Jingming

Chapter 187

Wang Wensu knew that His Majesty was studying his "Baojian of Mathematics", so he frantically compiled this book in the past year when he didn't have to worry about any other trivial matters.

Now, the emperor showed Wang Wensu the results of his "study", but he found that he couldn't understand it.

It's not that they can't understand: "Your Majesty... this seems to be the Western Regions?"

Naturally, Wang Wensu knew Arabic numerals, but there were still many strange symbols in His Majesty's manuscripts.

In addition, these calculation formulas were written horizontally. Wang Wensu suddenly couldn't turn the corner. After looking at it carefully, he asked again: "His Majesty's manuscript...is it to be read from left to right?"

Zhu Houcong smiled and nodded.

Knowing Arabic numerals, and looking at the values ​​before and after the formula, Wang Wensu naturally understood the meaning of some mathematical symbols with his basic skills.

After all, the first few sheets are examples.

Such as plus sign, minus sign, multiplication sign, division sign, equal sign... Maybe some of these series of mathematical symbols have appeared in Europe, maybe some haven't, Zhu Houcong didn't even bother to care about them.

At least he didn't see these things in Wang Wensu's "Baojian of Mathematical Sciences".

All of Wang Wensu's calculations are still expressed in calculation chips and some words, and they are written vertically.

Wang Wensu didn't understand why the emperor expressed it in this way: "Your Majesty, these characters... are very difficult to remember. I don't know what is so good about writing calculations with this method?"

Since the emperor showed him these things, he naturally thought it was better, but Wang Wensu couldn't turn the corner for a while.

One has long been used to the current calculation formula, those calculation chips are very close to him, and it is easy to remember.He is also very familiar with the methods of using the old formulas.

The other is more accustomed to the calculation method of Arabic numerals, and knows how important a more systematic mathematical expression is to the development of mathematics.

So Zhu Houcong said: "I have roughly studied your masterpiece. Mr. Wang, why don't you come up with some questions to test me, and then see how I calculate it?"

The specific calculation process is more convincing. Zhu Houcong must first let everyone in mathematics pay attention to these most basic symbols: to some extent, this is a change in the language of mathematics, like the foundation.

Wang Wensu is obsessed with mathematics, and is still interested in this.

And to test the emperor, to be honest, is a bit exciting.

"Baojian of Computing" is actually mainly a book of "applied mathematics".

In other words, mathematics was originally summarized from specific applications.Rules, moments, standards, and ropes are the earliest mathematical tools. The decimal system, ninety-nine multiplication table, four arithmetic operations and even fractions have appeared in the Spring and Autumn Period.

After years of summarization, nine specific mathematical application types, such as Fangtian, Corn, Difference, Shaoguang, Shanggong, Even Losing, Equation, Winning Insufficiency, and Side Key, are called "Nine Numbers".

"Nine Chapters of Arithmetic" is based on these nine numbers. "Nine Chapters of Numbers" is also divided into nine categories of 81 questions, including Dayan, Tianshi, Tianyu, Surveying, Taxation, Money and Valley, Construction, Military, and Market Change. Wang Wensu The "Baojian of Computing" listed various mathematical application problems, verified and listed various solutions, and added some of his algorithms.

Zhu Houcong was an accountant in the past, and he is not bad at mathematics, but what needs to be done now is to promote the "applied meaning" of mathematics to the aspects of ease of learning, ease of use, and systematization.

The best leader for this work is Wang Wensu.

Let Wang Wensu come up with a question, and naturally he will no longer come up with the original question mentioned in "Baojian of Mathematical Sciences".But Wang Wensu has already formed a family of his own, and it is easy to come up with a few topics.

The first three questions were not difficult. After all, he is the emperor, so we should save him some face.

They are "zero due to total loss" in the fourth volume, "division and change" in the sixth volume, and "round field calculation" in the eighth volume.

He could only look at Zhu Houcong's calculation "upside down" from the front of the imperial case, and saw that the emperor only spent a few sips of tea to complete the calculation, so he picked up the piece of paper and showed him upside down: "Is there any miscalculation? "

"...Your Majesty is truly a genius."

Zhu Houcong didn't want to show off, he said leisurely: "Mr. Wang, you might as well come up with some questions after the twenty volumes."

If it weren't for making him notice the efficiency of the new mathematical tools, Zhu Houcong didn't need to do this: you should focus on the questions in junior high and high schools, not in elementary school.

Wang Wensu also became serious now.In his "Treasure Book of Mathematics", after [-] volumes, there are many problems in mathematics that everyone has to study painstakingly throughout the ages, such as calculating the product of a cubic circle, delaying the journey, concealing the difference, borrowing the original, and entering the equation. Stocks, diameters and arrows seeking strings...

But in Zhu Houcong's eyes, these problems are nothing more than some one-dimensional and two-dimensional equations, one, two, three times.In addition, they are all simple problems in the fields of plane or solid geometry, functions, etc., at least not beyond his mathematical level.

Seeing that the emperor's pen kept running and quickly figured out one problem after another, Wang Wensu was a little skeptical about life.

Although the types of questions are similar, even he has to use calculation chips or abacus to fiddle with these calculation questions before he dares to say that the result will not be wrong.

But judging from the emperor's algorithm, he calculated very quickly, and the steps were much simpler.

Probably because... each number does not need to be written one stroke at a time, and most words are completed with one stroke?And those symbols...

After Zhu Houcong showed him the calculation process and result of the last question, Wang Wensu's throat twitched, and he asked in a harsh voice, "Your Majesty has memorized many calculation formulas fluently, and did all the calculations in his mind?"

"There are calculation formulas here. The mental calculation part is just the simplest addition, subtraction, multiplication and division." Zhu Houcong said, "The secret lies in these calculation formulas. The numbers and symbols used are clear at a glance."

In the original calculation formula, counting chips are like gossip symbols, and a number needs to be written in several strokes; but to record the calculation formula vertically, and the operators representing the relationship between numbers are also Chinese characters, and the writing efficiency is very low. .

Transformations in equations and complex calculations are first disassembled into steps to calculate simple calculations. Zhu Houcong's high efficiency is the embodiment of many mathematical ideas after mathematics has been perfected from generation to generation.
Wang Wensu was greatly shocked.

Zhu Houcong did not understand the so-called algebra, geometry, analysis and other systematic ideas in mathematics, nor did he know when the basic axiom system in mathematics was systematically sorted out, but the mathematical training he received was comparable to that of Wang Wensu, a contemporary Mathematics everyone wrestling wrists even inspired him.

What he wants is not just one Wang Wensu, but thousands of talents with certain mathematical skills.How to make mathematics education easier is what Zhu Houcong hopes Wang Wensu will do.

As for more advanced mathematical research, as long as the base is large, geniuses will always emerge.

Wang Wensu listened to the emperor talking about the meaning of different mathematical symbols, and why the formulas should be arranged in such a way, and what is the reason for each step of the formula...

Suddenly, I felt that I was not a math teacher, but a student.

"Mr. Wang thinks, how about these algorithms?"

"...Your Majesty is pedantic about heaven and man, and I admire you so much."

Zhu Houcong looked at him: "Mr. Wang, I am discussing with you the magic of these algorithms, not to be flattered by you. Mr. Yang Ge and others please implement the new method, one of the major changes is the new accounting method. In that new Under the accounting method, in the future, land, taxes, checking accounts... many places will have to understand the calculation. Mr. Wang, I think this calculation should not be more difficult than the Four Books and Five Classics, right?"

Wang Wensu's heart was greatly shaken when he heard this: "...Your Majesty, does it mean that scholars all over the world will be able to learn calculations in the future?"

"I don't want him to become a master, but rites, music, archery, censorship, calligraphy, and mathematics are originally one of the six arts that scholars need to understand." Zhu Houcong nodded to express his intention, "It's just that mathematics has been passed down for so many years. The calculation problem is longitude and latitude, so it is naturally difficult to learn. There are also natural principles in mathematics, just like the ninety-nine multiplication method. If you can find out the most commonly used and simplest natural principles in the avenue of mathematics, you will have an easier way to learn. Can flexibly grasp most of the arithmetic problems in this "Treasure Book of Mathematical Sciences."

"Mathematics... Dao?" Wang Wensu muttered to himself.

In his "Baojian of Mathematics", the guidance of thought is actually the art of solving problems.In this world, apart from Confucianism, Buddhism, Taoism, etc., how can the rest of learning dare to be called Dao?
"Naturally there is a great way in arithmetic." Zhu Houcong took this opportunity to express his point of view, "From my point of view, the principles of heaven are above, and physics and human principles are below. This physics is not changed by people's wishes, and everything is indestructible. Great truth. This is the case with arithmetic. The same calculation problem, no matter who solves it, the result will not change, and the numbers will not deceive people. If you keep walking on the avenue of mathematics, you can get a glimpse of the law of heaven!"

Wang Wensu is not a master of Confucianism. He didn't know that he was the first person who heard of the three principles of "heaven, things and people" besides the counselor and the accompanying bachelor.

In his opinion at the moment, this is the emperor's recognition and encouragement of mathematics.

Not only is it called Dao, but it also means that mathematics will be included in the imperial examination in the future?
He understood the purpose of being left today, and looked at the manuscript and the calculation process handed to him by the emperor: "Your Majesty wants me to recompile the "Treasure of Mathematical Sciences", advocating new numbers and formulas?"

"Any knowledge should be easy to get started." Zhu Houcong stood up, and took down a few thicker books from the nearby bookshelf, "I have studied and read "The Treasure of Mathematical Sciences" one by one, and compiled it with new formulas. Mr. Wang , what I want you to do is not to recompile "The Treasure of Mathematical Sciences", but I hope you can master these new numbers and new formulas, find out some of the simplest arithmetic rules, and write two or three volumes. Teaching materials."

Wang Wensu stared blankly at the thick stack of books. After flipping through them, he found that they were all written by the emperor.

Only then did he know that the Emperor had really read his own "Treasure Book of Mathematical Sciences", volume by volume, and rewrote it stroke by stroke into what it is today.

It is hard to imagine how much time and pen and ink His Majesty spent in this emperor's study besides handling so many state affairs.

Tears welled up in Wang Wensu's eyes, and he choked up and said, "I... will live up to your Majesty's high hopes..."

Zhu Houcong encouraged him: "Let's rest for a while, take care of your body before starting. If I realize something, I will write it down and give it to you. I think that this arithmetic may be the foundation of the Dao of Tianli. No arithmetic."

Whether it is arithmetic or mathematics, Zhu Houcong is not entangled in the title.

However, once the foundation of mathematics has been laid, many subjects such as physics and chemistry will be able to use it as a tool in the future. Zhu Houcong is clear about this.

Now it is necessary to popularize mathematics more, so that other subjects can not only rely on experience, but have the habit of quantifying everything.

In this way, there is a smooth path for experimentation, analysis, and progress.

When Wen Suyun and Wen Zhengming came to express their thanks to the emperor after their narration, they saw the emperor standing in front of the desk with a brush in hand to write and draw pictures together with the math priest.

Hearing her voice, old man Wang Wensu lowered his head and didn't dare to look around, but Zhu Houcong just said to her: "Go back first."

After agreeing in a low voice, when he walked towards the harem, he heard His Majesty continue to say: "This algebra is to be included in the calculation formula first. Although I don't know the number, but it can be substituted into the equation for calculation. I just searched for this first. symbols, but after careful consideration, I feel that replacing strokes with hexagrams and lines is still too much, what other ideas do you have?"

The sound is getting smaller and smaller.

Wen Suyun only felt very puzzled: the emperor is studying algorithms?Why listen, he seems to be teaching that arithmetic offering?

Didn't dad say that Wang Gongfeng is a rare master of mathematics in the world?
……

Guangdong in the early spring of the second year of Jiajing was full of new ideas.

Just after the new year, sociology and county schools all over the country began to hear the sound of books.The announcement of the Chief Envoy Si Yamen has been circulated to all counties. In May of this year, the ceremonial office will send chief examiners to hold the enco examination in all prefectures. In August, the Ministry of Rites will hold another provincial examination in Guangdong. Bang Enke.

There will be a large number of new talents and candidates in Guangdong this year.

To correspond, of course, there are many new official positions in Guangdong.

After the reform, the top-down chief officials of the Guangdong Government Office have been in place, but there is still a shortage of a large number of officials.

Guangdong Chief Envoy Si Yamen, Huang Zuo in charge of the Office of Officials, Gui E in charge of the Household Office, and Zhai Luan in charge of the Ceremony Hall, one is busy selecting officials and appointing officials, the other is busy compiling and reviewing discipline rules, and the other is busy with this year's Enke.

Concubine Li's father, Zhang Ji, and Concubine Jing's father, Chen Wanyan, both worked as clerks in the auditorium.

Cao Cha, the father of concubine Duan, was transferred from a magistrate in Fujian to the head of the Criminal Division in Guangdong.And Anpin's father, Ma Yong, was transferred from the chief military officer of Jizhou to the chief of the public security department.

As for Guangdong's original procuratorial envoy, Wang Hung, was transferred to the newly established post of governor in Fujian. One of his main tasks when he went to Fujian was to strengthen the military equipment of Haiphong Road.

People in Guangdong are now discussing two things.

"I heard that if the newly measured official land is rented out, we will only pay five buckets of grain every year for three years, just like our own land. Is it true or false?"

"That's right! Didn't Yang Shenzheng tell us personally?"

"Aren't you stupid! It's more cost-effective to buy it."

"You're so stupid! It turned out that the Guifu Zun in Huizhou was setting the amount of miscellaneous taxes that will be paid after next year. I heard someone say that the bottom of the field should be counted as a sum, and the surface of the field should be counted as a sum."

"Isn't that why we have to pay two rations for our own fields?"

"I don't understand... But Yang Canzheng said that the two payments will only be counted after the number of fields is counted. It is only collected from high-ranking officials and wealthy households!"

"Master Guan can be so good? Don't wishful thinking!"

"..."

Many year-old and sit-offs stipulated by the imperial court are now purchased by the Ministry of Households from Guangdong.Some local government expenditures are also borne by the Guangdong Household Office. Some large-scale projects are purchased by the Household Office from Huangmingji Labor Service Bank and other private commercial firms. Tax.

The imperial court and Guangdong are still discussing how to collect this tax, anyway, it will be after next year.

There is another thing that people are talking about right now.

"Pei Lizheng, is what you said true? Are you really paid?"

"Master Zhang told me so." Lizheng from this mile replied, "In the past, the county used to exploit us, the Lizhengs, but Master Zhang said that things have changed in the future. I'm afraid it's better to rely on land to make money Procurement makes money. But the director of the Gongting Office said that although the commercial hall has not yet been established, the company’s license and regulations already exist. After contracting the purchase, it is necessary to record the account and check the account before paying the final payment. The hired workers must be paid, otherwise the license will be invalid there is none left."

"Where is Huang Mingji? Is it the same?"

"The same is true of Huangmingji, but I heard that Huangmingji now uses barbarians to work."

"Why use barbarians? Why don't you earn money for us?"

"...I don't know about that."

"..."

Huangmingji has brought back nearly [-] exiled laborers from Nanyang, one ship after another. They are specially restrained by people, living in the same camp, and doing the most labor-intensive work-renovating the Chidao Road in Guangdong.

Now, Zhang Tingbo, Liang Chu’s in-law Zhang’s family’s family, only listened to Wei Bin’s light voice: “Brother Zhang, don’t worry. If Huang Mingji takes everything down, and Guangdong’s gentry and rich households have no way out, how can we Okay? Not to mention that there are still a lot of purchases, you can go to the industry hall to submit an application for recruitment, even my Huang Mingji Maritime Trading Company has a lot of purchases."

"So that's the case, then I can tell the shopkeepers of other companies." Zhang Tingbo laughed with him, "Maritime Trade will still build ships and buy goods this year?"

"That's the case. Last year, the wind was strong and many ships were destroyed." Wei Bin smiled, "Yang San and Dai Ming, who were recruited by Wang Futai last year, went to Beijing to serve as His Majesty's offering, and the other stayed in Guangdong. The capacity of the shipyard is limited, and the Haiphong Road needs a lot of ships. Our family has already asked His Majesty, can we try to open privately built sea ships for the Huangmingji Maritime Trading Company. Although the decree has not yet come down, but It should be possible."

Zhang Tingbo's heart skipped a beat.

In fact, the privately built seagoing ships have never been cut off, and the Zhang family has gradually accumulated a large fleet of ships.

But in terms of ship shape, try to avoid overstepping.If you have this "license", can you build a large ship with hundreds of materials?If such a large ship is purchased in its entirety, the unit of a large ship is a thousand taels of silver.

Wei Bin went straight to the point: "The situation is overwhelming. Since Brother Zhang knows the direction of the sea, you, the leader of the Guangzhou line, can do a lot of work. The crew and workers of the Maritime Trade Bank will not hire barbarians. What is going on now? How to determine the taxation has not yet been decided, but after all it is related to the fields and people. There are still so many hidden fields and hidden people, which is harmful but not beneficial. Those who know current affairs are heroes, and those who only keep their eyes on the fields are no different from fools ?”

The procurement of various offices is creating countless huge opportunities in Guangdong and requires a considerable amount of manpower.How Guangdong's real population should be balanced between agriculture and industry and commerce is being adjusted through new rules.

Sun Jiao, who went south to supervise the reform of the Guangdong government office, is a little embarrassed now.

"Congratulations to Mr. Jiufeng, you are growing old and strong!" Liang Chu looked at him with a funny face, "This good news must be presented to His Majesty."

"..." Sun Jiao actually had nothing to do in Guangdong, just avoiding the limelight, who knew that once he avoided, he would avoid problems, "Don't make fun of me, Mr. Liang."

"This is an auspicious omen!" Liang Chu said solemnly, "Perhaps when the good news comes to Beijing, the good news for the empress will follow."

Sun Jiao was very entangled and distressed.

To be honest, at such an age, I can still be happy when I am old, and I really can't bear to let the newly adopted "bed-warming concubine" in Guangdong not want this child.

I'm also a little proud.

But my queen's daughter is an "old woman", and now the good news that her daughter is not pregnant has spread to Guangdong, and he, the father of the country, is going to give her a younger brother or sister in Guangdong, what is this?
He didn't take the initiative to report, but the news quickly reached Zhu Houcong through Jin Yiwei.

Zhu Houcong was dumbfounded: Isn't it already seventy years old?The majesty of the head of state is so terrifying!
(End of this chapter)