-vacuum conditions. From these experiments, we can explore the special laws of material changes or prepare special materials, and also have special chemical reactions.

Scientific experiments are flexible, and typical materials can be selected for experiments and research, such as ultra-pure materials and ultra-fine (nano) materials. Using Drosophila chromosomes to study genetic problems in biology also shows the flexibility of scientific experiments.

Scientific experiments also have the function of simulating research objects, such as doing pathological research with mice. Scientific experiments can provide new theories, technologies, methods, materials and processes for production practice. Generally, new industrial products are produced in large quantities through scientific experiments in the laboratory, such as the production of transistors.

Scientific experiment is a practical activity in natural science research. Respecting the facts of scientific experiments means adhering to the materialistic viewpoint, ignoring the experimental facts, or falsifying the experimental results, all of which are idealistic practices and will inevitably hit a wall in the end. Any natural science theory must be based on the real information in rich experimental results, and then abstract the theory and hypothesis through analysis and induction. A scientist must be down-to-earth, which is the scientific experiment and its results. Therefore, materialism is one of the basic qualities that every natural scientist should possess.

Second, mathematical methods.

There are two different concepts in mathematical methods. The mathematical method in the methodology book refers to the thinking method when studying and developing mathematics. The mathematical method to be expounded here is a thinking method often used in natural science research, and its connotation is; It is a scientific and abstract way of thinking. Its fundamental feature lies in putting aside all other characteristics of the research object, only extracting various quantities, changes of quantities and relationships between quantities, that is, symbolizing and formulating scientific concepts or principles under the objective premise, and carrying out logical deduction, operation, calculus and quantitative analysis of conformity with mathematical language (that is, mathematical tools), thus forming a mathematical explanation and prediction of the research object, thus revealing the research object quantitatively. This special abstract method is called mathematical method.

(B) the basic process of using mathematical methods

In scientific research, it is often necessary to carry out scientific abstraction, through which the regularity of the research object is quantitatively revealed by mathematical methods. The basic process is: (1) First, abstract the prototype of the research into an idealized physical model, that is, transform it into a scientific concept; (2) On this basis, an idealized physical model (a form of scientific abstraction) is abstracted in mathematical science, so that the relevant scientific concepts of the research object are quantified in symbolic form, and a mathematical model is initially established, that is, an idealized mathematical equation or a specific calculation formula is formed; (3) Verify the mathematical model, that is, apply it to the prototype after a little modification, and make a mathematical explanation to see how approximate it is: a high degree of approximation means a good mathematical model, and vice versa, which needs to be refined again. This basic process can be represented by the following figure:

Mathematical method, also known as mathematical modeling method, is abstracted as physical model in the first step. Because mathematical method is a quantitative analysis method and most of the quantities in natural science are physical quantities, mathematical model essentially expresses the relationship between physical quantities, which needs to be expressed by mathematical equations or calculation formulas. The verification process is usually a process of measuring various physical quantities in the research object (through experiments). Therefore, the first step in the process of mathematical modeling is often called physical modeling, in other words, it is difficult to do mathematical modeling without physical modeling; However, if only physical modeling is used, it is difficult to form theoretical equations or calculation formulas, and it is difficult to achieve the purpose of quantitative analysis and research.

(B) the characteristics of mathematical methods

The length is highly abstract: although all natural sciences and even social sciences are abstract, mathematics is more abstract, because there are no other features of things in mathematics, only numbers and symbols exist, and they only show the quantitative relationship and operational relationship between symbols. Only in this way can the regularity of the research object be revealed quantitatively.

2. High accuracy: This is because accurate calculations can be made through mathematical models, and only accurate (that is, high approximation) mathematical models are the mathematical models that people ultimately need.

3. Strict logic: This is because mathematics itself is a science with strict logic. At the same time, when using mathematical methods to solve and study natural laws, mathematical models are always based on mastering a large number of sufficient and necessary data (that is, experimental information), and first, physical models are established by using logical reasoning methods, so mathematical models must contain more rigorous logic.

4. Full of dialectical characteristics: because the quantity in the mathematical model is often a symbol, such as f = ma stands for Newton's second law, the sizes of the three quantities are both changing and interrelated. Therefore, the mathematical model embodies two main characteristics of dialectical relationship: change characteristics and contact characteristics.

5. Wide application: Professor Hua once pointed out: "The universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical engineering, the change of the earth, the mystery of biology, the complexity of daily use, and mathematics is everywhere." This is because all changes in the world are caused by sports and obey the law of quantitative change to qualitative change. Therefore, only through quantitative research can we reveal the laws of nature more deeply and more accurately grasp the key to qualitative change-the problem of degree.

6. Randomness: Randomness means that there is inevitability in contingency and experimental information is accidental. Through mathematical modeling, it is often possible to give an inevitable result (the continuous change relationship between quantities) from multiple accidental data, that is, a regular conclusion.

(3) Types of mathematical methods

1. Classification of natural things and phenomena

The application of mathematical methods and mathematical modeling depends on the nature of natural things and phenomena. There are many kinds of natural things and phenomena, and the number is unlimited. In the world, you can't find two identical things, which means that there must be differences between similar things. Therefore, when studying the regularity of things quantitatively, we can't establish a mathematical model for a specific thing, but always aim at similar things and phenomena with the same regularity. This requires: according to the needs of mathematical modeling, things should be classified according to certain factors in order to use mathematical methods more conveniently. To sum up, all kinds of things and phenomena in nature can be generally divided into four categories: the first category is natural things and natural phenomena with definite causal relationship, which is called inevitability; The second category is uncertain causality, which is called random natural things and phenomena; The third category is unclear, called fuzzy natural things and natural phenomena; The fourth category is abrupt natural things and natural phenomena. Inevitable things and phenomena, like what you plant and what you plant, have a completely certain causal relationship. Random things and phenomena are just like the collision of gas molecules. It is not inevitable that two molecules will collide soon, but gas molecules do collide frequently, so it can be said that the collision between molecules is inevitable, but the collision between two molecules is random. The understanding of vague things and natural phenomena can also be illustrated by examples. Many national boundaries are divided by the center line of the main channel of the river. Where the center line is, it can only be a vague boundary, and it can't be strictly divided. Because there are many rivers and few rivers, the cave water flows, and the waves keep beating against the river bank, it is impossible to make absolutely accurate measurements, so the boundary is blurred. The sudden occurrence of earthquakes and the sudden fracture and collapse of bridges are all sudden things and phenomena.

2. Classification of mathematical methods

According to the types of natural things and phenomena, according to the needs of theoretical calculation and solving practical problems, people have created many kinds of mathematical methods, which can be summarized as follows: constant mathematical methods: all the methods used in ancient and modern elementary mathematics are constant mathematical methods, mainly including arithmetic methods, algebraic methods, geometric methods and trigonometric function methods. Constant mathematical method is used to quantitatively reveal and describe the quantitative relationship and the regularity of spatial form (or structure) when objective things are in a relatively static state in the development process. Variable mathematics method: it is a mathematical method to quantitatively reveal and describe the relationship between the changes of various quantities and quantitative changes in the process of movement, change and development of objective things. Among them, analytic geometry and calculus are the most basic. Analytic geometry method, founded by mathematician Ducal, is an algebraic method to study the characteristics of geometric figures. Calculus (usually called advanced mathematics) method was founded by Newton and Leibniz. This method is mainly used to find a certain rate of change (such as the running rate of objects, chemical reaction rate, etc.). ); Find the tangent (tangent plane) of the curve (surface); Find the extreme value of the function; Solve vibration equation and field equation.

Mathematical method of inevitability: This method is applied to inevitable natural things and phenomena. Mathematical tools to describe inevitable natural things and phenomena are generally equations or equations. There are mainly algebraic equations, functional equations, ordinary differential equations, partial differential equations and difference equations. Using the equation, we can calculate the unknown data from the known data under the condition of following the reasoning rules and rules. For example, this method can calculate the temperature distribution of each part of the steelmaking furnace according to the thermodynamic equation. Therefore, the best design scheme of steelmaking furnace can be determined and selected through theoretical calculation.

Random mathematical method: a mathematical method to study, reveal and describe the regularity of random things and random phenomena through specified quantities. It mainly includes probability theory method and mathematical statistics method.

Mathematical method of mutation: a mathematical method that only reveals and describes the regularity of abrupt things and phenomena through the study of specified quantities. It was founded by the French mathematician Thom in the 1970s. Through strict logical and mathematical deduction, Thom proved that there are seven types of abrupt changes in discontinuous processes under the condition of no more than four control factors, namely, inflection point type, sharp angle type, dovetail type, butterfly type, hyperbolic umbilical point type, elliptical umbilical point type and parabolic umbilical point type. These catastrophe mathematical methods and catastrophe theory are very useful for solving complex catastrophe events (such as earthquake prediction) and phenomena in the field of geological research. Some experts predict that the mathematical method of mutation may become a powerful mathematical tool to solve complex problems in the geological field.

Fuzzy mathematical method: it refers to a mathematical method to study, reveal and describe fuzzy things, fuzzy phenomena and regularity with quantitative methods. There are a lot of fuzzy things, fuzzy phenomena and fuzzy information in nature, which cannot be dealt with by accurate mathematical methods. The establishment of fuzzy mathematics method makes human beings find an effective way to deal with this kind of problem. The effect of this method is called "seeing the light in the blur". "Fuzzy mathematics" is not the fuzziness of mathematics. This kind of mathematics itself is also a kind of precise mathematics with strict logic, so it is named because it is used to deal with vague things.

Axiomatic method: it refers to a special method to establish a mathematical model by starting from the initial scientific concepts and some self-evident mathematical axioms, following the rules of logical thinking and reasoning, and dealing with some related problems with correct logical reasoning forms. Axiomatic method was initiated by Euclid, an ancient Greek mathematician, and formed the theoretical system of Euclid geometry. The core of axiomatic method is to study how to axiomatize a scientific theory, and then build an axiomatic theoretical system. In this system, axioms are first established, that is, some initial scientific concepts in a certain discipline are axiomatized, and then theorems are derived from axioms, thus forming an axiomatic theoretical system.

(D) General steps to improve the mathematical model

The so-called refining mathematical model is to use scientific abstraction to transform complex research objects into mathematical problems, and after reasonable simplification, establish mathematical relations (or equations) that reveal the regularity of the number of research objects. This is both the most critical step and the most difficult step in mathematical methods. Generally, the following six steps are adopted to improve the mathematical model:

The first step: according to the characteristics of the research object, determine what kind of natural things or natural phenomena the research object belongs to, so as to determine what mathematical methods to adopt and what mathematical models to establish. That is to say, firstly, it is determined whether the object and the mathematical model that should be used belong to the "inevitable" or "random" class; Is it a "mutation" class or a "fuzzy" class.

Step 2: Determine several basic quantities and basic scientific concepts that reflect the state of the research object. This needs to be determined according to the existing scientific theories or hypotheses and the analysis of experimental information. For example, in the study of mechanical systems, the first physical quantities to be copied are mass principal quantity (M), velocity (V), acceleration (α), time (T), potential vector (R) and so on. It must be noted that the basic quantities to be determined should not be too many, otherwise there are too many unknowns and it is difficult to simplify them into possible mathematical models, so we must choose substantive and key physical quantities.

Step 3: Grasp the principal contradiction and make scientific abstraction. The actual research object is complex, and many factors are mixed together. Therefore, it is very difficult to turn complex research objects into simple idealized research objects, and the key is to distinguish between primary and secondary. How to distinguish priorities can only be analyzed in detail, but there are also two basic principles: first, the mathematical model must be possible and at least an approximate solution can be given; Second, the error of the approximate solution cannot exceed the allowable error range of the actual problem.

Step 4: Calibrate the simplified basic quantity and endow it with scientific connotation. That is to say, point out which are constants, known quantities, unknown quantities, vectors and scalars. What are the physical meanings of these quantities?

Step 5: Find the result according to the mathematical model.

Step 6: Verify the mathematical model. During verification, the model can be modified according to the situation to make it more consistent. Of course, this is based on the principle that the original model is basically consistent with the actual situation.

(e) The role of mathematical methods in science

1. Mathematical method is one of the main research methods in modern scientific research.

Mathematical method is a quantitative research method needed by all natural sciences, especially in the era of rapid development of science and technology in the world, computers have been widely used, and even an extremely complex partial differential equation can be solved digitally by discretization. For example, the data processing of aeromagnetic exploration and seismic exploration is extremely complicated, and its mathematical model is a partial differential wave (field) equation. Of course, such problems need to be carried out in very large specialized computing institutions. Because of this, many problems that could not be studied quantitatively in the past can now be studied quantitatively through mathematical modeling. Of course, the key to research is how to model. At the same time, only through quantitative research can we reveal the inherent laws of natural things and natural phenomena more deeply and accurately. Otherwise, the establishment of all scientific theories and the accuracy of theoretical research will be difficult to achieve.

Marx once pointed out: "A science can only get real development when it can use mathematics". This is just like the traditional Chinese medicine in China for thousands of years, because its curative effect and effective components failed to reach the level of quantitative research, so its development was slow. At present, all major countries in the world are making quantitative analysis and research on China's traditional Chinese medicine. Some Chinese medicines are made into fine products by other countries and have the patent right of dumping in China, which fully embodies the significance of quantitative research.

2. Mathematical methods provide concise and accurate quantitative analysis and theoretical calculation methods for many scientific researches.

Mathematical language (equation or calculation formula) is the most concise and accurate formal language. Only this language can give the theory and calculation method of quantitative analysis, and the information given by theoretical calculation can provide people with some kind of prediction and forecast. This kind of foreshadowing information may not only bring some discovery, invention and creation, but also bring great economic and social benefits, so that people feel its weight especially.

3. Mathematical methods provide logical reasoning, dialectical thinking and abstract thinking methods for many scientific research.

Mathematics, as a reliable tool of natural science research, is obtained through strict logical deduction, so it also provides many logical reasoning methods for scientific research; At the same time, mathematics is also the language of dialectical thinking and abstract thinking, so it also provides methods of dialectical thinking and abstract thinking for scientific research.

Third, systematic and scientific methods.

System science is a science about systems and their evolution laws. Although this subject only came into being in the first half of the 20th century, it has developed rapidly due to its wide application value, and now it has become a scientific field including many branches. Including: general system theory, cybernetics, information theory, system engineering, large-scale system theory, system dynamics, operational research, game theory, dissipative structure theory, synergetics, hypercycle theory, general life system theory, social system theory, pansystems analysis and grey system theory. These branches study different systems. Nature itself is an infinitely complex system, which contains many different systems, and the system is a universal existence. All things and processes can be regarded as systems with different degrees of organization, thus making the principles of system science universal and highly universal. The method of studying the structure, function and evolution law of various systems by using the principles of system science is called system science method, which has been widely used in various research fields, especially in the biological field (ecosystem) and the economic field (economic management system). System science research has two basic characteristics: first, it is closely related to engineering technology, economic construction, enterprise management, environmental science and so on, and has strong application; Secondly, its theoretical basis is not only system theory, but also depends on various related specialized disciplines, which is closely related to some branches of modern mathematics. Because of this, people think that the system science method generally refers to the study of the mathematical model, structure and design method of the system. Therefore, we will briefly discuss the system science method in the above sense.

(A) the characteristics and principles of systematic scientific methods

The so-called system science method refers to a scientific research method that uses the theory and viewpoint of system science to put the research object in the form of a system, from the whole and the overall situation, from the unity of opposites between system and elements, elements and elements, structure and function, system and environment, to investigate, analyze and study the research object in order to get the optimal solution to the problem. The characteristics and principles of system science method mainly include integrity, comprehensiveness, dynamics, modeling and optimization.

(1) Characteristics and principles of wholeness: This is the primary characteristic and principle of systematic scientific method. The so-called holistic characteristics and principles refer to treating the research object as an organic whole system. Although each element in the system is limited in terms of its individual function, it is the basic element of the system. As far as the whole system is concerned, it is difficult for any element to play the function of the whole system. Just like a car, it is a complete system, and the defect of any part may affect the function of the whole system, and even a trivial screw defect may cause some kind of accident. Therefore, we must regard the research object as an organic whole with qualitative change. The calculation relationship here should be1+1>; 2. This is similar to the motto "Two people are United, loess becomes gold", that is, the overall function of the system is greater than the sum of the functions of each element. This is the so-called additive law of the function of each element of the system. On the one hand, this regularity requires people to explore the relationship between the system and its components from the perspective of an organic whole, on the other hand, it requires people to study the relationship between the system and its surrounding environment from the perspective of an organic whole, give play to the function of the system, and grasp the essence and motion law of the system.

(2) Comprehensive characteristics and principles: This characteristic and principle includes two meanings: on the one hand, it means that objective things and projects are a system, a complex synthesis composed of many elements according to certain laws, and have their special properties, laws and functions; On the other hand, the study of any objective thing and specific system must be comprehensively investigated from its components, structure, function, environment and other aspects. These factors are interrelated, interactive and mutually restrictive. The optimization goal of the system is determined according to the results of comprehensive investigation and research on the research object by system science method.

(3) Dynamic characteristics and principles: it refers to revealing their properties, laws and functions in the dynamic process of material systems. Because all systems actually exist in the objective world, whether between internal elements or between systems and the environment, there are cycles and exchanges of matter, energy and information, so the actual systems are in a dynamic process, not static, so we must adhere to the principle of dynamic.

(4) Characteristics and principles of modeling: It means that when investigating a relatively large and complex system (such as a large-scale engineering project), it is difficult to fully understand all the factors and relationships for a while, and even some factors are not necessary to fully understand. When starting to study and deal with problems, it is often necessary to carry out quantitative analysis, which requires establishing a mathematical model, that is, simplifying the system into an ideal model, so that through experiments and research on the model,

(5) Optimization principle: When solving practical problems by using system science method, the best scheme is selected from multiple possible schemes, so that the operation of the system is in the best state and the best function is achieved. According to the principle of optimization, the relationship or structure between the elements in the system and between the system and the environment must be in the optimal state in order to give full play to the special functions of the system.

(B) Introduce several commonly used systems science methods.

1. Functional analysis method

function