The absolute continuity of motion cannot be understood by human intellect.Human beings can gradually understand the law of any movement only when examining the subdivision units of any movement extracted at will.But then most of the misunderstandings of human beings arise due to the arbitrary division of continuous movement into discontinuous units. It is a well-known ancient rhetoric that Achilles cannot keep up with the tortoise in front of him, though he goes ten times faster than the tortoise; A tenth of this distance has been covered; Achilles has covered this one tenth, the tortoise has gone ahead by another one hundredth, and so on, endlessly.This formula is an ancient and insoluble arithmetic problem.The absurdity of the answer (that Achilles can never catch up with the tortoise) is only due to the rash assumption of discrete units of motion, whereas the motion of either Achilles or the tortoise is continuous.

-------- ① Achilles is the hero in Homer. By dividing the unit of motion into finer and finer parts, we can only get close to the answer to the question, but never get the answer.Only by assuming infinite decimals and the series below one-tenth produced by infinite decimals, and then finding the total amount of this geometric series, can we get the answer to the question.A new branch of mathematics, having solved a technique for dealing with infinitesimals, is now able to find answers to other, more complex problems of motion that previously seemed insoluble. This new branch of mathematics, unknown to the ancients, when studying motion problems, assumes infinite decimals, so that the main condition of motion (absolute continuity) can be restored, thereby correcting human wisdom and replacing pairs of pairs of motion units with individual motion units. Mistakes that cannot be avoided when conducting research in continuous motion.

The same is true in the discussion of the laws of historical motion. Human movement is produced by the random actions of countless people, and it is continuously carried out. To understand the law of this movement is the purpose of history.However, in order to understand the law of continuous motion formed by the sum of people's random actions, human wisdom assumes that random units can be intercepted and are incoherent.The first step of historiography is to randomly extract a series of consecutive events and study them one by one separately, so that there is no beginning of any event, and one event will always emerge from another event without interruption. .The second step consists in studying the actions of individuals, kings, and generals, as the sum of the unconscious actions of men, which the actions of individual historical figures never reflect.

In its own operation, historical science often divides into small and small units for research, so as to approach the understanding of truth.But no matter what kind of small units historiography divides, we feel that assuming units that are disconnected from each other, assuming that there is a beginning of a certain phenomenon, assuming that the random behavior of all people will be reflected in the actions of individual historical figures, the It is false in itself. Any conclusion of historiography can be disintegrated without the trouble of critics, and all that is needed is for the commentator to examine a large or small incoherent unit; critics always have the right to do so, and any historical Isn't the unit intercepted arbitrarily?

It is only by taking the infinitely small units of observation—the differentials of history, the common tendencies of people—and applying the method of integration (that is, to arrive at these infinitely small sums) that we can hope to understand the laws of history. During the first fifteen years of the nineteenth century there was an unusual movement of millions of people in Europe.Men abandoned their day-to-day occupations to scramble and kill from one side of Europe to the other, triumphant and groaning in despair, so that the course of the whole life fluctuated from year to year, showing a violent movement that first rose and then fell.What is the reason for this movement, and what law does it operate in accordance with? ——Human wisdom needs to be clarified.

The historian answers this question by telling us the words and deeds of dozens of people in a building in the city of Paris, which he calls revolutionary; The effect on others is to say: this is why this movement happened, this is its law. But human intelligence not only refuses to believe this explanation, but simply says that this method of explanation cannot be trusted, because it regards the weakest phenomena as the strongest arguments.The sum of the unconscious actions of men which produced the Revolution and Napoleon, and it is only the sum of these unconscious actions which tolerated and then annihilated both.

"But whenever there is a battle, there will be a conqueror; whenever there is a change in the country, there will be a great man." History says so.In fact, whenever a conqueror appears, war breaks out. This is the answer of human wisdom, but this does not prove that the conqueror is the cause of war, and the law of war can be found in the individual actions of individual characters.Whenever I look at the clock and see that the hands of the clock go to ten, I hear the bells of the neighboring church striking, but from the fact that the prayer bells strike when the hands go to ten o'clock, I have no right to draw conclusions Say, the position of the hands is the cause of the movement of the church bell.

Whenever I see a locomotive start, I hear the whistle, see the valves open, and the wheels turn; but I have no right to conclude from this that the whistle and the wheels are the real cause of the locomotive's motion. Farmers say that the cold wind blows in late spring because the buds of the oak trees bloom, but in fact, every spring when the oak trees bud bud, there is a cold wind.But though I do not know the cause of the cold wind when the oak buds bud, I do not agree with the farmer that it is the cause of the cold wind when the oak buds bud, because the buds do not affect the wind.I see only the coincidence of conditions in the phenomena of everyday life, and I know that no matter how closely I look at the hands of the clock, the valves and wheels of the locomotive and the oak buds, I still cannot understand the cause of prayer bells, locomotive motion, and late spring cold .To understand it, I had to change my point of view entirely, and study the laws of motion of steam, cathedral bells, and wind.So should historiography.And someone has tried it.

In order to study the laws of history, we should completely change the object of observation, open up the emperors, ministers and generals, and turn to study the same type of infinitesimal factors followed by the people.No one can say how much acquaintance with the laws of history can be gained by this method; Describe the actions of emperors and generals, and one millionth of the energy expended to exert their imagination according to them.