Chapter 41: 040 The Celestial Element Method?

Another evening fell.

After school let out, Fei Chun was sent to the mess hall to wait for the meal service, while Pang Chunlai had an upset stomach and was squatting in the latrine.

Fei Yuanjian stayed behind foolishly in the classroom, fidgeting as if he had some hyperactivity disorder. He didn't want extra lessons every day, but aside from Zhao Han and a few others, none of the other students would play with him — they even mocked him when they saw him.

Was being a good student really this hard?

Fei Ruhe was in much the same boat, leafing through *The Unified Lineage of Computational Methods* while his thoughts had already drifted to the heavens — damn arithmetic was even harder than the Four Books.

At last, Fei Ruhe couldn't hold back. "The teacher went to relieve himself and hasn't returned for ages — he must have an upset stomach. I'd say we can skip today's arithmetic lesson."

"Right, right, no need to study anymore." Fei Yuanjian quickly chimed in. He was here to make friends, not to work hard at studying together. With his foundation of knowledge, if he truly wanted to apply himself, he'd first have to go back to the beginner's school and redo the children's primers.

Xu Ying didn't dare speak. Though he wasn't quite as afraid anymore, he still felt a barrier between himself and these young masters from wealthy families.

Zhao Han laughed. "Then go practice martial arts in the bamboo grove."

Fei Ruhe, who had already stood up, sat back down at these words and chuckled sheepishly. "If you're not going, then I'll stay here too."

Fei Ruhe likewise had a guilty conscience — he'd had a hand in putting up those big-character posters, and he absolutely didn't dare be alone with Fei Yuanjian.

"Ha ha, then I'll stay and study too." Fei Yuanjian echoed with a foolish grin. He had nowhere else to go; he'd offended too many classmates before, and the moment he was alone, he was liable to get beaten up by a gang.

Fei Chun made several trips back and forth, finally bringing everyone's meals over.

Not long after, Pang Chunlai returned to the classroom as well. He picked up his chopsticks and said, "Eat while you learn. This path of computational methods is far more practical than classical studies. In the future, whether you serve as local officials, march to war, or manage family estates, you will certainly need arithmetic."

"Yes," Fei Ruhe, Fei Yuanjian, and Fei Chun answered, all three with miserable expressions.

Xu Ying, on the other hand, sat upright and proper, thirsting eagerly to learn new knowledge.

As for Zhao Han, he remained silent the whole time, burying his head in familiarizing himself with the various ancient technical terms.

For instance, "length" and "width" were often called "breadth" and "depth." If he didn't get this straight, no matter how good his math was, it would be useless — he wouldn't even be able to understand the problem statement.

Another example was the units of time: *shi*, *ke*, *geng*, and *dian*.

A day had twelve *shichen*, and one *shichen* was two hours — everyone knew that.

The *ke* divisions, however, were somewhat troublesome. Previously, a day had one hundred *ke*; after Western clocks arrived, a day was changed to ninety-six *ke*. He'd heard that in Beijing, someone had proposed changing it to one hundred and eight *ke* — a complete mess, anyway.

Beyond these, there were also uncommon time units like *miao*, *mang*, and *hu*.

Moreover, Zhao Han was astonished to discover that ancient China actually had the "week," and it had been in use for two thousand years.

A common week was seven days, and an intercalary week was eight days. During the Qin and Han periods, it was used to set working days, with court officials working only six days a week. But because the common-intercalary conversion was troublesome, it later fell out of use — the monthly three *xun* divisions were more intuitive and convenient.

The term "star period" also existed, specifically referring to the seventh day of the seventh month, and by extension came to mean a wedding date.

"The star period approaches" meant the wedding date was near.

Zhao Han had already thoroughly mastered calculation rods, and after that he was reluctant to study further, pestering Pang Chunlai to explain various units and terminology instead.

⊥〣＝‖_×

Can you tell what that means above?

It's the calculation-rod version of 6322.14 (the decimal has to be half a grid lower).

Actually, once you get used to it, it's no different from Arabic numerals — just a different set of symbols to express the same thing.

…

Seeing that Zhao Han only cared about specialized terminology and had no interest in learning basic arithmetic, Pang Chunlai smiled and set down a problem: "Zhao Han, can you solve this?"

The truth was, Zhao Han was progressing far too quickly and was clearly showing an aversion to studying — a difficult problem had to be set to knock him down a peg!

Xu Ying, Fei Ruhe, Fei Yuanjian, and Fei Chun all curiously read the problem, then collectively stared blankly.

The problem's content was roughly: "The front line has only 280,000 *shi* of army provisions remaining, and consumes 7,000 *shi* per day. If a supply convoy is dispatched, it takes 25 days to arrive, and it consumes 1,000 *shi* per day en route. Determine how much grain must be transported so that the frontline soldiers can hold out for 90 days."

Xu Ying carefully pondered a method to solve it, but his mind was a complete muddle — he had only just begun learning multiplication.

Fei Ruhe couldn't help saying, "Teacher, aren't you just making things deliberately hard for him?"

"I'm not asking you to solve it," Pang Chunlai said, smiling as he looked at Zhao Han. "If you can't work it out, then from now on, you'll apply yourself honestly!"

Zhao Han didn't answer immediately. Instead, he asked, "After the supply convoy completes its military orders, does it remain on the battlefield for the ninety days, or does it immediately return by the same route? Or, once the army provisions are delivered, is the convoy's fate simply ignored? The teacher's problem is ambiguous — there are three different answers."

Pang Chunlai burst out laughing. "Meticulous thinking — truly rare. Work out all three solutions."

Zhao Han picked up a sheet of rough paper, set the transport grain quantity as X, and began laying out an equation.

A one-variable linear equation — elementary school stuff.

Three answers were quickly tossed out.

The assembled students were instantly awestruck. Whether good students or bad, all looked at Zhao Han with gazes of worship.

Pang Chunlai snatched Zhao Han's calculation draft. The strings of mysterious code made his head spin — to him, modern equations were a book from heaven.

"What country's script is this?" Pang Chunlai asked, baffled.

Zhao Han probed, "Has the teacher heard of Xu Guangqi?"

Pang Chunlai nodded. "This Xu Guangqi — though I, your teacher, have never met him, and don't even know his courtesy name, I have long been familiar with his reputation. After the great defeat at Sarhū, he was ordered to train a new army at Tongzhou. Now that the new emperor has ascended the throne, according to court dispatches, he has been reappointed as Army Inspector."

"Army inspection" meant auditing the military's condition, including officers, troop strength, training, provisions and pay, weaponry, and so on.

Xu Guangqi's current post was to take imperial orders and inspect the Great Ming's armies.

Since Pang Chunlai said he'd never met him, Zhao Han could freely spin any tale he liked.

Without so much as blinking, Zhao Han launched right in: "In the West there was a missionary, named Matteo Ricci, who brought the *Elements of Geometry* to the Great Ming. Xu Guangqi translated this book. My late father was fortunate enough to read it in his lifetime — these numerals all came from the West."

"Do tell," Pang Chunlai said, his interest immediately piqued. He told the students to eat and work on the problem, while he himself inquired about Western arithmetic.

Zhao Han wrote out the Arabic numerals, then wrote out the various operational symbols, annotating each with Chinese characters beneath.

Pang Chunlai had no particular fondness for the Arabic numerals, but he was astonished by the convenience of the Western operational symbols. However, to introduce those operational symbols, one would have to adopt the Arabic numerals alongside them.

Expressing them with calculation rods wouldn't work, because the calculation-rod "4" looked exactly like the multiplication sign, and "2" looked much like the equals sign.

Pang Chunlai could only forcibly compare the two sets of symbols, and then look at Zhao Han's equation.

"This is the Celestial Element Method!" Pang Chunlai slammed the table.

Xu Ying and the three Feis, chopsticks in hand, stared over blankly — they couldn't understand a word of what was being said.

The Celestial Element Method is simply equations.

Pang Chunlai added, "That is the Western Celestial Element Method, which only sets up a single unknown. Can it solve two unknowns, three unknowns, four unknowns?"

Zhao Han asked curiously, "Sir, can you use counting rods to solve for four unknowns?"

Pang Chunlai shook his head. "Some can, but I cannot. I have heard that the great Yuan-dynasty mathematician Zhu Shijie once devised a method for solving four unknowns. But I have only read his *Introduction to Mathematical Studies*; I have never had the chance to see his *Jade Mirror of the Four Unknowns*. Enough talk — I shall set a problem, and you solve it using the Western Celestial Element Method."

Very quickly, a problem was produced.

Zhao Han solved it using a system of two linear equations in two unknowns and handed over the solution draft. "Sir, please look it over."

Pang Chunlai, still unfamiliar with Arabic numerals, could only check it slowly by comparison, then clapped his hands in praise. "Marvelous, marvelous!"

Using counting rods to solve a system of two linear equations in two unknowns is actually very fast — its efficiency is not inferior to setting up equations.

However, the solving process of the rod-based Celestial Element Method is far more cumbersome when expressed on paper, nowhere near as concise as equations.

If it were a problem of two unknowns to the second degree, then the Celestial Element Method would be even more cumbersome!

Pang Chunlai laughed heartily. "This art is a work of divine ingenuity. Come, teach it to your teacher."

A student teaching the teacher?

Xu Ying and the three Feis were even more dumbstruck, feeling that Zhao Han was truly formidable!

Pang Chunlai said to the four of them, "You will all learn it together."

From then on, the speed at which they learned mathematics doubled compared to before, and even Fei Yuanjian found it easier.

After all, none of them were fools.

Fei Yuanjian's relationship with the others had always been rather delicate.

Every day, as if stuck together with glue, they studied texts, practiced martial arts, and learned mathematics together. Xu Ying soon accepted him, but the others still harbored misgivings, remaining neither close nor distant, always holding something back.

In the blink of an eye, it was the winter solstice.

The chaste-widow memorial archway had already been completed, but the official approval from the court had yet to arrive.

This sort of thing required layer upon layer of review by the authorities, and then an imperial bestowal in the name of the Emperor.

But by the late Ming, it basically just took money.

For a slow process, you sought out the County Magistrate; for a fast one, you sought out the Regional Inspector of Censors. Once sent to the court, the Emperor paid no attention at all. The Grand Secretariat directly tossed it to the Ministry of Rites, and the officials there would approve it as long as they got paid.

Chastity archways were also the exclusive preserve of the rich!

Because the court only allocated thirty taels of silver, which was nowhere near enough to erect an archway, and greasing palms up and down the hierarchy required even more money. For commoners without money or status, unless a local official sought to boost his political record, no matter how chaste and martyrly they were, they could never get an archway built.

Does ritual doctrine devour people?

My apologies, but if your family has no money, you do not even qualify to be devoured.

(Asking for monthly tickets and recommendation tickets. Friends reading this book on overseas sites, this book debuts on Qidian Chinese Network — you can download the "Qidian APP" and come join the fun.)

(End of chapter)