Liu Bin, who possessed remarkable alcohol tolerance, became intrigued when he saw his newly betrothed son-in-law challenging Wu Zong. Swirling a wine cup in his right hand, he asked, "Jinzhou, tell us what this 'emergency wind' is you speak of?"
"It's calculus—advanced geometry," Cheng Jinzhou replied, lifting his bleary eyes to meet the gazes of those around him who seemed "thirsty for knowledge." He continued, "Take land surveying, for instance. No plot is perfectly regular. Calculus deals with how to handle those irregular portions."
Wu Zong, also deep in his cups, waved a hand dismissively. "For irregular areas, we use the methods of dissection and compensation. The intricacies of dividing and compensating points could take a decade to explain fully."
"Intricate? You're trying to measure the infinite with the finite!" Cheng Jinzhou suddenly felt as if he were back in university, substituting for some unscrupulous professor lecturing undergraduates. A foolish grin spread across his face, the kind that might lure female students. "With truly irregular shapes, no matter how you dissect and compensate, you're still approximating. And approximation means error. How can you guarantee accuracy? Practical mathematics can be precise, but never perfectly accurate."
Wu Zong jolted as if sobered halfway by the words. Disbelieving, he asked, "You can calculate irregular shapes without dissection and compensation?"
Liu Bin, somewhat confused, interjected, "Master Wu, what do you mean by this?"
Wu Zong ignored him, staring fixedly at Cheng Jinzhou. Mathematics dealt in concrete realities—no room for fantasy. That this young man understood advanced problems like the heptadecagon proved he wasn't spouting nonsense. Moreover, he'd earned the recognition of Liu Kuang, a fourth-level astrologer.
Given Cheng's sickly constitution, a few cups had left him thoroughly drunk. After vomiting, he'd regained just enough clarity to slur out more bold claims: "Measuring irregular shapes? That's fractal geometry's domain, not mine. But for land surveying, I can casually apply calculus."
As he spoke, he dipped a finger in wine and began drawing twisted lines on the tablecloth.
The astrologers employed by the Cheng family showed interest, as did several high-ranking nobles who crowded around.
Cheng Jinzhou sketched a simple waveform—the first illustration in any calculus textbook—muttering, "If you consider a curve as a collection of countless points, can't you measure any shape precisely? The finer your points, the greater the accuracy—until it kills you with the work."
No concept emerges from nothingness. The core idea of calculus—the limit—was formalized by Cauchy in the 19th century, though its roots traced back to the Greek "method of exhaustion" in the 5th century BCE. While Wu Zong couldn't decipher the formulas Cheng used, he grasped the underlying principle immediately.
The rice wine's effects had long since evaporated from Wu Zong. He too dipped his fingers in wine, heedless of the soup stains on his sleeves, and drew two irregular shapes. "Apply your method here. Let's calculate the results..."
"Since when is calculus proven through trial and enumeration?" Cheng Jinzhou gave Wu Zong a drunken look of disdain but provided the answer nonetheless.
It was, unquestionably, correct.
"My mind was clouded. My mistake." Wu Zong's lips went dry, his curled beard forgotten in his excitement. After admitting fault, he pressed, "How did you derive this formula?"
"It's called deduction, and it's not just one formula." Cheng wiped his hands on the tablecloth. "The process is tedious. Can't be bothered to write it all out."
The content was indeed extensive—but mainly because Cheng couldn't remember it all.
Wu Zong hesitated awkwardly until Liu Bin mediated: "Master Wu, what riddle are you two solving? Explain it to us."
Now it was Wu Zong's turn to show impatience, though he restrained himself out of respect for the earl's status. "Whether riverbanks or woodlands, nothing in nature has perfect geometry. The dissection method involves cutting excess areas to fill deficits, but there's always error. Even the finest astrologers can't achieve perfect balance. It suffices for daily use, but Master Cheng's method—if valid—has applications far beyond land measurement."
The crowd marveled. While calculus's significance in mathematics was immeasurable, these nobles appreciated its tangible, straightforward benefits more readily.
Cheng Jinhao glanced back nervously. The noblewomen and young ladies had long fled the pungent atmosphere, missing Cheng Jinzhou's performance entirely. The thought that Liu Qingshuang had only witnessed Cheng's disgrace brought him perverse satisfaction—even if gossip spread later, it wouldn't compare to seeing it firsthand.
The astrologers now regarded Cheng Jinzhou with the fervor of dieters spotting meat, their eyes bloodshot with hunger, practically brandishing imaginary knives and forks.
Having vomited extensively and waved his wine-stained hands with drunken enthusiasm, Cheng's mind finally cleared. Seeing the standard calculus diagrams on the tablecloth, his remaining intoxication fled with a cold sweat. Refusing to engage further, he yanked the cloth free, sending dishes clattering, and rolled it up to leave.
The crowd instinctively parted—a capable astrologer was always this world's most coveted individual.
Only Liu Bin chuckled, stroking his beard in self-congratulation. As Cheng reached the door, he called out, "Son-in-law! Remember to visit this old man tomorrow."
His hand kept waving long after Cheng had turned the corner.
The banquet concluded naturally—dramatic in process, delightful in outcome, leaving all satisfied, perhaps excessively so. Liu Bin returned to his quarters still grinning and stroking his beard.
His wife, who'd returned earlier, was displeased. While directing maids to wash and change him, she complained, "How could you arrange the marriage without consulting me? That Cheng Jinzhou—I've heard he was sickly before. He's improved somewhat, but started studying far too late..."
Noblewomen of the Great Xia Dynasty held considerable status, reminiscent of Louis XIV's France. As she bustled about, she listed Cheng's shortcomings intermittently.
Liu Bin merely chuckled. After removing the hot towel from his face, he sighed contentedly and asked, "Shuang'er, what are your thoughts?"
Liu Qingshuang shook her head gently. "This daughter merely wonders why Father values him so."
Her tactful counter delighted Liu Bin. "Well answered! Worthy of that boy." He laughed heartily. "That lad's no simpleton, though he is rather frail. Hmm... Let's give him Meng Da and Meng Er."
His wife froze mid-motion. "They saved your life at Tucheng! You praised their exceptional valor—"
"Precisely such warriors deserve a great astrologer." Liu Bin tilted his head slightly. "My judgment has never failed."