To Li Shimin, the memorial submitted by Fang Xuanling and Du Ruhui could only be described as meticulous.
Judging purely by his own level, the mathematical skill displayed inside was already bordering on the unfathomable. Fortunately, the final conclusions were clear enough that, after prolonged contemplation, he could still grasp them.
The two ministers had first listed the household figures of Huxian during the former Sui dynasty, recording them once every five years. From this, they constructed a complicated formula, calling it a "calculation model", and named this step "extracting the cause".
The second step used the household numbers from the first year of Wude, applying that same model to calculate Tang dynasty household growth in Huxian. This step was called "verifying the result".
The calculated figures were placed on the left, while the Ministry of Revenue's actual recorded household numbers were placed on the right. Compared side by side, the differences existed but were not large. This alone left Li Shimin deeply shaken.
Of course, this calculation could not be perfectly accurate. The household registration systems of Tang and Sui differed in many ways, and Yang Guang and Li Shimin held completely different attitudes toward uncovering hidden households.
Still, it offered at least one thing.
A glimpse into the future.
On the memorial, the Ministry's official household figures stopped at the fourth year of Zhenguan. Beyond that, the page was blank. Yet the numbers calculated through mathematics continued marching forward without pause.
Even more considerately, Fang Xuanling had listed the amount of farmland each household would possess alongside those future figures.
According to this projection, a hundred years later, the people of Huxian would each possess only twenty mu of good land per household.
Twenty mu was enough to raise one son and one daughter. If the uncountable factor of land annexation was added into the equation, the outcome would only look worse.
And what was a hundred years later.
It was the collapse of High Tang.
The emperor fleeing.
Chang'an falling again.
Princes and nobles turning on one another.
Elite troops dying in internal chaos.
Commoners dying beneath Tang blades.
An emperor promising that Chang'an itself could be plundered.
It was a stretch of history Li Shimin found nearly impossible to imagine. Yet now, through a rough and imperfect calculation by his two chancellors, he was peering at a corner of that future's livelihood.
The hundred years of Tang splendor were dazzling beyond measure, yet they seemed to have little to do with the water that bore the boat.
In the end, those gentle waters of the people transformed into raging waves, overturning the great vessel of Tang.
Empress Zhangsun listened quietly as the emperor spoke. She watched as his expression shifted between heroism and grief, until finally his ambition drew inward, as though a new goal had taken shape.
"If that is the case," she said softly, "then the Crown Prince should also understand some mathematics."
Li Shimin agreed. His only hesitation was whether Fang Xuanling would be willing.
After settling that matter briefly, Empress Zhangsun asked with curiosity, "When Your Majesty previously asked how many children common households usually have, was it for this reason?"
Li Shimin sighed again and shook his head.
"Xuanling and Kemin, while calculating household numbers, also calculated the growth of mouths within a single household."
Explaining it with words was cumbersome, so Li Shimin simply issued an order on the spot. He had attendants cut tree branches into finger-length sticks and bring in two large armfuls.
Pointing at the pile, Li Shimin smiled.
"If one stick represents one person placed on the ground, how many generations of descendants do you think these sticks could form from a single household?"
The description was vague, but Empress Zhangsun understood. After estimating for a moment, she replied uncertainly, "Perhaps enough for more than ten generations?"
At that, she saw Li Shimin burst into laughter, laughing so hard that she could not understand why.
The attendants quickly began arranging the sticks as instructed. At the top, they placed one pair to represent the first generation. Beneath it, they placed three pairs to represent the second generation.
Then they repeated the process, placing three pairs beneath every pair.
As the arrangement expanded, Empress Zhangsun's eyes slowly widened in shock.
Li Shimin gazed at the sticks with a look of awe, recalling the words written by Fang Xuanling in the memorial.
"Examining the records of the Ministry of Revenue, taking one household becoming three as the base, a hundred years of peace can pass five generations. Thus one household may become a hundred households. Later generations call it infinite. I believe the term is fitting."
Fang Xuanling had also offered his advice.
"If the state is not to grow strong while the people grow poor, one must measure farmland to fix household limits, and imitate the empire named England in the far west of later generations, opening the seas to release surplus labor."
Beyond the hundred-year mark, Fang Xuanling had also calculated further figures. Li Shimin remembered those immense numbers clearly.
The sixth generation exceeded two hundred households.
The seventh exceeded seven hundred.
The eighth surpassed two thousand.
The ninth reached over six thousand.
The tenth approached twenty thousand.
These calculations were idealized. They did not account for disease, disasters, land annexation, or sudden war.
Yet Li Shimin understood even more clearly that the more peaceful an era became, the fewer such accidents would occur, the faster population would grow, and the heavier the burden on land would become, eventually triggering the end of a dynasty. Calling it a trap was entirely appropriate.
Moreover, commoners suffered from these forces, while aristocratic clans could continue producing large numbers of descendants even during national decline, those descendants occupying far more land than ordinary people.
At this thought, Li Shimin could not help recalling Zhuge Liang, who had once watched the light screen with them, and his lord Liu Bei.
Liu Bei's ancestor, Prince Jing of Zhongshan, Liu Sheng, was the perfect illustration of these numbers.
Although many of his descendants had fallen into obscurity, there was already a saying among the people that half of the Liu clan today traced their ancestry back to that Prince of Zhongshan.
Thinking of Emperor Zhaolie and Zhuge Liang, Li Shimin grew curious.
With the light screen's help, and with the barbarians already crushed, surely by now they had watered their horses at the Gobi Sea and reopened the Western Regions.
He decided to ask the next time the light screen appeared.
Empress Zhangsun also silently resolved that while she did not require her sons to master mathematics, they at least had to understand it.
The memorial of Fang and Du had shaken Li Shimin deeply. The most immediate consequence was that, in the twelfth month as the fourth year of Zhenguan neared its end, the emperor issued an edict further strengthening maritime policy.
Officials naturally cried out in misery. The year's end was already busy enough. Issuing new orders at such a time was one thing to hear about, but another to bear personally. It threatened to ruin even the ten days of New Year rest.
Complaints aside, the policies still had to be carried out. Yet this maritime reform instead thrilled the Shandong sea merchants.
Previous policies had focused only on shipbuilders and sailors. This new decree, unprecedented in history, introduced official ships leased to civilians.
Commoners could form their own crews and travel to Dengzhou or Laizhou to rent government ships. In the first year, they had to serve assigned routes under the direction of the local naval forces.
After one year, if they passed inspection, they could sail freely. Each return voyage required only that forty percent of the cargo be turned over to the navy.
The great Shandong clans scoffed at this. The risks of going to sea were far too high. How could it compare to forcibly seizing land.
But to the coastal commoners of Shandong, this was irresistible.
Perhaps because of the obvious tilt of maritime policy, when the New Year celebrations ended in the twelfth month, Li Shimin could sense that the envoys from the Western Regions were harboring mixed thoughts.
Those who dominated the region felt relieved that Tang seemed to be turning its gaze overseas and might not spare attention for them, like Gaochang.
Smaller states hoping for Tang support feared that Tang's disinterest would leave them without backing, like Kucha.
Li Shimin had no interest even in coldly observing these reactions. After the busy New Year passed, he simply retreated to the inner palace, spending time with Guanyinbi and strengthening bonds with his children.
Then, early on the morning of the third day of the first month, Li Shimin eagerly headed to Ganlu Hall and issued summons to his key ministers still in Chang'an.