Chapter 126: Seeking Guidance with an Open Mind

The first solar eclipse following the new emperor's ascension concluded with a non-event, despite the official predictions. To preserve the dignity of the Imperial Court and soothe the hearts of the subjects, the officials of the Directorate of Astronomy were forced to search their scrolls for obscure precedents, eventually explaining the failure in calculation as a sign that "the new emperor’s virtue has moved the Heavens, thus sparing the land from this calamitous omen."

Zhu Qiyu, having been manipulated into this situation, was naturally displeased with the Directorate of Astronomy. However, since the incident served to bolster his own image, he had no choice but to accept this narrative. Xu Dun, in a shameless attempt to curry favor with the Emperor, even submitted a memorial requesting permission for officials to present congratulatory messages celebrating this "auspicious sign." Fortunately, Zhu Qiyu had enough self-respect to avoid turning a funeral into a wedding, and he issued an edict forbidding officials from submitting such messages, effectively suppressing the matter.

Only once this trouble was resolved did Xu Dun find the time to shut his doors and investigate the culpability behind the miscalculation. The Astronomical Section was overseen by Assistant Director Gao Mian. Under his supervision, the astronomical students had spent over half a month calculating the exact timing of the eclipse, only for the results to be completely inaccurate. He bore full responsibility. Gao Mian, however, felt wronged; he had strictly monitored the calculations and verified every detail prone to error, leaving no possibility for oversight.

After the rituals to "rescue" the sun concluded, Gao Mian and several other officials skilled in eclipse prediction urgently re-verified their results. Even Guo Gui hurried back from the Observation Platform to hunt for the source of the error. Yet, after rigorous analysis, the officials found no flaws. There was only one possibility left: the mathematical constants used by the Astronomical Section contained inherent inaccuracies, leading to a "miss by a hair that results in a loss of a thousand miles."

Faced with the failure of the traditional orbital calculations, even Guo Gui had to admit that, as his son had suggested, certain parts indeed required revision. However, he did not believe it necessary to be as radical as Xue Rui, who insisted on discarding the old methods entirely. He argued that simply adjusting the corresponding parameters through practical measurements would save a great deal of time. As for his wager with Xue Rui, Guo Gui gave it no thought. If the entire Directorate, with dozens of men, could not get it right after half a month, what could Xue Rui and his son Guo Heng possibly achieve in ten days?

Xu Dun, however, kept the wager in mind. This major miscalculation had only been smoothed over because they had a "good omen" to explain it away. The next time, they might not be so lucky. If a miscalculation led to a failure to perform the rescue rituals, there would be no excuses left for the Imperial Court, and the officials would be held strictly accountable. Remembering that Xue Rui had also calculated the timing, Xu Dun hurried back to his office, retrieved the envelope pressed under his desk, and tore it open.

What he saw left him utterly astonished. It clearly stated: "The solar eclipse on the first day of the tenth month will not be visible in the capital region!"

"Could it be that the boy actually succeeded?"

The shock was overwhelming. Among the hundreds of people in the Directorate, aside from Xue Rui himself, surely no one believed he could succeed. At the time, Xu Dun had dismissed it as a joke; had it not been for Guo Gui’s bet, he wouldn't have bothered to pay attention at all. Yet, the results proved Xue Rui correct. Was this mere blind luck, or had he truly mastered the correct calculations? To confirm this, Xu Dun ordered someone to find Xue Rui, intending to question him personally.

At that moment, Xue Rui was suffering from a headache. Earlier, when he had calculated that the eclipse would be invisible, Guo Heng had been skeptical, as he knew from his father that the Directorate had predicted an eclipse. Though he wasn't told the exact time, the difference between "visible" and "invisible" was absolute. In his heart, he leaned toward the Directorate’s results. The traditional orbital calculations, while rigid, were the consensus of many experts over half a month, which seemed far more reliable than Xue Rui’s few days of work.

However, reality had proven otherwise. Xue Rui had used the most streamlined method to achieve the most accurate result, leaving Guo Heng deeply impressed. In order to learn this skill, Guo Heng set aside his pride as a scion of an astronomical family and intended to become Xue Rui's apprentice.

Watching Guo Heng kneeling before him with a teacup in his hand, Xue Rui felt his head throb. If someone else were so sincerely seeking knowledge, he might have considered it. But who was Guo Heng? He was the great-great-grandson of Guo Jingming. If he were to apprentice under someone like Xue Yuanhao, it would be understandable, as Xue Yuanhao had genuine expertise. Even though Xue Rui’s reputation was rising, he was still a newcomer who had been in the Directorate for only two months. If he accepted Guo Heng as a disciple, he would likely be criticized to death, and Guo Gui might even try to kill him. This apprentice, he absolutely could not accept.

Just as Xue Rui was fretting over how to refuse, a student entered the office and said the Director wanted to see him.

"Ah, the Director must have something important; I must go!"

Xue Rui was overjoyed, abandoned Guo Heng, and slipped out of the office. Upon arriving at the Director's office, Xu Dun greeted him warmly: "Come, come, have a seat."

"What does the Director need from me?" Xue Rui asked, feigning ignorance despite his suspicions.

Xu Dun went straight to the point, waving the paper in his hand: "Is the eclipse result you calculated based on the streamlined orbital method you mentioned?"

"Exactly," Xue Rui confirmed with a nod.

"Then can all future eclipses be accurately predicted using this method?" Xu Dun asked with a hint of excitement.

Xue Rui said awkwardly: "Well, I cannot say for sure. It still requires time for verification. After all, the revisions were done in a rush and some parts are not yet perfect; errors might still occur." He dared not speak too confidently, as the astronomical data of the era was not very accurate. Even though he was doing his best to refine it, there would inevitably be errors. If he were wrong, it would be a slap in his own face.

Xu Dun, however, did not mind. He smiled and said: "That is fine. Just give me the streamlined method. For the parts that are incomplete, I will mobilize the entire Directorate to help you perfect it."

"This old man is trying to steal my credit?" Xue Rui understood Xu Dun’s intentions perfectly. The talk of helping him perfect it was merely a pretext; Xu Dun clearly saw the potential in the method and wanted to seize it. If he managed to "perfect" it, most of the credit would be stolen.

However, Xue Rui was not worried at all. Instead, he said happily: "With the Director's word, I am much more at ease. Please wait a moment, and I will fetch it."

"Good, good, good! I shall wait and see!" Xu Dun was overjoyed, not expecting Xue Rui to be so compliant. He had feared Xue Rui might turn hostile. It seemed the small favors he had shown in the past had finally paid off.

Soon, Xue Rui returned with a stack of manuscript paper. Xu Dun took it and glanced at it; the content was indeed different from the old orbital calculations—this was the streamlined version Xue Rui had spoken of!

"Not bad. They say the student surpasses the master. You haven't been in the Directorate long, yet you've made such a name for yourself. It shows your talent in astronomical calculation is not low. If you weren't so young and lacking in seniority, I could easily recommend you for a Ninth-Rank official position based on this merit alone." Xu Dun flipped through the pages, uttering these empty, flattering words.

"Director, please don't! I am not cut out to be an official!" Xue Rui didn't know how much of this was sincere, but he had never had the ambition to be an official. He was very satisfied with his current job. If he were promoted, his life of leisure would be ruined—how would he "lie flat" then?

Xu Dun thought he was just being modest, and set the manuscript down: "Officials in the Directorate of Astronomy are different from those in other offices; if you have genuine skill, you can succeed. Rest assured, in three to five years, based on the merit you accumulate, becoming a Morning-Calling Official (Wuguan Sichen) will be no problem. I have high hopes for you."

"Ah, thank you for your favor, Director. I am deeply grateful." Faced with Xu Dun's empty promises, Xue Rui could only put on a look of being moved.

"Alright, go on now. I will look over these drafts first to see how they should be perfected." Having secured the streamlined method, Xu Dun had no interest in humoring Xue Rui any longer and dismissed him.

Once Xue Rui left, Xu Dun sat behind his desk and began to study the contents in detail. If he could learn this method, he could use it as a template to streamline the other orbital calculations. Then, the lion's share of the credit would go to him. With such a revolutionary contribution in hand, even if he couldn't rise further in the Directorate, he could potentially secure a title as a Minister of the Court of Imperial Sacrifices or the Court of Diplomatic Ceremonial, or even a Vice Minister in the Ministry of Rites!

Alas, Xu Dun's plans were grand, but when he actually began to study the streamlined method, he found many parts incomprehensible. He couldn't even figure out how some of the results were calculated. As the Director of the Directorate of Astronomy, Xu Dun considered his skills second to none in the agency. He had even studied the traditional orbital calculation processes thoroughly years ago. Unlike the students who only knew how to plug in numbers, he truly understood the underlying logic. But Xue Rui’s streamlined method truly stumped him.

"If a mere boy can calculate this, why can't I?" Xu Dun refused to believe it. He picked up his brush to work it out, but by the end of the shift, he had made no progress. Desperate to crack the mystery, he brought the drafts home to study through the night.

The next day, Xu Dun arrived at the Directorate very late. To the surprise of the officials, he looked haggard with dark circles under his eyes, appearing utterly exhausted. Upon arrival, he summoned Xue Rui with a grim face, claiming he had matters to discuss.

Seeing Xu Dun’s panda-like eyes, Xue Rui asked curiously: "Director, do you have any instructions for me?"

*Thwack!*

Xu Dun threw the manuscript on the desk, his face livid: "What kind of mess is this? Are you trying to fool me?"

"Director, I am wronged! This is the streamlined orbital method!" Xue Rui protested.

Xu Dun didn't believe him for a second. "Then why are the simplified calculation methods in here completely different from anything I have seen before?"

"Oh, you mean that!" Xue Rui suddenly realized, explaining: "To be honest, some of the differences are calculation methods I devised myself. They might be a bit obscure, but once you grasp the underlying principles, you can apply them to other areas, and you won't be stumped again."

"Methods you devised yourself?" Xu Dun paused. Ancient Chinese mathematics had developed significantly over the centuries, and the Directorate of Astronomy was the place where mathematics was used most. Most of the officials there were well-versed in advanced mathematics. Yet, among the nearly two hundred people, no one had ever devised their own calculation method. Xue Rui’s claim made Xu Dun suspect he was boasting.

However, Xue Rui spoke with such conviction that Xu Dun began to waver. He knew Xue Rui wasn't one to spout nonsense; the boy must have had some confidence to challenge Guo Gui so openly. Coupled with the accurate prediction of the previous eclipse, perhaps this new method really did have merit. Perhaps it truly contained self-devised methods?

Xu Dun desperately wanted to ask how these methods were derived, but he couldn't bring himself to lower his pride and ask a mere boy for guidance. After much thought, he decided to dismiss Xue Rui and spend more time studying it himself to see if he could get useful results. "No wonder I found it strange; it’s because you changed the calculation method. Since that is the case, I will have to look at it from a different perspective. You may return to the files office; I need to study whether there are any major omissions here."

"Then I shall take my leave." Xue Rui backed out of the office with a smirk on his face. In truth, he had intentionally left out certain parts specifically to prevent the officials from stealing his thunder. It was precisely because Guo Heng wanted to learn these parts that he was willing to apprentice himself and serve tea.

After dismissing Xue Rui, Xu Dun abandoned his other work to study the methods. He spent the entire morning and used dozens of sheets of paper, yet gained nothing. Having no choice, he had to summon several officials to consult on the manuscript together. Since he couldn't swallow the achievement alone, he had to share the credit and use the collective strength of the group to make a breakthrough.

Upon entering Xu Dun’s office, Gao Mian picked up a manuscript and frowned: "Director, this seems to resemble the content of the eclipse orbital calculations, but it has many errors and omissions. Could it have been copied incorrectly?"

"This is not the orbital calculation we use, but a streamlined version given to me by Xue Rui!" Xu Dun scanned the faces of the group and saw their utter shock.

Gao Mian slapped the manuscript on the table in anger: "The boy doesn't know his place! He had to go and bet with the Lingtai Lang (Astronomer), and I suspect he just wrote down a bunch of nonsense to try and muddle through."

Xu Dun smiled bitterly: "I thought the same. However, he used this streamlined method to calculate the exact timing of the eclipse the other day!"

"Truly?" The officials were stunned and rushed to examine the manuscript. If this method could really predict eclipses accurately, it would save them an immense amount of time. Alas, they were met with the same cold bucket of water as Xu Dun. Some of the calculation methods were not only incomprehensible to them, they had never even seen them before. They had no idea how Xue Rui had come up with them.

After studying for a long time, the officials remained at a total loss. Just then, Guo Gui arrived in a hurry.

Xu Dun said happily: "Master Guo, you have come at the right time. We were just waiting for you."

"Director, is it true that the Xue boy's streamlined orbital method successfully predicted the eclipse?" Guo Gui asked anxiously, forgetting even to offer a formal greeting.

"It is true. Master Guo is a scion of an astronomical family and must be well-versed in mathematics. Please take a look and see how some of these parts are calculated; we can't make heads or tails of it," Xu Dun said with a bitter smile.

During the Yuan and Ming dynasties, the Guo family had produced two famous mathematicians: Guo Shoujing and his grandson, Guo Boyu. As a descendant of the Guo family, Guo Gui considered himself highly skilled in mathematics. Yet, as he carefully studied the streamlined version, he found many points of confusion. Based on his knowledge, these were not just random scribbles as Gao Mian thought, but were based on sound mathematical principles. The reason they couldn't understand them was simply due to the limitations of their own knowledge.

After a long silence, Guo Gui sighed and said to the others: "Gentlemen, it seems we must set aside our pride and humbly ask Xue Rui for guidance..."