Chapter 122: National Destiny in Mathematics, the Strategy to Topple a Kingdom

“In fact, the knowledge in this world can roughly be divided into two kinds: one is metaphysics—the doctrines formed by ancient sages through subjective speculation about the origin of the world. The other is the study of the laws governing things through the phenomena observed in nature.

If we use the cultivation methods of our Daoist priests as an analogy, Laozi’s Tao Te Ching represents the former, while our alchemy belongs to the latter.

The former is the Way; the latter is the Technique.

If we apply this logic to Confucianism, the Four Books and Five Classics left by the Sage Confucius embody his understanding of the Way—how to govern the country.

Successive emperors have revered Confucius and practiced his Way. I cannot say that there is no merit in this.

But, Uncle, have you noticed something missing in the way talent is selected?”

“Technique!”

What Zhang Yi wanted to guide Zhu Yuanzhang and Zhu Biao to understand was precisely this.

When the Zhu father and son answered, he nodded:

“That’s right. The upper echelons of the Ming Dynasty, or rather the ruling class of Huaxia since ancient times, have always emphasized the role of the Way but neglected the minor techniques. They fail to realize that Technique is like the relationship between knowledge and action. Some say knowledge must precede action—that’s reasonable. Others say knowledge and action must be united—that’s also reasonable.

What’s truly problematic is knowing without doing. Since the establishment of the imperial examination system, for most of the time, talent selection has been all about the Way but devoid of Technique.”

“Here’s a copy of Sun Tzu’s Art of War—can you lead troops with it?”

Zhu Yuanzhang shook his head.

Zhang Yi continued:

“Is there any book that can make Brother Huang a merchant like you by tomorrow?”

Zhu Yuanzhang shook his head even more emphatically.

“That’s the point. These things are absent in the Four Books and Five Classics, absent in the Tao Te Ching, and absent in Sun Tzu’s Art of War. These books offer high-level, overarching explanations attempting to reveal the essence of a certain field. Very few people can apply what they learn from them.

For some, a book like the Art of War is less practical than detailed manuals on training soldiers, arranging formations, or marching—these little details are more beneficial.

The imperial examination is no different.

The exam cannot select only geniuses. Most people who pass enter regional positions and have to start learning from scratch.

Those who learn well naturally become competent local officials; those who don’t become parasites in the court.

These costs must be borne by the government.

But if the government, before the exam, incorporated Technique as a necessary criterion for assessment,

Wouldn’t it be possible to filter out those who can only memorize dead texts? The remaining candidates, while not all perfect talents, would at least reduce the government’s hidden costs!”

“But why mathematics?”

Zhu Yuanzhang was intrigued by Zhang Yi’s reasoning and eagerly asked.

“Because mathematics is the root of Technique. We can’t expect candidates to know everything, but we can use mathematics to eliminate those with poor learning ability.

Principles can be memorized, but mathematics doesn’t lie. You either understand it or you don’t.

To master mathematics, logical ability is crucial. Those who only memorize dead texts will find it difficult to pass this test.

Moreover, adding mathematics to the imperial exam has an advantage: it belongs to the minor ways and won’t trigger disputes over the Way.

Scholars might quarrel over whether knowledge precedes action or whether the two are united; Mr. Xu might even advise the emperor against certain policies for political reasons—but it’s unlikely they’d argue over mathematics.

Since mathematics is Technique, not the Way, there’s no dispute, yet for selecting talent, I believe it’s even more cost-effective than the Four Books and Five Classics themselves!”

“Is mathematics really that important?”

This field was indeed not the strong suit of the Zhu family, so Zhang Yi’s suggestion was met with some resistance.

Zhang Yi shook his head. The Huang family father and son were merchants, arguably the people closest to mathematics in daily life.

Yet even they were skeptical about introducing mathematics into the imperial exam, which speaks volumes about the decline of mathematics in ancient times.

Not that it had truly declined. There were significant studies in mathematics during the Song and Yuan dynasties alone: methods for extracting square roots and fourth roots, formulas for summing higher-order arithmetic series, approximate formulas for the length of bow-shaped arcs, equations with negative coefficients, solving higher-degree polynomial systems, advanced interpolation methods, and so forth.

Though these achievements might be impressive by later standards, they were not highly regarded in mainstream society. Mathematics was merely a toy for geniuses.

“Let me give you an example: using mathematics to calculate the fate of the Ming Dynasty…”

The phrase ‘fate of the nation’ startled the Zhu father and son.

Zhang Yi was usually reserved and seldom spoke of such weighty topics, but today he spoke up of his own accord.

Calculating the fate of a nation using mathematics was unheard of; the Zhu family soon forgot their initial purpose and were drawn into Zhang Yi’s discourse.

“Let’s set aside the princesses for now. The current emperor has seven sons. Excluding the crown prince Zhu Biao, the remaining six are future princes. Given the emperor’s indulgence, it’s not unreasonable to grant each prince an annual stipend of 20,000 shi of grain.”

Zhu Yuanzhang nodded; in fact, he intended to grant his children far more than 20,000 shi of grain.

Zhang Yi continued:

“That means, assuming the emperor has no more children, these six princes alone require 120,000 shi of grain annually—not a large amount.

Now, suppose each prince has five children. The third generation of the Zhu family would number thirty descendants.

The dukes, receiving less than the princes, say 5,000 shi each, would cost the government 150,000 shi annually for thirty dukes.

Zhu Yuanzhang and Zhu Biao frowned. Zhang Yi’s calculations thus far were not exaggerated; the royal clan’s annual consumption of 270,000 shi was not a huge fiscal burden.

But as Zhang Yi pressed on, Zhu Yuanzhang grew increasingly uneasy.

“Assuming dukes continue to have five children each, the fourth generation would number 150. If each receives an income of 3,000 shi, that’s a total expenditure of 450,000 shi.”

“The fifth generation, 750 members, at 2,000 shi each, would require 1.5 million shi…”

“The sixth generation, 3,750 members—at this point, I don’t even know how to calculate further, but we can imagine the seventh generation would reach 18,750…”

“Stop calculating!”

Zhu Yuanzhang was overwhelmed by the flood of numbers Zhang Yi laid out. Though he didn’t fully grasp Zhang Yi’s method, hearing these figures made him realize that trouble was imminent.

Though Zhang Yi’s assumptions were not entirely realistic—no royal clan member would have exactly five children, and not all would survive—the underlying principle chilled the emperor.

Zhang Yi had based his math on six children, yet Zhu Yuanzhang’s lifetime would certainly involve more than six.

If the number of children doubled, the emperor dared not imagine how the court could possibly cover the clan’s expenses.

Currently, the Ming government’s annual revenue did not exceed twenty million shi of grain.

These twenty million had to cover military expenses, officials’ salaries, government operations, disaster relief, and myriad other expenses, leaving little surplus.

Zhu Yuanzhang’s expression darkened. Though he had conquered the realm, his dream of providing his family with a comfortable life was but a fool’s hope.

His simple, peasant dream had shattered.

Before he could even bestow princely titles upon his children, Zhang Yi mercilessly destroyed his illusions.

“Looks like Uncle Huang also understands the power of mathematics…”

Zhang Yi paused, smiling faintly at the dazed Zhu Yuanzhang. Zhu Biao was no better.

They had coaxed Zhang Yi to learn more about matters concerning the Ming Dynasty, but when he truly revealed the truth, they found it unbearable.

Moreover, Zhang Yi’s revelation was not some vague prophecy or divine scripture.

It was merely a simple mathematical problem.

But cruelly, calculating the fate of the Ming with mathematics cut deeper than any mystical revelation.

“So, if the emperor grants titles to the royal clan as you hypothesize, it will become the foundation that drags down the Ming Dynasty?”

“This isn’t an ‘if’…”

Zhang Yi chuckled. Zhu Yuanzhang and Zhu Biao exchanged troubled glances.

Not an ‘if’—Zhang Yi was essentially saying this is the inevitable future.

Zhu Biao stared at his father, seeing his intense reaction and understanding his thoughts.

“Mathematics never lies. That’s why it’s the source of all Technique. An official governing a territory on behalf of the emperor faces countless calculations daily.

And the Ministry of Revenue, which manages the empire’s finances, relies heavily on the official’s mathematical proficiency to determine work efficiency.

Even the emperor himself, if versed in mathematics, won’t be easily deceived by the accounts presented.

Yet, our talent selection system has long excluded this vital component.

Granted, many who pass the exams later learn mathematics anew to manage local affairs or serve in ministries like Revenue or Works.

But throughout history, those who pass the exams in their teens are rare; those in their twenties common; and those over thirty dominate the ranks.

If such men marry early, they become grandfathers within a few years. Can we expect them to make progress in mathematics then?

Mathematics should be taught from childhood.

Therefore, if I were to propose reforms to the imperial exam, I would definitely include mathematics!”

Zhu Yuanzhang lowered his head, seriously considering the matter. Without Zhang Yi’s mathematical calculation of the nation’s fate, he would never have held such high regard for mathematics.

The Way and the Technique.

Throughout the long history of Huaxia, the Way has always been exalted, and the Technique belittled.

Yet, when applied skillfully, Technique can accomplish feats rivaling those of immortals and deities.

“Your eyes deceive you; your ears deceive you; even your loved ones, your wife, can deceive you—but mathematics never will, because you either understand it or you don’t.

This is the difference between Technique and the Way. The Way is the sages’ understanding of the world; they try to explain the essence of the world through their insights.

Thus, there is Confucius with the Analects, Buddha attaining enlightenment under the Bodhi tree and passing down the sutras, Laozi exiting Hangu Pass to leave behind the five thousand words of the Tao Te Ching.

Even in later times, our sect’s founder realized the Way through the Tao Te Ching, founding the Five Pecks of Rice Daoism; Bodhidharma established Chan Buddhism; and Cheng and Zhu’s Neo-Confucianism emerged to revive Confucianism’s decline.

The so-called Way is the sages’ attempt to explain the world’s essence.

But have we ever considered whether the Way they explain is necessarily the absolute truth?”

Zhang Yi tentatively posed the question. Zhu Yuanzhang and Zhu Biao stared intently at him.

What did this young man mean by such words?

Was he questioning the sages’ teachings?

That would be heresy!

“What, then, is Technique?” asked Zhu Yuanzhang.

(End of chapter)