The Mo family's disciples' action to map Fengyi ended up taking almost a month and a half, and Dai Yan was not idle during this period, he was busy with another thing that he valued more. Pen "Fun" Pavilion www.biquge.info

It's about making paper that can be written. Since Dai Yan proposed geometry, the Mohists have been obsessed with the study of this science, but they have encountered another unsolvable problem: the results of geometry cannot be expressed in words.

On the one hand, of course, the current text is too complicated, and many geometric terms cannot be expressed in the current text. Faced with this problem, Dai Yan asked the Mohists to simplify the text on the one hand, and on the other hand, he asked the Mohists to create words to express it. Mohist is the first school of simplification in history, and later the Confucian Xunzi criticized Mohist, one of the reasons is that "Mohist is not good at use but does not know the text", but in fact Mohist is not bad at writing, but Mohist is more practical than practical. Mozi himself does not think that luxury ornaments are inherently bad, and literature is also a kind of good, but it must be "quality first and then text".

Simplifying and creating words can solve the difficulty of geometric textual expression, but the other problem is not so simple to solve. That is, the figure of geometry cannot be expressed. You must know that there are roughly two kinds of books at this time: silk books and bamboo books. This is divided by the material of the book, the silk book is written with silk, and the book is light and easy to carry, of course, it is a good writing material. However, the use of silk is too wide, and its greater use is as a clothing for dignitaries, and its price is so expensive that ordinary people simply cannot afford it. Bamboo books are books made from pieces of bamboo slips woven together with ropes, and this kind of book material is widely sourced, so it is cheap. Of course, there is no problem in writing general conclusions in bamboo books, but if the conclusions of geometry are recorded in bamboo books, bamboo slips cannot be drawn, so geometry cannot be expressed, and it is extremely unfavorable for the study of geometry.

After Dai Yan saw the scene of the Mo disciples sitting on the sand drawing drawings one by one to study geometry, he made up his mind to change this situation. Before he traveled, he had traveled to some remote towns and seen the most traditional process of making clay paper in China. In his mind, the main component of paper is nothing more than plant fibers, which is the main component of plant cell walls, and it should not be difficult to invent this thing.

He soon began to work, according to the process of papermaking in his memory, first selected bamboo as the raw material for papermaking, and dug a special small pond as a bamboo pond; Then the bamboo soaked in the bamboo pond is boiled with lime; Then with the help of the disciples of the Mo family, a special crushing machine was made, and after many crushing, the bamboo was beaten into a bamboo pulp; Then use fine bamboo to make a paper curtain, and put a special wooden bottom plate under the paper curtain as a paper bottom board; The last step is to use a paper curtain to catch the paper and dry it.

Dai Yan did get the paper he expected, but the paper he got didn't know what was wrong, it was extremely permeable, and a little ink drop on it could almost be spread on half of the paper, and it couldn't write at all. The paper obtained in the end can only be used as a product to replace toilet chips, which has slightly improved Dai Yan's quality of life.

When the giant Tian Jiu saw that Dai Yan had been busy for many days, and had also asked the disciples of the Mo family to help, what he got was just a substitute for Dai Yan, and he was furious. He immediately criticized Dai Yan and accused him: "Gongzi gathers the strength of everyone, and it takes many days to enjoy it for himself, and this trip is no different from the gang!" Dai Yandeng was aggrieved, claiming that his original purpose in inventing this object was only for writing, not as a substitute for toilet chips, but how could Tian Jiu believe it?

In the end, it was something brought back by a disciple of the Mo family who saved him. When Dai Yan asked the Mo disciples to survey the various parts of Fengyi, he also asked the Mo disciples to pay attention to the resources of each place, and paid special attention to the exotic flowers and plants, soil and stones. This disciple of the Mo family brought back a black stone, which Dai Yan initially thought was coal, but later discovered that it was actually graphite. Then Dai Yan crushed the graphite into powder, mixed it with the clay here, fired it into shape, and inserted the resulting thin rod into the thin bamboo pole, so that he got the large pencil of later generations. He used this newly invented pencil to write on paper, but this time the paper did not penetrate anymore.

Dai Yan asked Tian Jiu with his newly invented two things: "Does Mr. still think that my behavior is a deceitful act?" ”

Of course, Tian Jiu was able to recognize the great convenience of paper and pencil in the study of geometry, and immediately confessed his mistake to Dai Yan. Later, he listened to what Dai Yan said: paper, as an excellent writing material, is inevitably conducive to the dissemination of knowledge and the development of schools. He even personally led his disciples to participate in the improvement of paper and pencils, and finally made a qualified straw paper that could be written with a brush on the basis of Dai Yan, which also solved the shortcomings of pencil books that could not be preserved.

After obtaining the qualified paper and paper books, Dai Yan immediately ordered a change in the way of writing geometry. In Dai Yan's view, the traditional way of writing - from top to bottom, from right to left - this is the book of the bamboo slip era, and the book is of course limited by the fact that the bamboo slips are connected piece by piece. And paper and bamboo slips are completely different, paper is coherent, it will not be restricted, at this time, in order to facilitate the dissemination of knowledge, of course, how convenient how to come. He immediately changed the way the paper book was written from left to right, from top to bottom, and added various punctuation marks to help break sentences, and introduced ten Arabic numerals from 0 to 9, so that the new book could finally feel familiar to him.

At first, Tian Jiu was also opposed to this change, but Dai Yan quickly gave a high-sounding reason: it is more convenient for everyone to read from left to right, from top to bottom, and it is also more convenient for disciples to accept new knowledge. Tian Jiu thought about it, and finally personally asked the two disciples to read the books in two formats separately, and finally proved that it was indeed more convenient to read in the way of Dai Yan, so he also accepted paper books to write in this way. Of course, this is also the characteristic of the Mo family, the Mo family pays attention to utilitarianism and reality, as long as it is conducive to the life of ordinary people and the growth of the Mo family, the Mo family will not object. If this kind of literary reform had been applied to conservative Confucianism, it would never have been so easily accepted.

Dai Yan not only made changes in books, but also in teaching.

When another Mohist disciple brought back the raw ore of gypsum, he invented something new: chalk. Chalk is not very difficult to make, mix it with limestone and gypsum, and then solidify it with a special model. With the chalk, he asked the disciples of the Mo family to take a special wooden board and paint it black, so he got the blackboard again. With chalk and blackboards, it was more convenient for him to teach the disciples of the Mo family, a change that amazed Tian Jiu.

You know, the traditional way of teaching has always been the teacher's dictation, and the student's dictation, like this, has not even changed until the 19th century. More than 100 years ago, when Confucius was still alive, Confucius had 72 sages and 3,000 disciples under his name. In fact, among the disciples of Confucius, I am afraid that only these seventy-two sages can really read and write. This is the result that shocked the princes and nobles of the time, and Confucius became a saint. As the leader of the Mo family and the teacher of the disciples, how could Tian Jiu not understand the meaning of this new teaching tool?

A series of new tools, such as paper, pencil, blackboard, chalk, etc., have made it extremely convenient to disseminate knowledge, and have also led to the emergence of research results in geometry. In this way, an axiomatic world of geometry and mathematics began to gradually unfold in front of the Mohist disciples, and at the juncture of the nascent of this kind of geometry, the Mohist disciples were full of interest in the knowledge expressed in formulas, and they began to be dissatisfied with focusing only on geometry with this formulaic expression, and people began to bring it into everything in this world. In their view, the previous world was like a map of Fengyi like a landscape painting, and people could only see the general situation; Now with this new way of research, as long as they can work hard to study, they will eventually be able to depict the whole world clearly, just like the new map of Fengyi obtained by Dai Yan, for the first time, accurately measured everything within a radius of 50 miles of Fengyi, where there are mountains, where there is water, all clearly marked, and with the help of scale, as long as the distance is measured on the map, you can know the length in reality. This is an accuracy that has never been seen before in this era.

Dai Yan was also ready to carry out this inducement, but when he tried to make this effort, an urgent summoning order from Song Junzixi in Suiyang, the Song capital, forced him to suspend his teaching in Fengyi.