xymnovel Chapter 103 Calculations Without an Abacus: The Birth of the Sliding Ruler
Chapter 103 Calculations Without an Abacus: The Birth of the Sliding Ruler
At the foot of Zhongnan Mountain outside Xianyang City lies the Qin Dynasty's royal weapons testing ground.
Spring thunder rumbled, but the "thunder" here was louder than the thunder in the sky.
"Ready—Fire!"
With a wave of his command flag, Xiang Yu unleashed a roar from the newly launched "Shenwei" breech-loading smoothbore cannon (although still propelled by black powder, it already possessed the rudiments of modern artillery).
"boom!"
A solid iron bullet whistled out, tracing an imperfect parabola, and slammed hard into... a mound fifty feet to the left of the bullseye.
Mud flew everywhere, startling several wild rabbits that were grazing.
With a dark expression, Xiang Yu threw down the command flag and strode to the cannon position, looking at the group of Mohist disciples who were sweating profusely and frantically fiddling with abacuses.
"What's going on? How many times has this happened? Is this the trajectory you calculated? Is this cannonball drunk?" Xiang Yu roared. "According to the conservation of momentum and the parabolic equation, it should have hit that scarecrow squarely on the head! And now? It hasn't even touched the scarecrow's toes!"
The chief calculator of the Mohist school, an elderly man with gray hair, was kneeling on the ground, his fingers trembling as if he were playing a pipa. In front of him was a specially made, elongated abacus, the beads flying up and down, even emitting a wisp of smoke from the heat generated by friction.
"General Xiang... General Xiang, this isn't our fault!" the old man cried, "The 'drag coefficient correction' you requested is too complicated! And that 'Coriolis force' (although they don't know the term yet, Wang Jianguo mentioned the influence of the Earth's rotation), this... every parameter change requires dozens of multiplications and divisions, even square roots! We... our fingers are about to break!"
Nearby, a dozen or so young Mohist disciples were slumped on the ground, rubbing their hands. Their knuckles were red and swollen, and some were even wrapped in thick strips of cloth.
"Yes, General, this abacus is a wonderful tool for addition and subtraction, but it's just too slow to calculate multiplication of several digits and take the square root!"
"By the time we figure it out, the Hun cavalry will already be charging right in our faces!"
Xiang Yu looked at this group of pitiful "human computers" and felt helpless.
Although he had studied physics and understood the formulas, when it came to practical application, the enormous amount of calculation was like a mountain pressing down on the range of the artillery.
This is called the "computing bottleneck".
A voice came from behind.
Wang Jianguo, dressed in overalls and carrying two seemingly ordinary wooden sticks, strolled over leisurely. Ying Zheng followed behind him with his hands behind his back, looking with interest at the crater that had been blown off course.
"Greetings, Your Majesty! Greetings, Imperial Preceptor!"
Everyone quickly bowed in greeting.
"Get up." Ying Zheng waved his hand, pointing to the still-smoking abacus. "Jianguo, my Great Qin already has the muscles of steel (steam engine, internal combustion engine), and the keen nerves (telephone), but its brain (calculation ability) seems to be lagging behind?"
"Your Majesty is wise." Wang Jianguo picked up the abacus, fiddled with it a couple of times, and said, "The abacus represents the pinnacle of discrete computing, but it is indeed too cumbersome when dealing with continuous engineering mathematics, especially complex multiplication, division, and exponential operations. We need a new weapon."
"Weapons?" Xiang Yu's eyes lit up. "Even more powerful than cannons?"
"It's the eye of the cannon, the skeleton of the bridge." Wang Jianguo waved the two wooden strips in his hand, which were covered with dense markings. "It's called a slide rule."
The side hall of the Qilin Hall was temporarily converted into a lecture hall of the Qin Academy of Sciences.
A math problem that makes everyone's head spin is written on the blackboard: 387.5 × 42.6 ÷ √15 = ?
The audience was filled with the most outstanding mathematical masters of the Qin Dynasty, Mohist craftsmen, and even Xiao He and Zhao Gao, who were in charge of money (he was just there to join in the fun and see if he could use the money to calculate embezzled funds).
"I'll give you the time it takes for an incense stick to burn." Wang Jianguo lit an incense stick.
"Splash—"
A chorus of abacus clicks filled the air below, like a torrential downpour on banana leaves. The mathematics masters frowned, muttered incantations, and their fingers flew across the keys.
"Three down, five down, two... seven up, eight down... carry... borrow..."
Zhao Gao was also in that group, but he only knew addition and subtraction. When faced with this kind of problem, he could only draw a turtle on his face with a brush to relieve his boredom.
The incense stick was half burned.
"Is it not ready yet?" Wang Jianguo asked.
"Almost there! Almost there! They're extracting the square root!" The chief calculator was sweating profusely. "This square root of 15 is so hard to come up with!"
"Alright, stop calculating."
Wang Jianguo shook his head and took out his "magic weapon"—a ruler made of fine boxwood with a sliding groove.
"Watch closely."
Wang Jianguo gently pushed the slider in the middle with his finger, aligned it with a mark, glanced at it, and directly gave the answer:
"Approximately equal to 4260."
The audience was completely silent.
After a long while, the chief calculator finally put down the abacus with trembling hands, looking at the result he had just calculated: "4259.8... This... This..."
"Amazing!"
Xiao He suddenly stood up, his eyes almost popping out of their sockets. "Grand Preceptor, you didn't even touch the brush or the beads, you just pulled on the wooden strip and that's it?"
"This is unscientific! This must be sorcery!" Zhao Gao exclaimed from the side. "Is there a little devil hiding inside that piece of wood?"
"That's called a logarithm."
Wang Jianguo turned around and wrote a formula on the blackboard: log(a × b) = log(a) + log(b).
"Your Majesty, gentlemen. Multiplication is difficult, but addition is simple. On this ruler, the distance between the markings does not represent the numbers themselves, but rather the 'logarithm' of the numbers. When we add two distances together (pulling the slider), we are actually performing multiplication."
"Turning complex multiplication and division into simple addition and subtraction, and square roots into division. This is the dimensionality reduction attack of mathematics."
Ying Zheng looked at the formula on the blackboard. Although he didn't quite understand what logarithms were, he understood the words "dimensional reduction attack".
"Simplifying complexity, brilliant!" Ying Zheng exclaimed. "It's like how I standardized weights and measures, turning the complex rules of the world into a single ruler."
"Little G," Ying Zheng asked in his mind.
[Yes, Brother Zheng.]
"The principle behind this thing sounds simple, so why hasn't anyone thought of it before?"
Because mathematics requires accumulation. The concept of logarithms was invented by Napier in the 17th century. It was a great leap forward in the history of human calculation, an invention known as "extending the lifespan of astronomers." Previously, calculating the orbit of a single star could take months; with logarithms, it could be done in days.
In the Qin Dynasty, it would extend the lives of craftsmen, sparing them the arduous task of calculating the load-bearing capacity of a bridge.
The promotion of the sliding ruler caused a major upheaval in the Qin Dynasty's artisan community.
The Mohist disciples have gone completely mad.
Previously, designing a bridge required a dozen people working for half a month just to calculate the structural stress. Now? Everyone carries a "magic ruler" on their belt, a quick pull, and the result is in. Although the precision is only three or four significant figures, it's sufficient for engineering!
"Bravo science! Bravo logarithms!"
At the construction site, the Mohist disciples no longer greeted each other with "Have you eaten?", but instead pulled out their measuring tapes and began to compete: "Come on, calculate 3.14 squared!" "Sizzle—9.86!" "Awesome!"
This trend even spread to the military.
As a physics enthusiast, Xiang Yu immediately had a giant sliding ruler made of pure steel, one meter long (which could also be used as a mace to smash people).
On the artillery position.
"Reporting to the General! The enemy is 1200 paces away, wind speed is level 3, southeast wind!"
Xiang Yu pulled out his giant sliding ruler and pulled it in a dazzling series of motions (accompanied by sparks from the friction of metal).
"Elevation angle 35 degrees! Load five pounds of explosives! Windage correction to the left by two quarters of an hour! Release!"
"boom!"
The shot hit the scarecrow squarely on the top of its head, blasting it to pieces.
"Hahaha! Awesome!" Xiang Yu kissed the still-hot ruler. "This is true manly romance! Before, that was just wishful thinking; now it's 'precision guidance'!"
The most unfortunate of all was Zhao Gao.
As one of the "gods of wealth" of the Qin Dynasty, Zhao Gao saw that everyone was using sliding rulers, so he also got one inlaid with gold and jade.
One day, he was reporting the accounts of the Imperial Household Department to Ying Zheng.
"Your Majesty, last month we made money selling rubber... uh..." Zhao Gao took out a sliding ruler and pretended to pull it, "...earned approximately... ten million coins?"
"Approximately?" Ying Zheng frowned. "How can accounts be approximated? Even a penny less is a capital offense!"
Wang Jianguo, suppressing a laugh, said, "Lord Zhao, a sliding ruler is for engineering projects, where efficiency is key. If you need to be precise down to the last digit in your calculations, you should stick to an abacus. Sliding rulers have inherent errors, and your 'rough estimate' could cost you tens of thousands of coins."
Zhao Gao was so frightened that his hand trembled, and the ruler fell to the ground and hit his toe.
"This servant...this servant will move the beads instead."
The power of the sliding ruler lies not only in firing cannons, but also in construction.
A bridge of unprecedented scale is being planned across the Wei River.
In the past, bridges were either wooden bridges, which were prone to decay, or stone arch bridges, which had limited spans. But this time, Wang Jianguo proposed to build a steel truss bridge—the prototype of the railway bridge that would later become known—so that heavy trains could cross the Wei River.
This type of bridge has an extremely complex structure, with each steel beam experiencing different stresses. In the past, just calculating the thickness of these steel beams would have paralyzed the calculation department of the Imperial Household Department.
But now, we have slide rules and the "Great Qin Logarithmic Table" compiled by Wang Jianguo.
Inside the design studio of the Shaofu, dozens of young craftsmen each held a sliding ruler, with huge blueprints laid out in front of them.
"Third node, force analysis... *sizzle*... 5,000 kg of tension! Needs to be bolded!"
"Fifth node, bending moment calculation... *sizzle*... safety factor 1.5, passed!"
There was no noisy abacus, only the slight friction of a sliding wooden ruler, like a precise symphony.
In just three days, all the data that would have taken six months to calculate was completed.
When the massive steel bridge was erected over the Wei River, Ying Zheng personally walked onto the bridgehead. He looked at the crisscrossing steel beams and felt the solid ground beneath his feet.
"Jianguo, is this bridge stable?"
"Your Majesty, rest assured," Wang Jianguo patted the bridge railing. "This bridge was designed using mathematical calculations. Every steel beam has undergone the test of 'logarithmics.' Unless the Wei River rises to the heavens, it will not collapse."
Ying Zheng nodded and looked at the spirited young craftsmen with rulers hanging from their waists.
"I used to think that governing a country relied on half of the Analects. Now it seems that we also need to add this half of a wooden ruler."
However, technological progress is always accompanied by the lamentations of the old.
The accountants in Xianyang City have been quite anxious lately. Although sliding rulers can't be used for detailed accounting, the "one-click result" style makes their abacuses seem rather rustic.
More importantly, with the popularization of engineering mathematics, the traditional "Nine Chapters on the Mathematical Art" is no longer sufficient.
At the Epang Palace University, a reform of mathematics education is underway.
"Oppose! Strongly oppose!"
An elderly, white-bearded professor was slamming his fist on the table. "Mathematics is one of the six arts of a gentleman, 'number,' which emphasizes mental arithmetic and comprehension! What you're doing now with these logarithms and sliding rulers—these are just clever tricks! They're making students lazy! In the future, without a ruler, they won't even know how to do multiplication!"
Wang Jianguo stood on the podium, looking at this stubborn old Confucian scholar.
"Doctor, you're right. Tools do make people 'lazy.' But it's precisely because of this 'laziness' that humans invented the wheel, the steam engine, and the telephone."
"Our brains should be used to think about 'why' instead of wasting time on boring 'equals' questions."
Wang Jianguo turned around and drew a curve on the blackboard—the calculus symbol (Integral).
"The sliding ruler is just the beginning. Your Majesty, gentlemen, only when we get rid of tedious arithmetic can we explore the deeper mathematics—to calculate the rate of change, to calculate the area of irregular shapes, to calculate the trajectory of celestial bodies."
"This is the future of Qin mathematics."
The old scholar stared at the strange symbol, opened his mouth, but couldn't utter a word. He felt a profound sense of powerlessness. The wheels of time rolled on, crushing not only the abacus beads but also the old knowledge they were so proud of.
Act VI: A "Challenge" from the Western Regions
Just as the Qin Dynasty was basking in the joy of its "mathematical upgrade," an urgent telegram from the Western Regions (transmitted via a newly established relay station) shattered the peace.
[Zhang Qian's urgent telegram: I have discovered a strange weapon in Parthia. They use a huge torsion spring catapult with an extremely long range and remarkably accurate aim. It is said that... they have a group of scholars from Greece who are using geometry to guide their warfare.]
Ying Zheng looked at the telegram, his brows furrowing slightly.
"Greek scholars? Geometry?"
"Yes, Your Majesty," Wang Jianguo explained, "In the West, that's the birthplace of Euclid and Archimedes. Their achievements in geometry are no less than ours. It seems this is a mathematical war."
Upon hearing this, Xiang Yu suddenly drew the steel ruler from his waist, his eyes blazing with fighting spirit.
"Geometry? Can it stop my sliding-ruler cannon?" Xiang Yu sneered. "Your Majesty, let me take the new cannon and the new ruler to the Western Regions and have a go at those Greeks! Let's see if their compasses are more circular, or if my ballistics are straighter!"
Ying Zheng smiled.
"Granted. Bring along the Mohist School's most elite 'Calculation Company.' I want the Westerners to know that Eastern mathematics can not only calculate, but also predict fate—their fate!"
Epilogue: Ruler and Sword
Late at night, in the Imperial Study.
Ying Zheng toyed with an exquisite ivory sliding ruler. It was specially made for him by Wang Jianguo, and it was engraved with Qin seal script.
"Little G".
[Yes, Brother Zheng.]
"Tell me, which is more powerful, this ruler or my Tai'a sword?"
Brother Zheng, the Tai'a sword can sever an enemy's head, but the sliding ruler can measure the world. The sword is an extension of force, the ruler is an extension of wisdom. In this industrial age, wisdom is often more deadly than force.
"Measuring the world..."
Ying Zheng stood up and walked to the huge world map.
He picked up a sliding ruler and measured the distance from Xianyang to Rome on the map.
"Sizzle—"
The sliding ruler made a slight sound.
"It may seem far, but in the eyes of mathematics, it's just a few degrees of distance."
Ying Zheng's gaze became deep and fervent.
"Jianguo is right. To simplify the complex and make the distant tangible. This is the future I want."
He slammed the sliding ruler onto the map, as if he had struck a stabilizing force.
"Issue the order to classify the 'Great Qin Logarithmic Table' as a top-level state secret. At the same time, promote the use of the sliding ruler in schools throughout the country. I want every child in Great Qin to hold this key to unlocking the future in their hands."
Outside the window, moonlight spills onto the newly completed Weihe River Bridge, its steel trusses gleaming coldly in the night. It is a monument built of numbers, silently proclaiming the arrival of a new era that no longer needs abacuses.
Meanwhile, in the nearby treasury, Zhao Gao was fretting over a pile of obsolete old abacuses:
"So many beads... why don't we string them together into a necklace and sell it to the Xiongnu? Tell them these are the 'Wisdom Beads' of the Great Qin Dynasty, and that wearing them will make you smarter?"
"Tsk, let's do it!"