Chapter 773: Trainee Researcher

Old Bai Niu: Thank you friends for the monthly tickets, and also thanks to Mo Sheng and other friends for the tips.

To be honest I'm not a fast writer, I can only write five hundred to a thousand words an hour, and I use up almost all my free time every day — it's truly tragic. Sometimes I think it's still more comfortable being a reader. And I may suffer from obsessive-compulsive disorder; after finishing a chapter I always have to check it over several times, otherwise I feel extremely uneasy inside. The demand I place on myself is to do my utmost, so that after writing I have no regrets or remorse.

……

Tang Ruowang began working through the problems one by one with the priests. Each of them possessed rich knowledge of mathematics, physics, astronomy, and so on, and most of the problems still posed no difficulty for them.

However, one thing gave them headaches: how to translate the Chinese into Western terminology they could understand, especially given the breadth and depth of Chinese, where one word often has multiple meanings. Take this problem: "Using a rope to measure the depth of a well, folding the rope in three to measure, outside the well there remains four chi of rope; folding the rope in four to measure, outside the well there remains one chi of rope. What are the well depth and the rope length, each in chi?"

Although all the priests knew this was a linear equation problem in one variable, "folding the rope in three, in four to measure" — did you mean one-third and one-fourth, or thirty percent and forty percent, or other meanings? Every interpretation seemed to make sense somehow.

These things gave them headaches, so they had to do their best to adopt a Chinese mindset, especially selecting one priest proficient in Chinese studies to review and translate the problems, while the rest solved them.

Moreover, although Tang Ruowang and the others were profoundly learned, Chinese mathematics at this time did not lag behind the West, and in some aspects even surpassed it. For instance, this congruence arithmetic problem involving "the unknown number of things": "There is a number: counted in threes, two remain; counted in fives, three remain; counted in sevens, two remain. What is this number?"

The priests each displayed their skills. The algorithms were numerous and complex, and after half a day they still had not solved it, until one priest first calculated it using the Chinese "Dayan Seeking Unity Method." Looking at the answer on the paper, he sighed: "The great Chinese Remainder Theorem — Qin Jiushao, that wise man, belongs to this country, to this people, to that era, and indeed to all eras as one of the greatest mathematicians."

The priests held their goose-quill brushes, staring fixedly at the answer on his paper. The formulas and calculation process on it were so pleasing to the eye — concise, swift, and the data obtained accurate and refined. It was breathtaking.

One priest could not help but praise: "It is hard to understand how a country that does not emphasize logic could have such a wondrous method of calculation. Father, you are right — the Chinese mathematician who discovered this method is truly the most fortunate of geniuses."

Tang Ruowang said: "Fathers, every civilization has its crystallized wisdom. We should not envy or slander, but diligently absorb their essence and transform it into part of our European wisdom."

The men steadied their minds and continued calculating downward. Next were geometry problems, which posed no difficulty for the priests. The key was the terminology — for example, what was called "gen land," what was called "xun land," what was called "kun land" — these alone caused endless debate. Tang Ruowang wiped the sweat from his forehead and said: "Fathers, we must continue to deepen our understanding of this country's language and culture."

After who knows how long, they finally finished the preceding arithmetic problems. Even with the ability of men like Tang Ruowang, they felt utterly exhausted, mainly from the strain of reviewing the problems. Finally, they all looked together at that mathematical problem by Wang, and then, without prior agreement, a sensation of dizziness came over them. Some priests even felt an impulse to turn and flee.

Tang Ruowang drew a deep breath: "Alright, gentlemen... Fathers. We have finally reached our objective. Let us first review the problem."

He said: "The Jingbian Army has a general, Xiancai, skilled with firearms, and a general, Xuan, skilled with cannon. Xiancai daily shoots swans and piles them up; the higher the pile, the greater the stack. Xuan laughed and said: With one cannon shot I strike it, and your swan pile all collapses... How should this passage be interpreted? Father Luther, you are proficient in Chinese studies — you review and explain the problem."

That Father Luther furrowed his brow: "Taken literally, it tells of the Marquis having a general named Xiancai skilled with matchlock guns, and a general named Xuan skilled with muzzle-loading three-pounder cannons. This general called Xiancai daily shoots a swan and piles it into a heap... By Jehovah Almighty Lord above, what kind of bird is this 'ru'? I can only guess it is a type of swan."

One priest interjected: "Father Luther, are you certain General Xiancai used a matchlock gun, and that General Xuan used a muzzle-loading three-pounder cannon? Did they use matchlocks or flintlocks? Three-pounder or six-pounder cannons? This is critical."

Seeing that everyone was about to argue again, Tang Ruowang waved his hand to stop them with a headache: "Fathers, let Father Luther finish reviewing the problem first, then we will carefully go back and discuss it in detail."

He signaled Father Luther to continue. That priest stumbled and stuttered through reviewing the problem. The room fell silent for a full ten minutes. Father Luther was still rubbing his own temples; he somewhat understood why there were scholars in Xuanfu Garrison who coughed blood from the exams — he now felt the urge to spurt blood himself.

Tang Ruowang gave a light cough: "Alright, Fathers, let us analyze... Father Locke, you draw the diagram."

Tang Ruowang said: "Judging from the problem, it seems to involve the limit problem of a cone — infinitely large, and infinitely small. I recall the ancient Greek wise man Antiphon proposed the method of exhaustion, which specifically discussed this problem, and also the Chinese method of circle division, which has a similar concept. But I always feel that the mathematical methods used by both China and the West mentioned above are still insufficient to answer the Marquis's problem, because the methods they used are essentially static."

One missionary said: "Yes, Father. Look at this line, 'Xuan cannon-strikes it' — it seems to also discuss the motion of objects, involving problems of circles, ellipses, parabolas, hyperbolas, and so on, and moreover the relationships of their mutual motion. The wise man Galileo once discovered that objects move along parabolas, and Mr. Kepler also discovered that planets revolve around the sun along elliptical orbits. The sun, then, lies at one focus of this ellipse. This mathematical problem seems to bear some subtle similarity."

One missionary said: "Yes, you are quite right. It is just that the motion of objects, especially involving their conic section motion, is extremely complex to calculate. The wise man Apollonius once mentioned concepts of ellipses, parabolas, hyperbolas, and so on in his work Conics, but much of it was purely conceptual exploration. The wise man Archimedes specifically calculated the area inside a parabolic segment, but it is still insufficient to solve this thorny mathematical problem before us."

Another priest said: "Please note, Fathers, this problem is far from this simple. According to my speculation, this cone, infinitely large and infinitely small, under these settings, is also in constant motion. The geometry problems we calculated before were all static. For dynamic ones, where should we begin? How should we derive formulas for the base area and volume of this limit cone? How should the height be derived? How should the infinitely small cone tip be calculated?"

He said: "...No, 'only the upper four faces do not form a flat body but become concave; the more they multiply, the more concave they become.' Lord, the faces of this cone are still moving... And the parabola, the path of the cannonball leaving the barrel — different angles have different calculation methods. Before the cannonball reaches the cone, how should the area in between be calculated? When the cannonball strikes the cone, what is the relationship between the surface and the object? When the cannonball strikes the cone and then passes through it, what kind of path volume will they form?"

He cried out in alarm: "Oh, this is too terrible... Father, our manpower is far from sufficient."

Cold sweat broke out on Tang Ruowang's forehead. He said: "Stay calm, Fathers. There is always a solution."

He said: "As a saying in this ancient country goes: Without accumulating small steps, one cannot reach a thousand li. We shall start from the first step — first draw the diagram..."

This calculation kept Tang Ruowang and the others working from near noon all the way until evening. Tang Ruowang and the others could not even spare time for lunch, burying their heads continuously in the vast and complex geometric diagrams.

They first used the method of exhaustion to calculate static geometry. Then they tried to use Menaechmus's method of solving conic sections to shift to dynamic. But Tang Ruowang and the others discovered in despair that the workload was too immense. Not to speak of calculating for ten years or a hundred years — to calculate continuously for at least one year would be a perfectly ordinary matter.

The continuous racking of brains and high-intensity calculation left Tang Ruowang's complexion pale. He murmured: "We must find an entry point, to unify everything. But where is the entry point?"

Late at night, under the oil lamp, Tang Ruowang still stood in a daze. He gazed at the starry sky outside and muttered to himself: "Where is the entry point?"

The priests beside him were also utterly despondent, each staring blankly. They had exhausted every method and still could not find a way in. This problem — unless they used a human-wave tactic, there might perhaps be a faint clue... At this moment, they somewhat understood the suffering of the students at the Imperial Academy and elsewhere. This problem was truly monstrous.

Father Luther rose unsteadily to his feet. The excessive use of his brain made waves of dizziness wash through his head. He saw Tang Ruowang standing motionless, having stood there for a very long time. He walked up to him and said with concern: "Father, you have been thinking for too long. You must rest."

Just at that moment, Tang Ruowang's body suddenly collapsed stiffly backward. Father Luther hurriedly rushed forward and caught Tang Ruowang, shouting: "Father, Father, what is wrong with you... Oh, Almighty Lord..."

The room was filled with cries of alarm. All the priests crowded around. Tang Ruowang said weakly: "Fathers, do not worry. I am fine..."

He closed his eyes with a sigh. For a long, long time, he then opened his eyes: "Send this newspaper to the Church... I keenly predict that this mathematical problem will play a decisive role in altering the course of civilization... The torrent of the era, we..."

……

One day later, inside the imperial palace, Princess Kunxing, Zhu Meichuo, sat before a writing desk of elegant design. At this moment she was bent over it calculating something. Her figure had grown increasingly slender and graceful; her beautiful hair was done up in a bun, and above the upper edge of her fiery red sable fur, her jade-like neck was exposed.

Beside her, Princess Zhaoren, only a few years old, was kicking her little legs out of sheer boredom, occasionally looking at Zhu Meichuo's back and pouting her small mouth: "Bad sister, it's been days and you still won't play with me."

……

Shengjing, Chongzheng Hall.

Emperor Xuantong, Dorgon, paced with his hands behind his back. He held a copy of the Xuanfu Times between his fingers and muttered to himself: "What deep meaning does Wang Dou have with this move?"

The Qing state had already decided to soon attack and invade Japan, to plunder population and supplies. Of course, the circumstances of the Yuan dynasty's failed attack on Japan also left lingering fear in Dorgon's heart, so he had Abatai in Korea carefully investigate, and also had the Grand Secretary of the Hongwen Academy, Ning Wanwo, and others consult historical records to find the reasons.

According to the understanding Abatai and others gained of the circumstances of the Yuan attack on Japan's failure, they found that the monsoon factor was secondary; the main reason was that the warships of the time were extremely backward and of very poor quality — the keel rivets were too densely packed, the hull planks were lap-jointed, and many were riverboats, so they easily shattered under the pounding of huge waves.

The passive and slacking work of the Koreans at the time was an even more important reason. Therefore, Dorgon decided to improve the treatment of the Korean Eight Banners. Koreans who followed the army to plunder could likewise obtain spoils of war. In his imagination, historically the Mongol Eight Banners and Han Eight Banners had been very enthusiastic when plundering the Central Plains in the past.

Sure enough, this move by the Qing state successfully diverted the attention of the cruelly oppressed Korean people. After all, the enmity between Korea and Japan had lasted a thousand years. To be able to attack Japan and also obtain their own slaves and population, gold, silver, and wealth — many Koreans were still tempted.

Unable to resist the Qing state, they vented their fury upon their own old enemies. Many Koreans even became more zealous than the Manchus.

Moreover, the Qing army was merely imitating the "Toi" ancestors' raids, and also crossing from the Tsushima Strait — the danger was also less than that faced by the Mongol Yuan at the time. Dorgon's attitude was also to probe first. The first batch of allied banner troops was only less than ten thousand men; even if there were losses, it would not injure muscle or bone.

Just as the intense preparations were underway, Dorgon obtained this newspaper.

The Grand Secretary of the Hongwen Academy, Ning Wanwo, and others did not take it seriously, saying that mathematics was but a minor path, that the subtle words and great principles of the sages were the true orthodoxy, and advising the Emperor not to be overly concerned. Dorgon shook his head: "Every step Wang Dou takes has deep meaning. Our Great Qing must not treat this lightly."

He instructed Ning Wanwo and the others: "First solve this problem, then we will talk."

……

Shaanxi, Xi'an, the Viceroy's residence.

Sun Chuanting also saw the newspaper. Recently he had been harshly pursuing the back taxes owed by the gentry throughout the years. Those who dared to cause trouble were killed or imprisoned — a thunderous and ruthless approach. Throughout the Shaanxi region, "the sound of weeping shook the heavens." Not to mention the shock locally, even when the imperial court learned of Sun Chuanting's conduct, many people were stunned. What was Sun Baigu doing?

Facing external attacks and impeachments, Sun Chuanting remained unmoved. The grain and silver obtained were continuously poured into the recruitment of the new army and the reclamation of military farmlands.

Then he saw the contents of the newspaper, and with keen interest even spent several days calculating Wang Dou's mathematical problem. His aides advised that mathematics was but a minor path, that Shaanxi was at a critical juncture right now, and that Viceroy Sun must not be distracted by this. Sun Chuanting only shook his head: "The governance of a state lies in grain and silver; the way of grain and silver lies in mathematics. Mathematics is not a minor path, but a great path."

Of course, he also knew that the situation in Shaanxi was at a critical moment. Compared to his own grand scheme, this "Wang Mathematical Problem" was indeed a small matter. Very quickly, he cast this matter completely out of his mind.

……

As the newspaper spread, this "Wang's Mathematical Problem" stirred up a tremendous wave of excitement. When it reached Jiangnan, the Nanjing Imperial Academy was just as stirred — after all, the Emperor had personally issued the decree, yet the Beijing Imperial Academy had been powerless to solve it, which inevitably roused the competitive spirit of the Nanjing students.

Regrettably, they too returned in defeat. As word spread, more and more Jiangnan scholars grew interested in this "Wang's Mathematical Problem." At the same time, Wang Dou's image became ever more mysterious in many people's minds, as if veiled in a layer of hazy gauze — beyond martial man and able administrator, he now also took on the image of a wise man.

In the end, this "Wang's Mathematical Problem" traveled overseas and circulated through many countries. The waves of excitement it stirred up in all their variety were something even Wang Dou himself had not anticipated.

To Wang Dou, it was perfectly normal that people of this era could not solve this problem. Even when news reached him that the Western missionaries like Tang Ruowang had likewise returned in defeat, Wang Dou only smiled faintly.

They could not possibly solve it either — after all, this mathematical problem contained the ideas of analytic geometry and calculus.

Although in the tenth year of Chongzhen the French mathematician Descartes had published an appendix to his *Geometry* proposing the idea of analytic geometry, with a line of thought for calculating dynamic geometry, it was still in truth only a hazy conception of analytic geometry. Its true perfection would not come until the middle of this century.

Moreover, men like Tang Ruowang had come to China during the Wanli years — how could they possibly know Descartes' latest developments?

As for calculus, that was already a matter approaching the next century, even more out of sight.

At the same time, this was the watershed between Chinese and Western mathematics. Before this, Chinese mathematics had kept pace with the West, and in some areas even surpassed it. After analytic geometry, Eastern mathematics fell behind the West — to say nothing of calculus.

And the single most important point was the establishment of coordinates, which unified everything and made calculation possible.

Wang Dou's purpose in designing this mathematical problem was to draw the gaze of the many scholars, to turn their attention toward mathematics — for mathematics is the foundation of everything — and also to let them attempt logical reasoning, and ultimately establish a rigorous yet distinctively original Eastern mathematical system.

Moreover, the problem was set with whimsical ingenuity and contained a vast amount of content within it — even Daoist learning, parabolas, universal gravitation, and more were all included. If one could research and solve it step by step, even finding the first step toward establishing coordinates, the mathematics and various achievements of the Great Ming would receive an incomparable elevation.

He hoped that after this problem was posed, this land of China could give birth to a great host of masters of mathematics, and even masters of physics, masters of chemistry, masters of astronomy, and so on.

And after the clerk examinations, the shogunate side also used the standard answers to select a large batch of talent suited to the needs of Xuanfu Garrison. Huang Bowen, Liu Dongyang, and three other scholars were specially recruited into the university, preparing to enter the soon-to-be-established Normal University.

Each of them also obtained the status of "Probationary Researcher." Their task was to continue researching the "Wang's Mathematical Problem."

Zhao Zhongju indeed did not pass the examination. He stayed in Xuanfu Garrison and entered an elementary school, teaching the lower-grade students the courses of national literature and calligraphy. His wife opened a tofu stall near the school, and because business was very good, it later developed into a shop.

His daughter Bi'er entered a girls' school to study.

The family's life was peaceful and content. Amid the surging torrent of Xuanfu Garrison, they too were a single spray in the gathering waves.

……

After the intercalary month came the twelfth month. In the time that followed, Wang Dou remained in the midst of busyness. Once the new year passed and spring began, large-scale construction would commence in Monan, and everything had to be prepared and in place. The first batch of recruited clerks also had to enter the academy for a period of advanced study, which Wang Dou also needed to oversee.

Hastily it reached the latter part of the twelfth month. In two more days it would be the new year. All of Xuanfu Garrison was brimming with joy, and a thick festive atmosphere was spreading. Wang Dou also relaxed his mood and concentrated on staying at home with his family. He had been busy with government affairs lately and had somewhat neglected his family, especially the children, which made Wang Dou feel a bit guilty.

But Wang Dou was surprised to discover that Ji Junjiao and the others were also busy with something. When he asked, he learned that Ji Junjiao was preparing a book hall, sorting out books from various fields — such as literature, mathematics, music, fine arts, and so on — intending to open it to the public. Butterfly and Dragonfly were also accompanying her, bustling about.

When she spoke of it, Ji Junjiao was still somewhat worried about Wang Dou's opinion: "Would my lord think that your wife is not attending to proper duties?"

Wang Dou laughed: "How could that be? This is a good deed that brings blessings to the common people. What my wife does is a grand undertaking whose merit extends a thousand autumns and whose benefit reaches ten thousand generations."

He looked at Ji Junjiao. Originally he had been somewhat worried that after she was enfeoffed as a First-Rank Lady, she might develop certain ideas, but seeing that she still treated Xie Xiuniang with respect, he set his mind at ease. Moreover, he thought it was good that she found some proper work to do. This book hall was excellent — refined, tasteful, and also a blessing to the common people.

He mused: "I think the name of this book hall of yours... better call it a library."

Ji Junjiao was made very happy by Wang Dou's words. She kissed him and giggled: "My man certainly knows how to talk."

She enthusiastically spoke of her dream — to sort out the books of the entire Great Ming, especially books concerning music. Her goal was to become a female literary giant like Ban Zhao.

Wang Dou said: "What my wife does is a good thing, only do not tire yourself out."

Ji Junjiao laughed: "My lord is a great hero; your wife cannot fall behind others either."

Then there was Liu Qing. Liu Ji also shyly told Wang Dou that she wanted to establish a school specifically to provide education for adults, so that after graduation they could also receive a diploma and better seek a path in life. Wang Dou was very pleased. He said: "Your husband supports you in becoming a noble teacher of the people."

That evening, the family had a joyous reunion dinner. During it, several children climbed up and down on Wang Dou. Especially the daughter born to Liu Qing, Wang Yao, was lively and adorable, constantly acting spoiled toward Wang Dou. All the children shared one trait: they feared their mothers and loved being close to their father — also a result of Wang Dou's deep, innate love for his children.

That night, Wang Dou was slightly tipsy. He gazed at the bright starry sky outside. The Qing army incursion of the eleventh month of this year had not occurred. His arrival had changed the fates of many people. The common people of Shandong had also been spared this military calamity, and countless people had been saved from being torn from their families, their homes broken and their loved ones lost.

This was also a source of pride for him. He hoped that his arrival could change the fates of even more people.

In the first month of the sixteenth year of Chongzhen, Wang Dou traveled to Guihua City.

〖∷Fast Updates∷∷Plain Text∷〗