Chapter 15 Section 2 Contribution of Mohism to Mechanics

The Mozi school has a lot of research on mechanics, reaching the highest level in the world at that time. The "Sutra" says: "Force is the reason for shape", which means that force is the reason for the change of object motion. This content is Newton's second law, but the problem of acceleration is not explicitly raised.The Mozi school knew about acceleration, but it was not mentioned in this article.In fact, the so-called "fen" means variable speed movement.Another example is the "Jingxia" when talking about the boat (chuanchuan) car, there are some sayings such as "the one who is above will gain more, and the one who is below will perish", "the one who is above will lose more, and the one below will gain more".These "healing" characters all contain the meaning of acceleration. "Jing Shuo Shang": "Strength, heavy is called down, and heavy lifting is also vigorous."Here we talk about the falling of objects, that is, the inevitable phenomenon of gravitational force.Mozi is the earliest discoverer of the theory of gravity.When it comes to the discovery of gravity in the West, Newton in the 17th century is the first to be promoted, while Mozi raised the issue of gravity as early as 2,000 years ago, and "there is no power to draw", which can be regarded as the definition of gravity in Mohism.

The entries about mechanics in Mojing can be illustrated as follows: "Jing Shang": "Strength is the reason why form is vigorous." "Sutra": This is the basic concept of Mozi's school of force.From the point of view of "force, what the shape exerts", it is to explain the basic power of the object to change the state of motion and stop. "Jing Shuo Xia" "Force, the weight is called down" refers to the role of gravity.Objects don't fall without gravity.Mozi not only has insight to change the state of motion and stillness of objects, but is also the earliest discoverer of gravity. He said, "Yin, there is no force", which is very similar to the definition of gravity.

"Jing Shang": "Move, or follow." "Sutra": This one means that when an object is pushed from one side, it can move.This is like a door switch, which can be opened or closed by force from one side, but the latch must be removed. This article is a comment on the previous article, explaining the process of force exerting its function. "Jing Shang": "Stop, it will take a long time." "Jing Shuo Shang": "Stop, there is no end to it for a long time. A cow is not a horse. If an arrow passes a couplet, it will last for a long time. A horse is not a horse. It is like a person crossing a beam."

The so-called "stop" here means to stop the movement.This is done by force.Stopping depends on time to show, so it is said "stop, it will take a long time".This is static analysis.Use, refers to force.For a long time, once you do moxibustion, it means blocking.According to "Jing Shuo Shang", long time means "ancient and modern day and night", which should be a long time.Ying, the pillar in front of the hall.The arrow passes between two couplets, and it disappears in a blink of an eye. This is a dynamic.People walk across the bridge without stopping, which is another kind of dynamic.People depend on time and space, and as time and space change, characters also change. "Unstoppable for a long time" is more than just moving. "Infinite and endless" means that there is no movement without time.On the other hand, it means "more than a long time".This article says that it takes time for an object to be at rest or not to be at rest.Shi Guoying is very fast, and an instant is also time.Saying this is as correct as treating cattle as "non-horses".People cross the bridge very slowly, and the illusion of stopping every step cannot be regarded as really not moving.If so, it would be the same as mistaking a horse for a non-horse.As Liang Qichao said, there are two kinds of time, "no long time" and "long time".For a long time, it is easy to detect, but for a long time, it is short and difficult to detect.This one is about the movement of objects, which changes from time to time and is not easy to detect.

According to Tan Jiefu's "Classification and Annotation of the Mohist Classics", it should be: "The turbulent things must stop. This is the reason for the long-lasting force. This is as correct as the 'ox' is 'not a horse'. For example, one arrow passes two couplets. When the object (arrow) moves, there is an external force and the column will not stop for a long time. It is as incorrect to say that a "horse" is a "non-horse". It is also like crossing a bridge. When people are blocked by the river, they cannot move forward. .But with the bridge, you can move on. 'It's a long time to stop' is the norm, 'a long time to go' is a perversion."

"Jing Xia": "Combined and one, or complex, no. It is said to be rejected." "Jing Shuo Xia" None. This sutra has no text and is not easy to examine.There are two interpretations: One is according to "Mojing Classification and Annotation", this article belongs to mechanics.It means that combination is a resultant force, a synthesis of several forces. "One" is one force.Together and one have the meaning of hostility. "Fu" is a resultant force, or a reactionary force. "No" means "no more", and the force of words is too small to be easily noticed.Denial is resistance, resistance.

Second, according to the "Mozi Annotation", it is believed that this article refers to a contradictory relationship.After the combination of unity and unity, the thought itself breeds contradictions, gives birth to negative thoughts, and easily opposes each other. "Jingxia": "If you lose without giving up, you will win if you say it." "The next scriptures": This article explains: It is balanced for a person to carry objects with a pole.If one end is heavy, it is to fall.If it is not biased, it is "extremely victorious".The rope between the two pillars is bent even if it is not loaded, which is extremely heavy.To say "losing but not scratching" is to be able to bear the weight, that is to say "saying is winning".

"Jingxia": "A mystery must come out, and you can get it if you say it." "The next scriptures": When the scale is balanced, if one end is added to the weight, this end must droop.Because before adding weight, the weight (weight) and the object (heavy) are in balance.Therefore, it is said: "Weighing, add weight to the side, must be hammered, the weight is similar to a steelyard (as shown in Figure 18), the book is short, and the standard length. According to today's formula, the product of the length of the book and the suspended weight is equal to the length of the standard and the weight. The two ends will be balanced. At this time, if the two ends are equal in weight, one end of the weight will inevitably droop.

The above is different from the expression of the lever principle of Archimedes in ancient Greece, but the meaning is the same. "Jing Xia": "Putting out and closing the door (reverse), it is said that it is thin." "Jing Shuo Xia": "Extracting is powerful, but attracting is powerless. If it is not correct, what is drawn stops at giving. The rope controls it. If you use an awl to pierce it, pull it out, the long and heavy one will go down, the short and light one will go up, and the rope will control it. The more the ones gain, the more the ones below will perish. If the weights of the ropes are the same, then it is right. If you gather, the ones above will lose more, and the ones below will gain more.

This article follows the previous article on leverage.There are two kinds of power: speaking and drawing.Pull out, lift up.Receive, drag down.仮, the opposite of pulling out and retracting force, thin, force, force.Pulling out is opposite to retracting force, so it is said that "speaking is thin".Regarding the analysis of the direction of force, the viewpoints of "extracting strength" and "leading power" are put forward. A lever hangs an object at one end and a right at the other end.When the suspended object falls down, the weight must rise up.This is "the long and heavy ones go down, and the short and light ones go up."

The straight rope means that the rope of the suspended object and the weight is perpendicular to the beam.This equals balance.This is "the weight of the rope is the same, then it is right". Pulling out is the opposite of receiving. If the object is too heavy and the object falls, it will rise.Falling is the retracting force, and rising is the pulling force.The stronger the descent, the weaker the ascent.This is "the more the superior loses, the inferior gains more; the superior loses all his power, and then he will be pulled out." "Jingxia": "Those who rely on cannot be straightened, they are said to be shaving." "The next scriptures": This section is about the production and principle of the car.This car is characterized by low front and high rear.It is also called a ladder car.Place a heavy object in front of the car (before the rear wheels).One pull (pull) and one push (pull) can walk without too much effort, so it is called "pull and pull and walk".Because the car itself has the characteristic of being front-heavy, it can walk smoothly without lifting it on the top (do not pull it up), pulling it on the back (do not stow it down), or pushing it on the side (no robbery on the side).If there is a deflection, it will hinder walking. "Today the rocks are still lying on the flat ground" should be moved back.In the above experiment, it is the same reason to pull a cart with a rope and to pull a boat with a rope when sailing in the river.That's why it is said, "If a rope is used to guide a wheel, it is like guiding a boat from a boat." "Jing Xia": "The pile must be a pillar, said to be waste material." "Jing Shuo Xia": "Heap, 竮 [pingping] stone 絫 (tired) stone, its (ear) clip (宀xia broom) (sleeping) (pillar) column also. Fangshi supports the ground stone, and the stone is in the It is on (below), hang the thread on it. Make it fit to the square stone. If it does not go down, it will be a pillar. The glue thread will remove the stone, and it will be pulled out. The thread will be cut off, and it will be drawn. Solution 1: This section is about the theory of motion.The scriptures are relatively simple, just saying that stacking materials need support.The scriptures are more complicated. It says: a. The base of stone blocks, with pillars underneath; b. Silk tied stones, down to ashlar.When the pillar is removed, the square stone hangs in the air, which is the pulling force of the silk; c. The heavy wire of the stone is broken, and the stone falls, which is the gravitational force; Solution 2: This article is to explain the construction process, the waste is placed, and the material is stone. (Li Bing), and the complicated text of Bing.絫, through the tired.Er, Bi's provincial text.vice, two. (宀xiabroom), the province of sleeping.In the temple system, the middle is the Taishi, that is, sleeping.The hall before the sandwich room is the ear.Flat ground, that is, a flat foundation.Silk, ink thread used by craftsmen.Fangshi is the standard stone.The pillars are "fixed house feet".To remove the stone means to remove the excess part of the stone.To quote is to fill up, to supplement.The name Yi is fair, and harvest is achievement. The meaning of this paragraph is to say: the construction begins with laying the foundation.The process of mobilizing stone materials, designing wing rooms and sandwich rooms is called "stacking".Then stand the stone on the flat ground, taking one foot from the ground as the standard.If the stone is too big, it should be cut, which is to pull it out.If it is too small, it needs to be made up. This is the quotation.Appropriately called collection. According to this opinion, the text of "Jing Shuo Xia" should be: "Pile, (stand and combine) stones, 絫石, ear clips (宀xia broom), piles and pillars. Today, stones are also abandoned on the ground, and Fang Remove the ground ruler from the stone, close the stone under it, and hang the thread on it so that it fits under the ashlar. .” "Jingxia": "Nothing is equal. It is said that everything is equal." "Jing Shuo Xia": "Equal, the hair is evenly suspended. The weight is the same, and the hair is not even. Even, the absolute is also, not absolutely." This is the study of elastic mechanics.Liezi also talked about this issue. "Tang Wen" said: "Even hair is evenly weighted, but hair is never. Uneven hair is also. Even, it is absolutely, not absolutely." It also gave an example, "People think otherwise, and they know it. Zhan He (a native of Chu, good at fishing, heard of in the country). He used cocoon silk as a fiber, awn needles as hooks, wattle twigs as rods, and dissected grains as bait to lure fish that are full of carts." "Zhongni" also said: "When you start a thousand things, you can wait for the power." It can be seen that this was a relatively popular debate topic in ancient times. The scriptures say that the key to whether the hair will break or not depends on whether it is even.For uniform, monofilament has the problem of being uniform or not, and a bundle has the same problem.If the weight is not equal, it is not uniform, and the unevenness will inevitably break.Professor Yan Daoan pointed out that the proposal of this proposition is based on experiments.Such a realization is hard to come by without many painstaking experiments.

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