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Chapter 91: Looking for the Mojia of Mojia Technology I

Mozi was the first scientist in Chinese history to approach mathematical problems from a rational perspective, and he gave a series of propositions and definitions of mathematical concepts, which were highly abstract and rigorous.

The main mathematical concepts given by Mozi are: 1. The definition of "doubling". Mozi said: "Times, for two." That is, the original number is added once, or the original number is multiplied by two, which is called "times". For example, two feet is a "multiple" of one foot. About the definition of "flat". Mozi said: "Ping, the same as Gao." ("The Book of Ink") is the same height called "flat". This is the same as Euclid's geometry theorem, "the common perpendicular lines between parallel lines are equal".

2. Definition of "same length". Mozi said: "The same length, with the right to finish." That is to say, the lengths of two objects are compared to each other, and they correspond exactly one-to-one, and they are completely equal, which is called "the same length".

3. Definition of "medium". Mozi said: "Medium, the same length also." The "middle" here refers to the center of symmetry of the object, that is, the center of the object is a point at an equal distance from the surface of the object.

4. Definition of "圜". Mozi said: "Yuan, one middle school is the same length." The "circle" here is a circle, and Mozi pointed out that the circle can be drawn with a compass. It can also be inspected with a compass. Compasses were widely used before Mozi, but it was Mozi's contribution to give a precise definition of the circle. Mozi's definition of a circle is exactly the same as that of a circle in Euclidean geometry.

5. Definition of square. Mozi said that the four corners are all right angles, and the quadrilateral with the same length of the four sides is a square, and the square can be drawn and tested with a right-angle ruler "moment". This is also consistent with the definition of a square in Euclidean geometry.

6. Definition of a straight line. Mozi said that three points are collinear, that is, straight lines. Tripoint collinear is the definition of a straight line, which has been widely used in measuring the height and distance of objects in later generations. Liu Hui, a mathematician of the Jin Dynasty, in his monograph on surveying "Island Calculations", used three-point collinear to measure altitude and distance. The sight "Wangshan" on the crossbow machine after the Han Dynasty was also invented on this basis.

In addition, Mozi also discussed the decimal value system. As early as the Shang Dynasty, the decimal notation was widely used in China. Mozi was the first scientist to summarize and elaborate the concept of place-value system. He made it clear. Numbers with different digits have different values. For example, on the same digit, one is less than five. And on different digits. One can be more than five. This is because on the same digit (single, ten, hundred, thousand, ......). Five contains one, and when one is in a higher digit, it is the other way around that one contains five. The invention of the decimal system. It is a major contribution of China to world civilization.

As Joseph Needham said in the mathematical volume of The History of Science and Technology in China: "The numeral system of the Shang Dynasty was more advanced and scientific than the fonts of the same era in ancient Babylon and ancient Egypt", and "without this decimal system, it would have been almost impossible to have the unified world we have now".

Mozi's research on physics involves mechanics, optics, acoustics and other branches, gives definitions of many physical concepts, makes many important discoveries, and summarizes some important physical theorems.

First of all, Mozi gave a definition of force, saying: "Force, the reason why the punishment (form) is also striving." That is, force is what makes an object move, even if the action of an object's motion is called force. In this regard, he gave an example, saying that it is like lifting a heavy object from the bottom up, that is, it can be done because of the strong action. At the same time, Mozi pointed out that when an object is subjected to a force, it also produces a reaction force. For example, when two objects of equal mass collide, the two objects move in opposite directions. If the masses of the two objects are very different, the reaction force will still exist although the object with the highest mass will not move after the collision.

Mozi then gave the definitions of "movement" and "stop". He believes that "moving" is due to the force pushing, and more importantly, he put forward the idea of "stopping, for a long time, not for a long time, when the cow is not a horse." This means that the cessation of the motion of an object comes from the action of resistance resistance, and if there is no resistance, the object will move forever. Such a view, which is considered to be the forerunner of Newton's law of inertia, is more than a thousand years ahead of the ideas of the whole world at the same time, and is also a sign of the birth and development of physics (Aristotle believed that force is the cause of the movement of objects, without force objects would not move, and that stopping is the nature of objects, such a view is in line with the results of ordinary people's observations, but it is superficial and wrong).

Regarding the leverage theorem, Mozi also made an incisive statement. He pointed out that the reason why the scale rod is balanced when weighing objects is that the "original" is short and the "mark" is long. In modern scientific language, "Ben" is the heavy arm, "Target" is the force arm, and the mechanical formula is the force× the force arm ("standard") = the heavy × heavy arm ("Ben"). Nowadays, people are generally accustomed to calling the lever theorem Archimedes' theorem, but in fact, Mozi came up with the lever theorem 200 years earlier than Archimedes, so it should be called Mozi's theorem to be fair. In addition, Mozi also conducted a series of studies on mechanical problems such as levers, inclined planes, center of gravity, rolling friction, etc., which will not be repeated here.

In the history of optics, Mozi was the first scientist to conduct optical experiments and conduct systematic research on geometric optics. It would not be an exaggeration to say that Mozi laid the foundation of geometric optics, at least in China. As Joseph Needham said in the physics volume of The History of Science and Technology in China, Mozi's research on optics was "earlier than what we know from Greece" and "incomparable with India".

Mozi first discussed the relationship between light and shadow, and he carefully observed the changing laws of the images of moving objects, and put forward the proposition that "the scenery does not migrate". In other words, the shadow of a moving object from the surface is also moving with the object, which is actually an illusion. Because when the position of the moving object is moved. The image formed in the previous moment has disappeared, and the image formed after its displacement is newly formed, rather than the original image moving to a new position.

If the original image does not disappear, then it will remain in its original location forever, which is impossible. Therefore, the movement of the image seen is only the result of the continuous and uninterrupted birth and death of the old and new images with the movement of the object, and it is not the movement of the image itself. This proposition of Mozi was later inherited by famous artists, and thus put forward the proposition that "the shadow of the bird has not moved". And with it. Mozi also discussed the question of the umbra and the paragram of objects. He noted. If the light source is not a point light source, the object will produce umbra and secondary shadows due to the repeated illumination of the light emitted from each point; If the light source is a point light, only the umbra appears.

Then. Mozi also carried out experiments on imaging small holes. He made it clear. Light travels in a straight line. The image formed by the object passing through the small hole is like an inverted image. This is because when light passes through an object and then through a small hole, the top of the object is imaged below due to the straight line propagation of the light. The lower part of the object is imaged on the top, so the image is inverted. He also discussed the relationship between the size of the image and the oblique positive of the object and the distance of the light source, pointing out that if the object is oblique or the light source is far away, the shadow is long and thin, and if the object is positive or the light source is close, the shadow is short and thick, and if it is reflected light, the shadow is formed between the object and the light source.

What is particularly valuable is that Mozi has conducted quite systematic research on plane mirrors, concave mirrors, convex mirrors, etc., and has derived a series of basic principles of geometric optics. He pointed out that the plane mirror forms an image of the same size, symmetrical from near and far, but reversed from left to right. If two or more flat mirrors are illuminated in the opposite direction, repeated reflections will occur, resulting in an infinite number of images. The imaging of the concave mirror is to form a positive image within the "middle", which is large from the far from the "middle", small from the "middle", and as large as the object at the "middle"; Outside the "middle", it is an inverted image, near the "middle" is like a large, far "middle" is like a small. Convex mirrors only form a positive image, with large near mirrors and small far mirrors. Although Mozi has not yet been able to distinguish the difference between the center of the sphere and the focal point, and confuses the center of the sphere with the focal point, his conclusion is basically consistent with the imaging principle of modern spherical mirror.

Mozi also conducted research on the propagation of sound, and found that the well and poppy have the effect of amplifying sound, and used it skillfully. He once taught his students that when defending the city, in order to prevent the enemy from digging tunnels to attack the city, dig a well every 30 feet, put a large poppy in the well, and put a thin cowhide on the poppy mouth, so that the person with good hearing can lie on the poppy to listen, so as to monitor whether the enemy is digging a tunnel and where the tunnel is digging, and prepare to defend against the enemy (the original text is: make the potter an poppy, and allow more than 40 buckets,...... Put it in the well, so that the deaf person can listen to it, know the location of the acupoint, and chisel it to welcome it). Although Mozi could not understand the mechanism of sound resonance at that time, this method of defending against the enemy contains rich scientific connotations.

Mozi believed that the universe is a continuous whole, and that individuals or parts are separated from this unified whole, and are all part of this unified whole. In other words, the whole contains the individual, and the whole is composed of the individual, and there is an inevitable organic connection between the whole and the individual. Starting from this continuous view of the universe, Mozi went on to establish a theory of time and space. He named time "long" and space as "yu", and gave the definitions of "long" and "yu", that is, "long" refers to all time including ancient and modern times, and "yu" refers to all spaces including east, west, middle and north, and space is continuous and uninterrupted. After giving the definition of space-time, Mozi further discussed the question of whether space-time is finite or infinite. He believed that time and space are both infinite and infinite.

For the whole, space-time is infinite, while for the parts, space-time is infinite. He also pointed out that continuous space-time is composed of space-time elements. He defined the space-time element as "beginning" and "end", "beginning" is the smallest unit of time that cannot be divided, and "end" is the smallest unit of space that cannot be divided. In this way, space-time is formed as continuous infinity, and this continuous infinite space-time is composed of the smallest unit, which contains infinity in infinity and discontinuity in continuity.

On the basis of the theory of space-time, Mozi established his own theory of motion. He unifies and connects time, space, and the movement of objects. He argues that in a continuous, unified universe, the motion of objects is manifested by sequential differences in time and displacement in space. There is no change in time sequence and position, and there is no movement. There is no such thing as mere movement out of time and space.

As for the question of the origin and properties of matter, Mozi also has an incisive exposition. Among the pre-Qin princes, Lao Tzu was the first to propose that the origin of matter is that "existence is born from nothing" (Lao Tzu, chapter 1), and "all things in the world are born from being, and some are born from nothing" (Lao Tzu, chapter 40).

Mozi was the first to rise up against Laozi's idea and put forward the proposition that all things begin with "being". He pointed out that there are two kinds of "nothing", one is that there was in the past and there is no now, such as some extinct bird, which cannot be denied that it was once "existing" because it no longer exists; One is something that has never been done before. Like the heavens falling. This is the "nothing" that does not exist in the first place. The "nothing" that does not exist in the first place does not give birth to "being", and what originally exists and then does not exist is not "being" born from "nothing". It can be seen from this that "being" exists objectively. Mozi then proceeded to elaborate on the question of the properties of matter. He thinks. If there are no stones. You won't know the hardness and color of the stone. Without sun and fire, heat would not be known. That is, the property does not exist apart from the material object. An attribute is an objective reflection of a material object. The reason why man is able to perceive the properties of matter is due to the objective existence of material objects.

Mozi is also one of the important pioneers of ancient Chinese logical thought. He consciously and extensively used the method of logical deduction to establish or justify his own political and ethical thoughts. For the first time in the history of Chinese logic, he also put forward the logical concepts of argument, class, and reason. It also requires debate to be learned as a specialized knowledge.

Although Mozi's "debate" refers to the technique of debate, it is based on the knowledge of the class (the kind of things) and the reason (basis, reason), so it belongs to the category of logical analogy or argumentation. The "three forms" mentioned by Mozi are not only the ideological standards of speech, but also contain the elements of reasoning and argumentation. Mozi is also good at using analogy to expose the contradictions of his opponents.

Due to the advocacy and enlightenment of Mozi, the Mohists developed a tradition of emphasizing logic, and the first system of ancient Chinese logic was established by the Mohists in the later period. The main contribution of Mozi's philosophical thought is in epistemology. He took the direct sensory experience of "the reality of the ears and eyes" as the only source of knowledge, and he believed that the existence and absence of things should not be judged by personal imagination, but by what everyone saw and heard. Starting from this simple materialist empiricism, Mozi put forward the criteria for testing the authenticity of cognition, that is, three forms: "the matter of the ancient saint king", "the lower plain examines the reality of the people's ears and eyes", and "abolishes (fads) as criminal government, and looks at the interests of the people of the country".

Mozi synthesized "facts", "facts" and "benefits", and took indirect experience, direct experience, and social effects as the criterion, and strived to eliminate subjective preconceptions of individuals. In terms of the relationship between name and reality, he put forward the proposition of "not by its name, but by its name", and advocated that the name should be justified by the real and worthy of the name. Mozi's epistemology of emphasizing the authenticity of sensory experience also has great limitations, and he once came to the conclusion that "ghosts and gods exist" on the grounds that some people "taste the things of ghosts and gods and hear the voices of ghosts and gods". However, Mozi did not ignore the role of rational cognition, and the Mohist school created the first logical thought system in China.

One view is that there are deep internal contradictions in Mozi's worldview. On the one hand, he emphasized "non-fate" and "Shang Li", believing that it is not "fate" but "force" that determines people's different experiences. On the other hand, Mozi affirmed the role of "Tianzhi" and "ghosts". He described "heaven" as a personality god with a will, and preached that "those who obey the will of heaven" "will be rewarded"; "Those who oppose the will of God" will be punished. He believes that "loving each other and benefiting each other" is "conforming to the will of heaven", and "don't be evil, be a thief" is "anti-heaven's will".

However, another point of view is that "non-fate" and "heavenly will" embody the strong thinking tension of Mozi's "debate between heaven and man", in Mozi's religious philosophy, heaven will and love but not control the mandate of heaven, heaven rewards diligence, and heaven likes people who strive for self-improvement.

Politically, Mozi put forward the ideas of "concurrently love", "non-attack", "Shangxian", "Shangtong", "sparing", "frugal funeral", and "non-music". "Combining with other things" is the core of his social and political thinking, and "non-offensive" is his specific program of action. He believed that as long as everyone "loves each other and benefits each other," there will be no strong bullying of the weak, arrogance and arrogance, wisdom and foolishness, and the phenomenon of countries attacking each other.

He sharply exposed and criticized the evils of the rulers' wars and the extravagances and pleasures of ordinary manners. In the principle of employing people, Mozi advocated meritocracy, opposed cronyism, and advocated that "officials are impermanent, and the people are not cheap". He also advocated that from the Son of Heaven, the princes and kings to the chiefs at all levels, they should "choose the virtuous and virtuous people in the world" to act; And the people and the Son of Heaven and the monarch must obey the will of Heaven, carry forward and love, and implement righteous government, otherwise, it is illegal, this is "Huangyu wheel thin"!

In the past few days, the Mozi Memorial Hall in Tengzhou, Shandong Province, Country C, has been overcrowded, and it is not only the increase in domestic tourists in Country C, but also a significant increase in foreign tourists. Most of these tourists have a very famous name, either famous scholars such as mathematicians, physicists, historians, historians of ancient science, and even the world's famous investment bank bosses, several major animation production company bosses, film company bosses, travel company bosses have arrived, as well as the world's top designers, planners, famous film directors, animation directors and so on. For a while, the entire Tengzhou city citizens and even the government were still in the dark, not knowing what these foreign tycoons and scholars were talking about.

After these people arrived, they went straight to the ink hall of the Mozi Memorial Hall, which is supposed to have an area of thousands of square meters, but there are too many people who come to sightsee or have other purposes, so they can only line up in a regular manner, and enter it round by round to visit.

Mozi Memorial Hall is located in Zaozhuang City, Shandong Province, Tengzhou Jingshui Riverside, Longquan Tower, is a collection of academic seminars, library collection, science and technology education, visits in one of the comprehensive courtyard building group. The Mozi Memorial Hall was built in 1993 and upgraded in June 2007, covering an area of 20,000 square meters and a construction area of 8,000 square meters. It is the only venue in the world that specializes in the study of Mozi culture, collects Mozi materials, and displays Mozi research results. The west courtyard has a pavilion and a gallery of celebrity inscriptions. The northern part is the library building, which collects books and materials for ink research at home and abroad

The Mozi Memorial Hall is composed of three parts: east, west and north, with the east courtyard as the exhibition hall and the main orderly hall, which is dominated by the statue of Mozi and the great man's evaluation of Mozi; The comprehensive hall displays Mozi's thought and the research results of Moxue, as well as the grand occasion of the previous International Symposium on Moxue; Science and Technology Hall, which displays Mozi optics, mechanics, space-time view, sonar principles, etc., some of which can be demonstrated; The Holy Miracle Hall, which is mainly painted with the "Mozi Sacred Miracle Map"; The Military Hall focuses on Mozi's military thought and defensive measures, and its highlights are city defense, crossbow and bow demonstrations, etc. The west courtyard has a pavilion and a gallery of celebrity inscriptions. The northern part is the library building, which collects books and materials for ink research at home and abroad. It is the best place for tourists to learn about excellent traditional history and culture, learn ink knowledge, and master Guteng culture.

The Mozi Memorial Hall adheres to the protective development and utilization of Mozi cultural resources, actively organizes and coordinates experts and scholars to research and excavate Mozi culture, and uses physical scenes to reproduce research results. In the small hole imaging room, visitors can experience the mystery of the small hole imaging principle of Mozi, and in the military hall, visitors can experience the scenes of the war in the Spring and Autumn Period and the Warring States Period. It is of great significance to do a good job in the protection and development of Mozi culture and to harmoniously integrate tourism and humanities to inherit Mozi culture, carry forward the spirit of Mozi, prosper history and culture, and achieve sustainable development.

The main buildings have exhibition rooms: Mozi Sacred Miracle Hall, Motang Hall, Science and Technology Hall, and Huiwen Hall. In the east courtyard, there are Mozi lecture stone busts, "Mozi" stone carvings, celebrity inscription inscriptions, in addition to the corner tower, cloister, Muyi Pavilion and other landscapes. The whole building is flat ridge and corner, square kiss buckle eaves, towering treasure roof, blue tile powder wall, black marble pedestal, solemn and simple; The doors are wide and the windows are high, and they are inlaid with sapphire glass, which is magnificent; The hall is connected with the corridor, the road winds and the path rings, the famous flowers and different grasses, the green trees are shady, it is the garden architecture group that combines the modern and national forms, embodies the three major functions of academic seminars, library collections, visits and tours, is not only the cultural landscape of tourism and sightseeing, but also an important window for Tengzhou City to open to the outside world.

In the Mozi Sacred Miracle Hall, a huge mural with a height of 2.5 meters and a length of 85 meters is exhibited, showing the glorious life of Mozi. In the ink hall, the 20 characters of "love, non-attack, Shangxian, Shangtong, thrift, funeral, non-music, non-life, Tianzhi, and Ming ghost" summarize his ideological proposition. Yilitang introduced his achievements in physics, mathematics, optics, and military affairs. The library building is the only ink research center in the world. (To be continued......)