To Li Shimin, the memorial Fang Xuanling and Du Ruhui turned in was a masterpiece of sharp thinking and hard work. The math inside was so far beyond his understanding that Li Shimin half suspected it might have been scribbled by an immortal.
The good news was the final conclusions were simple enough to follow. He just needed a minute to let the full horror sink in.
The two Chancellors started by laying out the raw census numbers for Hu County, recorded every five years back under the Sui dynasty. They used that history to build a complex mathematical model, or an algorithm as the Lightscreen called it.
This first step they named finding the cause.
Next, they plugged the starting numbers from Wude Year One, 618 AD, into the same model to project how Hu County's population would grow over time.
This step they called verifying the result.
The projected numbers sat neatly on the left side of the page while the Ministry's actual census data filled the right.
Lining them up side by side hit Li Shimin like a punch to the chest.
The gaps between prediction and reality were so small, almost nothing, yet the model was so frighteningly accurate it left him shaking inside.
Of course the math was not perfect.
Sui and Tang registered households in different ways.
Emperor Yang Guang had chased hidden households with wild aggressive drive while Li Shimin's approach was far more measured. Even so, the results were close enough to give him a genuine, clear look at what lay ahead.
On the memorial, the real data cut off sharply at the current year, Zhenguan Year Four, 630 AD. The rest of that column stood blank, waiting for years that had not yet come.
But the projected figures on the left kept marching forward, steady and unstoppable, year after year, decade after decade.
Fang Xuanling had thoughtfully added a third column right beside them.
It calculated exactly how much fertile land each household would have for every year the model covered.
In Tang census records, a household meant a whole family living under one roof, usually five to seven people including parents, children, and sometimes grandparents. So when the model talked about land per household, it really meant land to feed a family of that size.
The numbers were brutal. They laid it out plain: exactly one hundred years from now, the people of Hu County would be left with barely twenty mu of good land per household. Twenty mu was only just enough to keep two adults from starving, let alone a family with several children. And that was before counting how wealthy families swallowed up small plots one by one, a messy chaotic force pure math could never fully pin down.
Add that in and the true picture would be far worse.
What waited for them a hundred years down the line? Nothing short of total disaster: the High Tang crashing down in ruins. The Emperor running for his life. Chang'an falling again and again to foreign invaders. Princes and nobles tearing each other apart in endless civil wars. The empire's best troops butchering one another. Commoners cut down by their own soldiers. An Emperor promising foreign mercenaries the right to loot Chang'an just to buy their help.
It was a nightmare Li Shimin could barely wrap his head around.
Yet here, through nothing more than careful math, he finally saw clearly just how desperate the common people's lives would be when that time came.
The High Tang would enjoy a century of unmatched splendor and wealth. But all that glittering abundance seemed to have nothing to do with the very people who held the empire up.
And so in the end, those gentle hardworking folk would turn into a roaring tide that capsized the great ship of state.
---
Empress Zhangsun sat beside him listening as he explained everything. She watched his mood shift from grand ambition to deep sorrow before settling into a burning determination. He had clearly locked onto something huge.
"If this is how things are, then Chengqian must learn at least some mathematics," she said. Her instincts as both mother and stateswoman spoke at the same time.
Li Shimin nodded slowly.
"I agree completely. Chengqian needs to understand mathematics," he said, a faint smile tugging at his lips. "Though I do wonder, will Fang Xuanling really be willing to take on the headache of teaching the Crown Prince?"
"Husband, you simply must persuade our loyal Fang Xuanling," Empress Zhangsun said, her tone gentle but firm. "You do not want our son being swindled by schemers or manipulated by crooked ministers, now do you?"
"Fair point, fair point. I will handle it, Guanyinbi."
Once that was settled, the Empress looked over, curious. "So when you asked me earlier how many children a family might have, were you already thinking about all this back then?"
Li Shimin let out a heavy sigh and nodded slowly.
"While working out the population numbers for Hu County, Xuanling and Ruhui also calculated exactly how fast a single family can multiply over time," he said.
He paused, realizing that trying to explain all that in words would take far too long and only leave her confused. So he raised his voice and gave a quick order.
"Send someone out to cut small branches into sticks the length of a finger. Bring back two full armfuls."
A short while later, the eunuchs returned with two armfuls of fresh-cut sticks and set them in a pile on the floor.
Li Shimin looked at the heap and turned back to his wife with a faint smile.
"I will show you exactly what they meant."
Li Shimin pointed at the pile and gave a faint smile.
"Imagine one stick stands for one person. Guanyinbi, how many generations do you think this pile could represent?"
The meaning was vague, but the Empress grasped the general idea. She looked the pile over and guessed carefully, "More than ten generations, I would think?"
Li Shimin laughed.
The eunuchs set to work. At the very top they laid one pair of sticks for the first generation, husband and wife. Below that they placed three pairs for the second generation, three sons each with their own wife. Under each of those they laid another three pairs. They kept going down the line, and the shape of a pyramid began to spread across the floor.
The Empress's eyes went wide with shock.
Li Shimin watched the ever-growing pyramid of sticks and thought of what Fang Xuanling had written in the memorial.
"Reviewing the records of the Ministry of Revenue, we see one household can expand into three households with each generation. Given one hundred years of peace, that allows five generations to pass. In that time, a single household can multiply into more than one hundred. Future generations call this infinite growth, and this humble subject believes the name fits perfectly."
Fang Xuanling had gone on to offer a bold suggestion that could change the course of history.
"If we do not wish to see the state grow rich while the people starve, we must set strict limits on population based on the land available. We should also look to the future western empire known as Britain and open the seas to send our surplus people outward."
Fang Xuanling had also calculated the numbers past the hundred-year mark. Li Shimin remembered them all too clearly.
The sixth generation would reach two hundred households. The seventh would hit seven hundred. The eighth would climb past two thousand. The ninth would top six thousand. The tenth would approach a staggering twenty thousand.
These were ideal figures, of course. They ignored plagues, famine, natural disaster, land grabbing by the powerful clans, and sudden war. But Li Shimin understood the grim truth even better than the numbers showed: the more peaceful and prosperous the era, the fewer such disasters would come along to thin the population. So the people would multiply even faster until the land could no longer hold them, and the dynasty would break under the strain. Trap was exactly the right word.
Worse still, while ordinary folk would be worn down by hardship, the imperial clan and the high nobility would keep spreading their lines even as the state fell apart. Their descendants would take more and more land for themselves and drag the whole system to ruin that much faster.
Thinking of this, Li Shimin could not help but recall Zhuge Liang and Liu Bei, who were also watching the Lightscreen, though in their own separate time and place.
Liu Bei's famous ancestor Liu Sheng, the Prince Jing of Zhongshan, was the perfect example of those scary numbers in action.
A lot of his descendants ended up poor and unknown, but people these days joked that half the men surnamed Liu walking around could trace their blood straight back to that one Prince who just kept having kids.
Thinking of Emperor Zhaolie and Zhuge Wuhou, Li Shimin wondered what they were up to right now. With the Lightscreen giving them a peek at the future and the northern tribes surely crushed by this point, they must have already pushed their armies far into the northern wastes and reopened the Western Regions.
I will have to ask about it the next time the Screen shows their side of things, he told himself.
Meanwhile, the Empress had made up her mind. She did not expect all her sons to become math geniuses, but every single one of them would learn the basics of this vital knowledge, even if she had to use family law to make it happen.
---
Fang Xuanling and Du Ruhui's memorial shook Li Shimin's whole view of the world to the core. The first big change came in the twelfth lunar month of Zhenguan Year Four, early 631 AD, when the Emperor dropped a sweeping decree to completely overhaul the empire's maritime rules.
The officials groaned loud enough to rattle the palace walls. The end of the year was already a total paperwork nightmare. A new decree was bad enough, but if all the extra work landed right on their own desks, their ten-day New Year holiday was as good as gone.
No amount of complaining could stop the decree from going live. And while the bureaucrats moaned, the sea merchants around Shandong were absolutely over the moon.
All the old maritime rules had only cared about drafting skilled shipbuilders and experienced sailors. This new law brought something nobody had ever seen before: regular commoners could actually rent state-owned ships.
Ordinary people could gather their own crews, head straight to Dengzhou or Laizhou, and lease vessels right from the government. For the first year they would sail on official missions assigned by local naval commanders. If they passed the review after twelve months, they were free to sail anywhere they wanted for private trade. The only catch was handing over forty percent of their profits to the navy every time they came back.
The powerful Shandong noble clans turned their noses right up at the idea. Going out to sea was dangerous and unpredictable. Why bother with all that risk when buying up farmland from the poor was safe and made endless amounts of money?
But for the poor folks along the coast, this was nothing short of a miracle come true.
With the empire's gaze turning firmly toward the oceans, the Western Regions envoys in Chang'an wore polite smiles but hid very different thoughts underneath. Expansionist states like Gaochang quietly cheered, hoping the Great Tang was shifting its full strength to the waves and would leave them alone. Smaller bullied kingdoms like Kucha prayed the Tang would not lose interest in the west, because without the empire's protection they were finished.
Li Shimin could not have cared less what any of them thought. Once the exhausting New Year ceremonies were finally done, he retreated deep into the palace to spend some time with Guanyinbi and his children.
Early on the third day of the first lunar month, he hurried straight to the Ganlu Hall and fired off urgent summons for all his top ministers currently in Chang'an.