The branch of mathematics that studies the quantitative laws of random phenomena. Random phenomena are relative to decisive phenomena. The phenomenon that a certain result must occur under certain conditions is called decisive phenomenon. For example, at standard atmospheric pressure, when pure water is heated to 100℃, water will inevitably boil. Random phenomenon refers to the phenomenon that a series of experiments or observations will get different results under the same basic conditions. Before each experiment or observation, it is uncertain what kind of results will appear, which shows contingency. For example, flipping a coin may have a positive side or a negative side, and the life of light bulbs produced under the same technological conditions is uneven. The realization and observation of random phenomena are called random experiments. Every possible result of random test is called a basic event, and a basic event or a group of basic events is collectively called a random event, or simply called an event. The probability of an event is a measure of the possibility of an event. Although the occurrence of an event in random trials is accidental, those random trials that can be repeated in large numbers under the same conditions often show obvious quantitative laws. For example, if you throw a uniform coin several times in a row, with the increase of throwing times, the frequency of head appearance will gradually tend to 1/2. For another example, when the length of an object is measured many times, with the increase of the number of measurements, the average value of the measurement results gradually stabilizes at a constant, and most of the measured values fall near this constant, and its distribution presents a certain degree of symmetry. The law of large numbers and the central limit theorem describe and demonstrate these laws. In real life, people often need to study the evolution of a specific random phenomenon. For example, tiny particles in a liquid are randomly collided by surrounding molecules to form irregular motion (Brownian motion), which is a random process. The statistical characteristics of random process, the calculation of the probability of some events related to random process, especially the research on the sample trajectory of random process (that is, the one-time realization of the process) are the main topics of modern probability theory.

The law of large numbers was originally a concept in economics, specifically a concept in statistics, but there is no accurate definition in academic circles so far. According to the British economist Paul Siblett, "the law of large numbers generally holds that the average behavior of a large group of similar individuals is more predictable than that of a small group or individuals in a group." [3] The law of large numbers comes from the regularity of statistical data display. /kloc-John Gratt, a British economist who founded demography in the 0/7th century, revealed such a statistical principle: "Through a large number of sufficient statistical data, we can see that various phenomena (of which a single phenomenon is accidental) are governed by some strict regularity as a whole." [4] In fact, many natural laws are revealed by statistics, such as the alternation of day and night, seasonal changes and other natural laws. What we call the scientificity of natural laws can only be verified on the basis of statistical facts and scientific analysis. The characteristics of stability in human social behavior are often obtained through statistical induction. The earliest scholars engaged in social behavior statistics have realized that for a group, even if the individual motivation is not mastered, there will be regularity when the number of groups is large. In the formed groups, there will always be certain universal laws, certain * * * identical constraints, certain average trends and average performances. Although it is possible that each individual member can act quite freely in several choices, when it comes to long-term behavior, the overall behavior can be relatively predicted. [5] The most unpredictable events in nature seem to be random and accidental, but once they are involved enough times, they can show phenomena similar to mathematical laws, and people can make predictions accordingly. Therefore, although a single event is meaningless, if the event is repeated many times, the distribution of actual results will show a certain proportion. This is the law of large numbers. [6] Since the establishment of social statistics, social statistics has been applied to social science surveys, trying to find some universal and regular facts from the survey data, such as revealing the stable relationship between mortality and birth rate, gender and life expectancy, disease and occupation, education level and income through census and statistics. William petty, a famous economist of the same age as John Glauerdt, claimed that his method was to "express my own problems with words of numbers, weights and scales, and only demonstrate and investigate the reasons that can attract people's senses." [7] Malthus's theory about human beings is largely based on statistics. The predictability and stability of behavior revealed by social statistics, although people may not understand the reasons of human behavior or even put forward a convincing explanation, there are large-scale similarities and stability characteristics in social behavior after all. This shows that there is indeed a law in social behavior that can be called the law of large numbers. Under the domination of the law of large numbers, individuals often have to obey the law of large numbers shown by groups, and individuality disappears into the total number shown by statistical data under the domination of the law of large numbers. Statistics only provide data. From the statistical data, the law of large numbers often shows the similarity and stability of most people's behavior. The behavior of most people actually refers to the stable and repetitive behavior of a large number of people presented by probability in statistical data. The more similar or close a person's behavior is to most people, the more his behavior will be affirmed, at least not belittled. Even if this behavior itself is not good, it will be tolerated by people because the holders are the majority. For example, most people have understanding and sympathy for their unfilial son who has been ill in bed for a long time, at least there will not be too much condemnation. People will greatly praise the goodness that only a few people can do. For example, people will praise the dutiful son who is ill in bed. Therefore, statistically speaking, human's evaluation of moral good and evil is also supported by statistical data, not from the revelation of God, but from the usual performance of human nature. What most people can do is right or normal, and there is no distinction between good and evil. Above what ordinary people do, it is the good that people advocate, and under what most people do, it is the evil that people belittle. In this sense, moral creed is nothing more than the maintenance of the law of large numbers. Most people's behavior is often manifested as the behavior of ordinary people. The behavior of ordinary people refers to normal people or neutral people. Some scholars refer to China people, [8] some scholars refer to "standard people". [9] From the statistical point of view, most people's behavior often shows a stable behavior tendency and neutral person's behavior evaluation. Generally speaking, the behavior of most people is often the closest to that of ordinary people, and the scope of ordinary people's behavior is often more subject to the behavior of most people. The closer a behavior is to the average, the more it is often the behavior of the majority. The more similar a behavior is to the behavior of the majority, the closer it is to the scope of the average behavior. Regarding the behavior of ordinary people, French scientist Ketolet believes that all aspects of human beings as a whole belong to the scope of physical facts; The more people there are, the more personal wishes will be buried under a series of universal facts, which depend on the overall reasons that determine the existence and continuation of behavior. Since the "existence and continuity" of society is what people need, then the average behavior of people is "correct" behavior. The parameters, physical attributes and even moral and aesthetic concepts of "ordinary people" represent the perfect average situation that all people should pursue. Generally speaking, Excellence-a person who can show all the qualities of "ordinary people" in a certain period of time, he represents all the goodness, beauty and goodness of human beings at this time. Deviation from the non-average situation, no matter how big or small, will lead to the ugliness of the form and the imperfection of morality, so it is in an imperfect state of existence. [10] Because the behavior of ordinary people is considered to be the behavior of the middle class, people's behavior is generally neither high nor low, so it is considered to be the behavior of normal people. And if you deviate from this average, you will either be extremely praised or extremely belittled. Therefore, for the behavior of height and beauty, we can understand that it is only people's efforts to approach the average level, and there is nothing really abnormal. Social order is based on the daily life that is natural for ordinary people. [1 1] The law of large numbers is a rule set system that shows a persistent state or a stable tendency by averaging human behavior and most people's behavior. The law of large numbers shows the anthropological reasons for the establishment and maintenance of human social order. It is with the help of the law of large numbers that human society maintains a stable social evaluation system and a stable social order supported by this stable evaluation system. The existence of the law of large numbers has brought us respectable order and normality, and also saved the world from falling into the terrible realm of disagreement. [12] It is very important for the stability and aggregation of the group whether the members of the society abide by the agreed customs and habits. [13] "People often enjoy many standards and want to stick to them. If they do this, their society will be orderly. " [14] Therefore, even in the primitive society without laws, human beings can still effectively maintain the cooperation and trust among individuals in the group with the help of those spontaneously formed laws of large numbers, and shape the group into a closely United community.