1635 Han style rises again

January 1667, 1, Jianye, Tiangong College.

"Sir, we have been studying differential and integral for several days, but I still have doubts in my mind. I can't understand what is integral and what is differential?" In class, a young student said with a little shame: "Please Sir, can you use simple words to clarify my doubts for me?"

"Hehe..." Fang Zhongtong smiled when he heard the words, put down the books in his hands, and looked at the more than 30 students in the classroom, "Everyone, are you still confused with this classmate?"

The students looked at each other and nodded.

"It's no wonder. We haven't been in touch with the teachings of differential and integral for a long time. Many new concepts and derivation formulas are still learned from the king. Now, it is a bit difficult to suddenly teach you these cutting-edge mathematical knowledge. Understanding is inevitable. Let me use some simple language to explain these concepts."

"Students, in intermediate schools, you may have solved the problems of speed, time and total mileage. But at that time, our understanding of speed was still very shallow, and it was limited to the average speed. For example, a person It took 5 minutes to walk 200 meters, so what is the average speed of this person? We will divide 200 by 5 minutes, and we will get a speed of 40 meters per minute. However, the person’s speed in the process of walking The speed is not uniform every minute and every second. What if I want to know his speed at every moment?"

The students looked at Fang Zhongtong blankly, why should they know the instantaneous speed of this person?
"Among them, one way is to divide this person's traveling process infinitely into the smallest moments, so we can get the speed of this person at each moment? Here, we propose a concept of acceleration, When an object is stationary, if we push it, an acceleration will be generated instantaneously, and the acceleration will accumulate to a certain level before it will produce velocity, and the velocity will accumulate to a certain level before there will be displacement.”

"Although we see from the outside that we are pushing the object, but from the inside of the object, the whole process is like this: accumulating acceleration→turning into velocity→accumulating velocity→generating displacement. This process is integration. Conversely, it is differentiation : The first derivative of displacement is velocity, and the first derivative of velocity is acceleration. Therefore, acceleration is the second derivative of displacement.”

"Or, we can understand it this way. Integration is the process of accumulating from the micro to the macro, and differentiation is the process of dividing the macro into the micro. In this way, students can understand?"

Looking at the more than 30 students in the audience, only a small number of them showed stunned expressions and were overjoyed, while most of the students were still a little dazed and at a loss, and even showed a hint of shame on their faces.

Fang Zhongtong smiled helplessly. It is said that the concept of differentiation and integral has just been proposed in Europe, and has not yet formed a formal theory.However, the king of our country, who is full of talents, derived the differential and integral from the concept of geometry abruptly, and used the more intuitive circle area calculation formula to prove it.

"Students, in fact, in our daily life, the concepts of differentiation and integration are everywhere." Fang Zhongtong picked up a white charcoal pen and wrote three words on the blackboard, hard work, ability and success.

"You see, in each of us, is there such a process: if we regard hard work as acceleration, ability as speed, and final success as displacement. Then the relationship between these three is actually an integral The process. Short-term efforts cannot be transformed into abilities. We have to work hard for a long time to accumulate our own abilities, and it takes time for abilities to accumulate to success.”

"In this world, why do many people do nothing all their lives? Maybe it's not because they are not smart enough, but because they don't understand the thinking of differentiation and integration. The so-called unambitious people often make up their minds. When they first set their minds to do something, they will work hard for a while, but This burst of hard work will not be transformed into ability immediately because the time is too short, and the final success will be out of the question."

"The process from hard work to ability acquisition will isolate most people, and it will take time from ability acquisition to ultimate success. This process will isolate many people. This also explains why there are very few people who can achieve great things in the world The reason. Of course, sometimes, people's luck is also very important."

"However, when we delve into knowledge, we all need to have a long-term ambition, that is, to make it conform to the idea of ​​points. Given time, we will eventually achieve some small success!"

"Sir, if we are often slack and lazy in our daily life and study, then are we doing a reverse differential process?" A student asked thoughtfully.

"That's right!" Fang Zhongtong nodded with a smile and said, "Once we relax now, it may take several months or even years for the results of this relaxation to appear. And by that time, we won't reflect on ourselves until a few months ago. , The seeds of today were planted by not working hard in the past few years. Before the concept of calculus was proposed, we thought that there was no intermediate process from thrust to displacement, and we thought that thrust was the direct cause of displacement. As everyone knows, there is acceleration in the middle accumulation, as well as the accumulation of velocity, and finally the displacement of the object.”

"In the same way, everything in the world needs a process, and there are actually several mountains to climb between your starting point and the desired end point. The most terrifying thing is that we 'don't know that we don't know', when we don't know When you know these mountains, you will give up because the actual situation from the beginning to the end does not match your expectations. This is what we often call feedback lag.”

"Whether you are studying or doing various research work in the future, when you work hard, you will understand in your heart that to turn hard work into ability, it needs accumulation and a process, and from the accumulation of ability to achievement, it also needs It's a long process."
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"Mr. Fang is a great talent!" Wang Siyuan bowed his hands back to the students, and sincerely praised Fang Zhongtong: "It is my honor to be able to explain such a complicated and obscure concept of calculus through such profound and simple principles. I am ashamed!"

"Mr. Wang is absurd." Fang Zhongtong cupped his hands humbly, "My concept is not just picking up the wisdom of others, but I have been inspired by the king. Otherwise, with my dull mind, how can I understand what is integral and what is differential?"

"Mr. Fang, don't belittle yourself like this. In the entire Tiangong Academy, if it comes to the research and attainment of mathematics, we all admire you, and even the king respects and praises you very much."

Fang Zhongtong, born in 1634, courtesy name Weibo, was born in Tongcheng, Anhui, the second son of Fang Yizhi. He changed his name once and returned to his hometown of Tongcheng at the age of 14.Fang Yizhi lived in seclusion in Wuling, and was hunted and hunted by the Qing soldiers many times and hid everywhere. Fang Zhongtong almost ran around with his father.

In 1652, he and his younger brother Fang Zhongxue came to Hanzhou with his father Fang Yizhi and stayed in Jianye. With his outstanding knowledge, he was hired as a teacher of Tiangong College ten years ago .Influenced by his family education, Fang Zhongtong loved mathematics and astronomy since he was a child.First, he learned Guo Shoujing's "Shoushi Calendar" from Tang Shenghong (Liuhe native, fine astronomy and calendar), and then he was introduced by Xue Fengzuo to meet the Western European missionary Mooniger (Polish, the person who first introduced logarithm to China) in Nanjing, and learned from him. mathematical knowledge.

"Mr. Fang, I heard that "Shu Du Yan", which you spent ten years writing, has finished proofreading and will be published soon. By then, our culture and education in Qi State will add a new scientific masterpiece! Congratulations, congratulations!"

"Thank you, thank you!" Fang Zhongtong couldn't help showing a gleam of joy when he heard the words. He devoted himself to research for more than ten years, and finally achieved a small success, and he can also publish a book and make a statement like his father.

For all kinds of literati and scholars, no one can fully enjoy academic and ideological freedom than in Qi State.Of course, the premise of enjoying freedom is that you cannot openly make various remarks against King Qi and the government.

In terms of culture and education, this country advocates a cultural policy of a hundred schools of thought contending and a hundred flowers blooming. Various theories and different art forms and styles can be freely developed, and different schools of science can also debate freely.It can even be said that this period of Qi State was the most tolerant and open period in Chinese history for hundreds of years to various theories and ideas.

Although, after 30 years of development, Qi State has always paid more attention to those "unique skills and obscene skills" and other miscellaneous studies, but it has not abandoned Confucianism and other traditional theories. to a much lesser extent.

In order to support the cultural undertakings of Hanzhou, Qi State, in addition to constantly collecting and transferring various books, classics and cultural relics in Daming during the process of immigration every year, in order to enrich and expand the collection scale of Wenyuan Pavilion, also pays attention to those who come to Hanzhou. Many scholars and literati wrote books and made speeches, and also gave strong support.After being examined by the Ministry of Culture and Education and the polling office, if there is no reactionary speech, the Qi Royal Press will publish it for free and distribute it throughout the country.

Although Qi is a new immigrant country, as a branch of Chinese civilization, it has to inherit and carry forward thousands of years of traditional history and culture.What's more, a big country that is committed to colonizing the world and competing with European powers for world hegemony must not only rely on brutal force, but must also have connotations and a culture that can be exported to the world.

In addition, with more than 20 years of primary compulsory education, the literacy rate of the people of Qi has increased to over 35% (at the same time, England's literacy rate was 30%), which directly promoted the development of Qi's cultural undertakings.

In the past 20 years, Qi's book sales as a whole have seen amazing growth.In the past, workers and peasants from all over Hanzhou spent their long nights by doing some sports they loved after dinner, or telling their children stories about fairy tales, demons and ghosts passed down by the old people.

But now, they rely on listening to their children to read various small books, such as "The Romance of the Three Kingdoms", "Journey to the West", "Surprise at the First Moment", "Yu Shiming Yan"..., and some books published in books and newspapers. Serialize the storybook to kill some free time after dinner.

"So, compared with those novels, the books I have written have very few audiences!" Fang Zhongtong said with a smile: "It is said that some literati and scholars in the Jianye University Hall, through every ten days Helping the "Hanzhou Monthly" to write some novels, the embellishment fees received are tens of Hanzhou silver dollars. This is really enviable!"

"They write popular vernacular novels, and they follow the popular culture line of the lower Liba people. Those who we study and write articles are the most cutting-edge science today, representing the future of our country. There are naturally very few people who are compatible." Song Changwen shook his head and said, obviously looking down on those popular ghost novels.

"Brother Song is extreme." Fang Zhongtong smiled and said: "Actually, compared to studying these boring mathematics and science, I am quite interested in the serialized novels in "Hanzhou Monthly" Every time I read it, I am thinking about the next development of the serialized novels, looking forward to the next publication of "Hanzhou Monthly".

"Brother Fang, I didn't expect you..." Song Changwen couldn't help being stunned for a moment, then shook his head and smiled wryly, "I didn't expect you to be an elegant and vulgar person!"

"I heard that the circulation of "Hanzhou Monthly" has exceeded [-] copies due to the publication of several popular serial stories. The owner behind them intends to change this semi-monthly book into a weekly newspaper, so as to Cater to the needs of more readers." said a [-]-year-old teacher.

"Really?" Fang Zhongtong said with a smile when he heard the words: "The circulation of this semi-monthly magazine will be greatly increased when it is converted into a weekly newspaper. However, I am very curious. In this way, the cost of this book and newspaper will inevitably double. Growth. How will they support these increased costs, don’t release it for a period of time, and bankrupt the owner, and then there will be no new novels to read.”

"Brother Fang is overthinking!" Wang Siyuan said with a smile, "You may not know, but the owner behind this book is the royal family. With the royal family's strong financial resources, how can this book be destroyed?"

"Hehe..." Fang Zhongtong nodded, "That's good, that's good. Just now Brother Song said that I am elegant and vulgar, but I think that the royal family is elegant and vulgar. Not only has the Royal Academy of Sciences been established to commend and Funding all kinds of scientific inventions and creations in the country, but also a sum of money can be used to produce such a book with a strong sense of life, so that the people of the country can chat and entertain themselves."

"The king once said that although Hanzhou is located in the remote southern continent, we must use our hardworking hands to build a rich and prosperous royal paradise. And in terms of self-entertainment of the people, naturally we will not let it be barren and barren .Well, the so-called material civilization and spiritual civilization develop and progress together, and so on.”