Embers of the Broken River

People after Chapter 18

After that, no one mentioned Wang Shi again.

The list of menial workers had changed to a new page. The new worker, surnamed Chen, always pointed the kettle spout at the stove wall when boiling water. Every time Jia Xian reached for the kettle, the handle was always in the wrong direction. Chen didn't say anything and simply turned the kettle around himself.

The rubble on the ruins of the west corridor was cleared away, and a row of bamboo sheds was temporarily erected on the spot to serve as a storeroom. The charred brick fragments were piled in the corner of the yard, covered with a layer of frost. A few days later, the frost melted, and a very faint burnt smell began to seep out from the cracks in the bricks.

Every time Jia Xian passed that pile of broken bricks, he would slow down. It wasn't intentional; his feet remembered the location of that particular brick. The sixth brick had a hollow spot underneath, and stepping on it would produce a dull thud. That brick had been cracked by fire and replaced with a new one, which felt hard and made a different sound when walked on.

He stood by the ruins several times. Once, he saw a piece of burnt blue brick, covered with dried tea stains, shaped like a withered leaf.

He recognized it as the brick Wang Shi had stepped on when he carried the tea tray. That day, he stepped on the sixth brick while carrying the tea tray. Later, he walked through the corridor several times and counted the bricks. He found a diagonal crack between the fifth and sixth bricks, which had been run over by a donkey cart, when he came out of the side door.

He measured the crack with the sole of his shoe, confirming it was here. The crack was still there, but the brick was broken. He picked up the broken brick, wiped it on his sleeve, and stuffed it into his pocket. That spot already held manuscript paper, wooden plaques, tattered old manuscripts, and his father's "center of gravity," and now there was a broken brick. It was light, but it hurt terribly.

A few days later, the transfer order came down.

It wasn't dismissal, it was exile. He was transferred from the Chongtian Division to the Astronomical Observatory to do odd jobs, and all the night shifts that others didn't want to do were assigned to him.

His colleagues were not surprised by this arrangement: it was already merciful that a mad official who had almost had his manuscripts burned by his superiors and was almost burned to death in the archives could still stay in the yamen.

Registrar Lu inquired about it for him and said that the transfer order stated "temporary assignment," meaning that he might be able to return after a while. Jia Xian didn't ask any further questions; he simply packed up the calculations and the wooden plaque, and left with his old trunk on his back.

The astronomical observatory was located on a high hill in the north of the city. Its courtyard was much smaller than that of the Chongtiansi (a military command), with only two guard rooms and an observation platform. On the observation platform were bronze instruments and armillary spheres, exposed to the wind and sun without anyone's care. A layer of green rust had formed on the bronze rings of the armillary spheres, and they creaked when they turned.

He was the only one on night duty. Every night, he would refill the oil lamp, sit by the window, and gaze at the streets and alleys of Bianjing and the flowing waters of the Bian River. In the deep of night, he could hear the watchman striking the gong, one strike after another, as if counting the breaths of the city.

He drew triangles with his finger on the dust on the windowsill.

He expanded layer by layer. After finishing one layer, he erased it and started drawing again. This wasn't just killing time; he was etching his questions into his very bones. As his fingers brushed against the dust on the windowsill, they felt cool and smooth, a completely different sensation from the counting rods he used to lay out on the desk at the Chongtiansi Bureau years ago, yet the numbers were the same.

The first layer is 1, the second layer is 1-1, the third layer is 1-2-1. When he gets to the seventh layer, his finger pauses for a moment; he's pushed that layer countless times, and he can draw it with his eyes closed. He's still trying the eighth layer; he hasn't fully pushed it out yet, but he's not in a hurry.

During his night shift at the observatory, he used a triangular diagram he had rescued from the fire and his own recursive method to calculate the date of the solar eclipse for the following year.

The result was one day more accurate than the official prediction from the Imperial Astronomical Bureau. The Bureau used the old method, which employed a recursive approach that nested the three variables—eclipse limit, lunar velocity, and solar longitude—within a set of higher-order equations to approximate the eclipse step by step. The old method only considered two variables.

He verified it three times. The first time, he used the measured data of the winter solstice of the fourth year of Chongning from the old and incomplete records he brought out from the fire as the starting point. The second time, he used the lunar eclipse record of the first year of Daguan to correct the long-term deviation of the moon's orbit. The third time, he used the data of the conjunction of the five planets in the seventh year of Zhenghe to back-calculate the perturbation of the sun's ecliptic longitude.

The results of the three verifications matched each other, so the difference on that day was not a typo, but a problem with the algorithm itself.

He wrote the result on a piece of paper and folded it.

Then, instinctively, he reached out to hand it to the person next to him, but found no one there. The only people in the duty room were himself and his shadow on the wall. He paused, his hand still in mid-air, then put the paper in his pocket.

That night, he sat by the window and reached into his sleeve to feel the wooden plaque. From that day on, he developed a habit: he would fold up the calculations and put them in his pocket, keeping them there forever. He didn't know who to show them to, but he always kept them. Because he believed in "people in the future."

During the night shifts at the astronomical observatory, he would visit secondhand bookstores during the day. There were several secondhand bookstores in the back alleys of Bianjing's Horse Market Street, and he would browse through them with his meager monthly salary. If he couldn't afford to buy a book, he would squat on the ground and look at it.

Once, he came across a handwritten mathematics notebook. The signature had been crossed out with ink, but judging from the handwriting, it was probably left by a former mathematics official of the Chongtian Division. The pages had several holes from insects, but it was still legible. He took the notebook home with him and read it by the window by the light of an oil lamp all night.

One page in the notebook contained data on solar eclipses observed in a certain year and month, with a tiny note next to it: "Keep these numbers for future calculations."

Jia Xian ran his fingertip over the line of text; the characters had faded to almost nothing, but the brushstrokes were still there. He hadn't signed it; he had simply tucked the page into his own calculations.

Time passed slowly at the observatory. Sometimes, when he was on night duty, he would stand on the observation platform and watch the Bian River flow from north to south below. The sound of the water was very distant, mixed with the sound of the wind, and could not be heard clearly.

He felt that the river came from a very far place and went to a very far place, passing through this city, through this government office that had been burned down, and through the window where he was on night duty.

The river doesn't care who watches it. Just like those numbers, pushed out, folded, and put in its pocket, it doesn't know who will push them next, but they will flow on. Even if someone thirsty takes a sip and doesn't recognize who's upstream, the water is still alive.

Jia Xian didn't know where he would die. He only knew that the folded papers in his pocket would tell future generations: someone had asked these questions, he hadn't finished asking them, but he hadn't thrown them away either.

Years later, his calculations were discovered, compiled, and included in the "Detailed Draft of the Nine Chapters on the Yellow Emperor's Mathematical Methods." The manuscript was signed by someone else—the compiler, a person with an official rank in the Imperial Observatory. Jia Xian's name was not recorded.

However, the triangular diagram he left behind was engraved into a printing plate, and the original manuscript and the old, fragmented copy he salvaged from the fire were later placed in the same box by others.

He died unaware that his wooden plaque had been unearthed.

The person who turned over the wooden plaque was surnamed Qin and named Qin Jiyou. In the archives of the Imperial Observatory, he found a stack of burnt manuscripts. The edges of the manuscripts had scorch marks, and on the paper, a triangle made of numbers was drawn with charcoal, from the first layer to the seventh layer. Next to the seventh row, there was a scorch mark that had been wiped across the paper without touching any numbers.

Tucked inside the tattered manuscript was a small wooden plaque with the characters for "triangle" carved on it. Qin Jiyou didn't understand mathematics, but he recognized the two characters and could tell that the carver's knife skills were not strong, but the force was deep; each stroke seemed to be pressing something down hard with the last of their strength. He put the wooden plaque and the tattered manuscript into a box and took them back to his hometown in Sichuan.

Years later, his son, Qin Jiushao, opened the box at his mother's grave. The triangular diagram wrapped in oiled paper had yellowed, but the numbers were still there. Next to it was a wooden plaque, made of old locust wood, its rough edges worn smooth by generations of hands.

Jia Xian died at his post as a handyman at the astronomical observatory. Before he died, he touched his chest, where there were scorch marks from manuscripts, splinters from wooden plaques, and sharp edges from broken bricks. The three things were stacked in the same spot. He had covered his chest with his own weight.

The last habit he developed while on night duty was to fold up the calculated date of the solar eclipse and place it on the corner of the table—not in his pocket, but on the corner of the table—so that others could see it when they came in. Later, he died.

Someone came in to clean the duty room and saw a piece of paper on the corner of the table. They opened it, looked at it, but couldn't understand it, so they put it back. The paper remained there, splashed again and again by raindrops blown in through the window, and the ink gradually seeped in.

Then one day, a janitor who took over his night watch swept the paper into the bamboo basket along with other scraps of paper. Those papers were never left behind. But someone had already seen them. Each generation of people sitting in this watch room would draw a few numbers on the dusty windowsill with their fingers, like a ritual that didn't need to be remembered.

The Bian River has flowed for a thousand years outside the window. As the night deepens, a few fishing lights float on the river, their dark red glows rising and falling on the ripples, like oil lamps without shades lit at the bottom of the river. His questions were tucked away in his pocket for a lifetime, passed down from generation to generation, warmed by the palms of their hands.

The man who took the weight from his chest had already opened his father's old box at his grave in Sichuan. Under the oil lamp, he was smoothing out the yellowed pages, watching the numbers, which had been wiped clean by scorch marks and traced by him, pile up into the seventh layer.

He himself will only be a line skipped in history books. It doesn't matter. The river doesn't care. The river never asks the name of the person scooping up water.