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Ch89 - Obtaining
Squeezed among the crowd of refugees, Liu Jian realized, with shock, that Taihang Pass was vastly different from what he had imagined. The servant of the Liang Estate said a few words to the guards; then, the gates to the pass slowly swung open. Not only he and the people around him, but the rest of the refugees were let into the pass as well. And he hadn’t seen the soldiers take any tolls or fees for passage – were they just going to let them enter Bing Province?
But this was a major road from Si Province into Bing Province; taking the Taihang Pass could save you over a dozen days’ worth of travel over the winding byways. It should have been that even the Liang Estate’s people could not gain easy entry, much less all these refugees. Was that a dilemma that a few words could resolve?
Li Xin was, of course, ecstatic that they’d gotten through without fuss, but Liu Jian wasn’t that careless. He held it in time after again before he finally blurted, “Ah-An, why’s it so easy to enter the pass now?”
“It’s not easy,” Liang An chortled, “but who’d dare to stop us Liang Estate folk?”
Was the Liang Estate’s influence so great already? Liu Jian glanced again at the refugees behind, “What about these people? Don’t tell me they’re the Liang Estate’s people too?”
“Well, who knows. Apparently Gaodu City’s taking in refugees? I’ve been away for a couple months already, so I really couldn’t tell you how things’ve changed in the estate,” Liang An sighed wistfully.
How much could change in just two or three months? Liu Jian was confused, but thought it rude to ask, so he followed the party forth along the craggy little trail. A day passed just like that, and they stayed another night at Taihang Pass before setting foot in Bing Province.
The first place they stopped at was none other than Gaodu. There were shacks clustered about outside the city, on account of all the refugees, but it wasn’t at all a scene of chaos. A couple of bailiffs stood watch outside the city, and upon seeing the new wave of refugees, led them over to the shacks at once. It was all very orderly; they must have done it many times already. Further away, dozens of horses and countless men and women busied about in the fields, either tilling barren land or frantically sowing seeds.
The sight of the hectic masses brought Liu Jian some peace of mind. Even Qing Province hadn’t seen so much bustling agricultural activity in many years. By the looks of it, Gaodu must have a very industrious magistrate. The Liang Estate was just nearby, surely this benefited them quite well. Ah-An might not be blowing hot air after all.
But when the Liang Estate’s gatehouse actually appeared before them, Liu Jian was the one most shocked, “Does everything within those walls belong to the Liang Estate?”
It was no small amount of land; had Liang Estate claimed it all?
His eyes sparkling, Liang An said happily, “This gate wasn’t built yet when I left. They put up this fortress in just a winters’ time, what’ve you got to worry about now, Lord Liu?”
Could a fortress like this even be built in two months? The massive nine-meter-tall gates still had Liu Jian reeling with disbelief. But telling such a lie was utterly pointless – could it be that the Liang Estate truly had such wherewithal? Still moderately doubtful, he urged his horse into the gatehouse. Inside, he was greeted by the same scenery that he’d seen outside Gaodu; nay, this was even livelier. To the left and right of the road, farmers labored in the fields. There were even chain pumps, slashing water into canals that irrigated the crops.
We’re sorry for MTLers or people who like using reading mode, but our translations keep getting stolen by aggregators so we’re going to bring back the copy protection. If you need to MTL please retype the gibberish parts.
If he hadn’t known beforehand that Bing Province had suffered two years of drought, he’d almost have mistaken this place for a perfectly fair-weather paradise on earth!
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“So you’re the master of the Liang Estate? Will you help me print the manuscripts my shifu left behind?” was said very straightforwardly by Li Xin. Unlike the rest of them, he wasn’t the slightest bit awed by Liang Feng.
Liu Jian nearly leaped out of his skin, “Ziyue, you’re in the presence of Marquess Liang, mind your manners!”
“Of course,” Liang Feng said, smiling at the two travel-worn youngsters. “The Liang Estate is willing to print any version of ‘The Nine Chapters on the Mathematical Art’ annotated by the late Mister Liu. It is not impossible that, like ‘The New Treatise on Cold Damage,’ which has been printed two hundred times now, it should become known to all the world.”
Li Xin knew about “The New Treatise on Cold Damage” – it was this quality-printed book that had given him the resolve to leave Qing Province, but he was surprised to know that the book had two hundred copies already! Wouldn’t that mean that nearly every literate family in Bing Province had one? If the “The Nine Chapters on the Mathematical Art” his shifu had annotated were to be printed, would it not become known to everyone?!
Upon that realization, Li Xin instantly said to Liu Jian, “Shixiong, this place’s not bad! Let’s wait till all our books get printed before we leave!”
Liu Jian, “…….”
He’d warned him a hundred, a thousand times, but in the end, he’d taken none of it to heart! Liu Jian was almost too ashamed to even look at Lord Liang’s sardonic smile, “May I ask why you have invited us, Marquess Liang?”
“I’ve heard that the late Mister Liu once authored a chapter on the ‘double-complement’ method, which can be used to measure the heights of mountains and the depth of valleys. It just so happens that my estate has plans to create a map of the surrounding environs, and require your skills….”
Li Xin was wildly shaking his head before Liang Feng even got the chance to finish, “Measuring mountains and land takes too much time and effort, and it’s not engaging at all; no, I’m not doing it.”
Liang Feng choked, “Then would the two of you teach students so that they might do the surveying and map drawing?”
“There are too many idiots out there, who’s got the patience to teach them?” Li Xin scorned disdainfully, “I’ve still got to arrange my shifu’s drafts and continue my research – I can’t spare the time for that!”
He had just a ridiculous lack of common sense regarding anything related to social interaction; anyone else would have thrown him out the door already. No wonder he could be so outrageous as to turn his back on his first sect, run to Qing province to learn from another, then scoop up all the books his late teacher had collected over the decades, and scurry here to have them printed. A math savant obsessed with intellectual pursuits and ignorant of the ways of the world would not be moved by fame or profit.
After a moment of thought, Liang Feng said abruptly, “You know, there’s something I’ve always wondered about: is the earth beneath our feet a level plane?”
Li Xin scoffed, “Of course not. The earth is half-round, as Grand Astrologer Zhang said, ‘the sphere of heaven is like an egg, the celestial bodies are round as pellets, and the earth, like the yolk within the egg, floats solitary within.”
Such was recorded in Zhang Heng’s “Observations of the Sphere of Heaven.” It was wildly different from the previous supposition that the sky covered the flat earth like an overturned bowl. Zheng Heng believed that the heavens were a sphere and that the earth was a semi-ovoid, beneath which the waters and heavens were connected; only that could explain the fundamental principles of astronomy and mathematics. As Liu Hui was an accomplished mathematician – he’d written the chapter on the double-complement method – and had seen how the bases of mountains on distant islands sat below the horizon, having resided for years in Shandong, it wasn’t hard to come to a similar conclusion as Zhang Heng’s. But Liu Hui’s interest was in mathematics, and he didn’t delve deeply into astronomy. Li Xin knew this fact, but had never bothered to probe into it.
Liang Feng hadn’t expected that Li Xin knew the earth was round. The Sphere of Heaven Theory was probably, before gravity was discovered, the very limit of what people could imagine the world to be. Liang Feng said approvingly, “So it is true! I’ve noticed that going from east to west, the climate is much the same, but from north to south, the difference is stark as night and day. Only if the surface of the earth was round, would this phenomenon make sense. But if the earth was like a ball, then it must be possible to calculate its size. Might I inquire if the product of Mister Liu’s research would suffice to measure the area of the half-sphere that we stand upon?”
“Hm?” Li Xin blinked. The “Zhou Gnomon Classic of Arithmetic” had proved the dimensions of the earth, but if the earth was not flat, then how could the calculations possibly be correct? The cyclotomic and double-complement methods were both his shifu’s proudest achievements, it did seem possible to use them to measure the earth once more.
Liang Feng saw Li Xin waver, and pressed the advantage, “Measuring the earth is not the work of a single day. Why not stay at the estate and revise Mister Liu’s notes while you train a few assistants? Then, once the times are peaceful, bring your assistants with you to traverse the famed mountains and great rivers to ((measure the earth’s surface)) and illustrate a map that conforms to the study of double-complement; you could have the best of both worlds.”
Seeing Li Xin’s interest grow with every word he said, Liu Jian hurriedly cut in, “What you’ve said, Lord Liang, is truly fascinating, but in what we’ve inherited from our sect, there are many questions that still lack for answers. I fear if he were to use his lifetime’s focus on making a map of the world, it would impede his academic pursuits.”
If he really did allow Ziyue to go off and draw maps, he could very well spend his whole life on it. This marquess didn’t seem like an idle noble entertained by maths, there was no way to brush him off with empty theoretical conversation. They still had to pass down the knowledge his grandfather left behind.
Liang Feng was not annoyed at the interruption. He said smilingly, “And which field are you most skilled in, Liu-Lang?”
Liu Jian was not an all-around genius like Li Xin, he answered simply, “I’m more inclined to the cyclotomic method.”
“Hmm. The double-complement method can be used to obtain the scale of mountains and islands, what can the cyclotomic method do?” Liang Feng asked curiously.
For a moment, Liu Jian was at a loss for words. The cyclotomic method was his grandfather’s life’s work, but how was he to explain it to an outsider? Every chapter of “The Nine Chapters on the Mathematical Art” contained methods that addressed practical problems, even double-complement was no exception; the cyclotomic method should rightly have its use.
When Liu Jian didn’t respond, Liang Feng said, “As it deals with rounds, it must be applicable to many interrelated things. For example, the water wheel that the Liang Estate is researching is circular, but it is very difficult to make. It would be splendid if you could simplify the process or increase its efficiency! And since the path of an arrow from a bow is curved as well, could you use the cyclotomic method to calculate the optimal angle of force to increase its range and accuracy?
Liu Jian couldn’t help brightening when he heard Liang Feng’s words, “It’s worth a try!”
Practical application was every researcher’s Achilles heel, and Liu Jian was no exception. In truth, he wasn’t much inclined towards the esoteric maths his grandfather had researched. But he was absolutely absorbed by the cyclotomic method. If he could let the cyclotomic method be used in daily life, might it become widely known?
His excitement evoked a silent sigh of relief from Liang Feng. Math, especially geometry, was extremely impactful on science, engineering, and manufacturing. None of the workshops lacked for skilled artisans, but what they knew was only “craft,” vague notions touched upon through trial and error. The guidance of “methodology” could fill their gaps in understanding and solve problems that experience alone could not.
That was what “math is the mother of science” truly meant. He’d finally hoodwinked two of Liu Hui’s direct disciples, how could he waste their potential on cartography?
“That would be most excellent,” Liang Feng put on a warm smile. “Hereafter, you may continue your research here; the estate will take care of room and board. I will have a few clever students sent to you to learn the double-complement method. If there are issues the workshops are unable to resolve, they will ask for your advice.”
With his shixiong’s tacit acceptance, Li Xin immediately said, “I need two to shave bamboo as well; calculations consume so many bamboo slips!”
“The paper produced by the Liang Estate may be used for your daily activities. In addition, I will have the craftsmen make you blackboards to replace your sand trays,” Liang Feng said generously.
“Shixiong, we can even use paper here!” Li Xin was immediately overjoyed. Room and board were provided, as well as unlimited paper and the ability to print books; was there a better place than this?
Some hesitation later, Liu Jian asked, “Is there a monthly salary?”
It was wonderful, of course, that room and board were included, but they needed the assurance of financial solvency. He had to know for sure, even if it meant thickening his face.
“According to the estate’s standard, three stone of rice per month; if you successfully educate a student, an additional two rolls of silk; if you aid in the research of useful apparatuses, you may receive additional reward. Does this sound acceptable?” Liang Feng asked in return.
Gazing upon that person’s beaming smile, Liu Jian swallowed a mouthful of saliva, “That is very acceptable…..”