“Yes, tai-tai. It was an important dream. I dreamed I'd discovered how to do a Magic Square.”
He looked at me in the hopes my expression would change, but I didn't move a single muscle.
“Not the big Magic Square, of course,” he quickly clarified. “The small one, the path-of-energy one that appeared on the tortoise shell.”
“And when you woke up, you knew how to do it?” I asked coldly.
“No, tai-tai. It was just a dream. But it gave me an idea: If we can discover the mathematical trick for the small Magic Square, the three-bythree one we already know, then we can use that to solve the big one, the nine-by-nine.”
“And how many pages of my sketchbook have you ruined trying to decipher that puzzle?” I asked pointedly, having noticed a handful of crumpled pages on the floor.
“Don't be so harsh, Auntie,” Fernanda reprimanded. “We don't have anything else to write on. You can buy more sketchbooks in Shanghai.”
“But that one's from Paris,” I objected, “and my drawings from the trip are in it.”
“I haven't touched your drawings, tai-tai! I only used new sheets.”
I got out of bed, angry with myself. Who cared about a blasted sketchbook? Enough of this ridiculous possessiveness! All I wanted was another cup of tea.
“Carry on,” I told Biao without looking at him. “I just slept poorly.”
“You should do tai chi,” the antiquarian recommended.
“I certainly hope you did enough to improve your mood,” I retorted. “You've been unbearable ever since we reached the mausoleum. Aren't you moderate and Taoist? That's not how you've been behaving, Lao Jiang, believe me.”
He pursed his lips and lowered his gaze. My niece looked wildly around, and the other two pretended to be engrossed in their mathematical calculations. How awful it is when you don't sleep well! My head hurt.
“Yes, could be …” Master Red said, “but I don't see how you're going to place the numbers that are left over.”
“They're not left over, Master Red Jade,” Biao explained. “Since we already have the result, we know where they go. We need to see if there's any sort of rule that determines where they're placed.”
“Very well then, move the first number down.”
“Yes, but I'll use another color to see if a pattern appears,” the boy said, taking the red pencil out of the open box.
“Now move number nine up.”
“Yes, that's right,” Biao murmured. “Now I'll take the three over to the left and I'll put the seven in the empty box on the right.”
I was curious, and so, a cup of hot tea in hand, I came up behind the boy and looked over his shoulder. He had drawn a rhombus using the nine numbers that made up the Magic Square. That is, he had put number one at the top; underneath were four and two; on the next line, the middle and longest one, were seven, five, and three; on the fourth line were eight and six; and, finally, nine was at the bottom.
“Why did you arrange the numbers like that, Biao?” I asked, not expecting to understand but hoping to get an idea.
“Well, I noticed that in the Magic Square the diagonal that goes from the eastsouth to the westnorth consisted of the four, five, and six. So, following that guideline, I put the one above the two in the westsouth corner and the three below it. I now had two diagonal rows of consecutive numbers, so then I did the same with the seven and nine, putting them above and below the eight in the eastnorth corner. Now I had three diagonal lines of numbers from one to nine. Once I took away the numbers that repeated on the inside of the Magic Square, I was left with this shape—”
“It's a rhombus.”
“—this rhombus that Master Red Jade and I have been studying. We've come to a few conclusions. When you asked, we were putting the numbers back in the Magic Square to see where they came from and whether there's a common rule for this movement.”
“And is there?” I asked, taking a sip of my tea.
“It seems there is, madame,” Master Red replied, “and the most admirable thing of all is its simplicity. If the reverse flow of energy fits, then I think Biao has found the formula for creating Magic Squares, one of the most complicated mathematical exercises there is.”
With a false modesty betrayed by his red ears, Biao drew the rhombus again so I could see the whole process. I smiled at Lao Jiang, thinking I'd find him calm because things were going well. Instead his face was wrinkled in displeasure, his eyes were blank, and his fingers were twirling the silver lighter. I felt a strange, undefined fear. That image of Lao Jiang set off my old neuroses, and my pulse quickened. But the poor antiquarian wasn't doing anything unusual; he was just standing there lost in thought, far away from us all. There was no reason for me to be so afraid. I'd never be free of these sick apprehensions. I'd always have to fight the ghosts called up by my irrational fears.
With every ounce of will, I focused instead on the rhombus of numbers Biao had just drawn.
“Can you see it clearly, tai-tai?” he asked.
“Yes, perfectly.”
“Now I'll draw the borders of the Magic Square over the rhombus. Do you see that?”
Indeed, he enclosed the five middle numbers in a square, as if it were a die: four and two up top, five alone in the middle, and eight and six below. He then added the two vertical and two horizontal lines needed to make a grid with nine squares.
“Do you see what's happening?” he asked nervously.
“Yes, yes. Of course,” I replied kindly.
“Well, now we have to take the numbers that are outside the grid and put them in the empty squares.”
Using the red pencil, he crossed out the one on its own up top and wrote it in the space below the five. Then he crossed out the nine down below and scribbled it in the top space. The three that was on the right he placed on the left, and the seven on the left he moved to the right. There was the completed Magic Square, fully restored and absolutely perfect.
“You see?”
“Certainly, Biao. That's fascinating.”
“The rule is that you move the leftover numbers into boxes along the same line but on the other side of the five, which is the center.”
“Do it again using the Magic Square for the descending path of energy,” Master Red said.
Biao quickly noticed that the diagonal from southeast to northwest, which previously contained the four, five, and six, now consisted of the six, five, and four. That little clue led him to reverse the layout of the numbers in the rhombus, and after that the rest of the process was exactly the same. When he was finished, he had another perfect Magic Square.
“Will you be able to apply that to a square as big as the one on the floor, Biao?” I asked.
“I don't know, tai-tai,” he said nervously. “I hope so. It should work, but we won't know until we do it on paper. There'll be many more numbers from the rhombus that fall outside the borders of the square, and we won't be able to refer to the finished Magic Square to confirm that we're doing it right.”
“Just get on with it,” Lao Jiang ordered as he continued to fiddle with his lighter.
The boy began to write tiny little numbers so they'd all fit on the sheet of paper.
“In the three-by-three Magic Square, the diagonal rows in the rhombus consisted of three numbers. Since this one has eighty-one squares, I'm using nine,” he explained as he continued to write numbers in diagonal lines.
Finally he wrote the number eighty-one in the bottom vertex.
“The middle number obviously isn't five,” he muttered to himself. “It's forty-one. So … if this is the middle, then the borders of the Magic Square would be here, here, here, and here,” he sang softly as he drew the square. “Done!”
He proudly held the sketchbook in the air, and we all smiled. He had enclosed the eighty-one squares in a nine-by-nine grid, with many of the boxes still empty. The absurd idea that Lao Jiang adopt Biao no longer entered my mind. The antiquarian would be a terrible father, even if he could pass on
his deep cultural values. Still, it was clear to me that Biao shouldn't go back to the orphanage. Would Wudang Monastery be a good place for him when all this was over? Would they give him what he needed to develop his talent, which, like painting, required long, hard years of study? I'd have to give it some thought. I couldn't take him back to Father Castrillo, nor could I take him with me to Paris, so far from his roots. He would be a second-class citizen there; they'd always look at him as if he were an exotic Chinese souvenir. Maybe Wudang was the best option for him.
“Now you've got to take all the numbers left outside and put them in the Magic Square,” Master Red said to Biao.
The boy became visibly distressed, anxious.
“Yes, that's going to be the hard part. I'll use the red pencil again.”
A pyramid of four rows of numbers was left above the square, as well as others below, to the left and right of it. In theory, all those numbers had to go back into the square following the rule Biao had found earlier: Place them in boxes along the same row or column but on the opposite side of center, which was now the number forty-one.
Each of these leftover pyramids consisted of ten numbers, which meant there was a total of forty that had to be put back in the grid. Biao began with one, which was at the vertex of the pyramid on the top: He crossed it out and wrote it underneath forty-one. He then repeated the same operation with the vertex of the pyramid on the bottom: He crossed out eighty-one and wrote it in the square right above center. He did the same with the nine located at the vertex on the right, placing it to the left of forty-one, and took seventy-three from the vertex on the left and wrote it on the right of forty-one. The little square consisting of the nine middle boxes was complete. Now he had to do the rest.
“I'll start putting those cylinders in their holes,” Lao Jiang said impatiently as he got to his feet.
“No, Da Teh, please,” Master Red begged, hurriedly trying to stop him. “Wait until we've finished. We'll put the stone rolls in their places once we've added up the lines, columns, and diagonals, making sure they come to the same amount. If we make a mistake with one number, just one, the lock won't work. What Biao's doing is not easy. He could make a tiny mistake without even realizing it.”
The antiquarian grudgingly sat back down and once again became absorbed in contemplating his lighter.
Meanwhile, Biao continued to move numbers from outside the Magic Square to the inside. He was surprisingly determined and meticulous, following his own rule with the utmost care.
“There!” he exclaimed once he'd put the last number in its place.
“Let's add them up,” Master Red proposed. “You do the rows and I'll do the columns. I wish I had an abacus!” He sighed.
Biao and Master Red Jade squeezed their eyelids shut at the same time, opening them every now and then to look at the numbers and then closing them again. Biao was the first to finish.
“All the rows add up to three hundred sixty-nine, except for the third,” he lamented.
“Do that one again,” I recommended.
He looked back at the numbers and closed his eyes. Master Red finished just then.
“All the columns add up to three hundred sixty-nine,” he announced.
“Add the diagonals while Biao double-checks the rows,” I told him.
“There can't be a mistake, madame,” Master Red said in surprise. “If the columns are fine, then the rows have to be fine. If there was an error in a row, I'd have found an error in a column.”
Biao finished in the meantime and smiled from ear to ear.
“I must have misread some numbers,” he explained in relief. “This time I got three hundred sixty-nine.”
“Do the diagonals,” I encouraged.
Lao Jiang couldn't wait any longer. Seeing that we had the solution in hand, he quickly stood and walked over to the pile of stone cylinders.
“Master Red Jade,” he called. “Since you and I are the only ones who know how to read Chinese numbers, you pass me the cylinders and I'll put them in their place. You, Elvira and Fernanda, stand them all up so Master Red Jade can find them quickly. Biao, take your book and read the numbers aloud.”
“Could you hold on just a second?” I spit out. “We haven't finished yet.”
“Yes we have,” he parried. “The Magic Square is complete, and as an old Chinese saying goes, ‘An inch of time is an inch of gold.’ We have to get down to the First Emperor's mausoleum right away.”
Please! It's not as if we were being chased by the Green Gang! What was his hurry? And yet we all obeyed like simpletons. Biao and Master Red rose and walked over into the middle of the tables. The boy stationed himself in front of the board with his book open as if he were an altar boy ready to recite psalms in a church. Meanwhile, Fernanda and I stood the stone tubes so that the Chinese characters were visible.
“Read the numbers by row, starting at the top,” the antiquarian ordered.
“Thirty-seven,” Biao began.
Master Red found that cylinder and handed it to the antiquarian, but Lao Jiang didn't move.
“What's wrong now?” I asked.
“Where should I put it?”
“What do you mean, where should you put it?” I asked. “Put it in the first square in the first row of the grid.”
“Yes, but which is the first row?” he replied uncomfortably. “There are four sides, and not one of them is marked with anything that says ‘Top’ or ‘Start here.’ ”
Well, that was a conundrum. However, as with everything else, there had to be a logical solution. Staying within the area flanked by the tables, I walked over until I was in front of the seat of honor, with the identically carved stone slab hanging behind it. Vertically, it was quite clear which was the top row and which the first square in that row. I began to walk backward, careful not to run into the cylinders, and kept going until the square on the floor was in front of me. I then pointed to the top line.
“There. Facing the seat of honor, that must be the proper orientation.”
Lao Jiang did as I said, placing the cylinder marked with the number thirty-seven in the top right-hand corner.
“Seventy-eight,” Biao intoned, reminding me of the children from San Ildefonso school in Madrid who'd been singing the winning national lottery numbers for two centuries.
Fernanda and I stood the cylinders on end as fast as possible so Master Red could find the one Lao Jiang needed. The antiquarian grew impatient. Master Red was going too slowly, and Biao wasn't speaking clearly, and the two of us, who weren't doing anything, were getting in the way. It was impossible to please him. Everything was wrong as far as he was concerned.
After some time we reached number forty-one in the middle of the square; all that work, and we'd gotten through only four and a half lines. I consoled myself with the thought that things would go much faster as we went on, because Master Red would have fewer and fewer cylinders to look through.
And indeed we made up for our slow start during the second half. My niece and I formed a chain to pass the cylinder with the number that Biao sang out from Master Red to Lao Jiang. Before we realized it, the last stone roll had passed from my hands into the antiquarian's.
“There,” I said with a triumphant smile. “We've done it.”
He smiled, too; hard to believe, but he'd actually smiled. It was the first time in a long time, and so I smiled happily back. Lao Jiang, however, was determined to finish the job and turned indifferently around, dropping the cylinder in the last hole.
As had happened in the chamber with the Bian Zhong, there was a metallic click followed by the grinding of stone on stone. The floor shuddered, and we all looked at one another a little frightened. We knew where the sound was coming from but couldn't see any means of access to the next level. Then the floor behind the stone slab began slowly, gently lowering, becoming a ramp that landed with a thud on the floor below, shaking the entire banquet hall.
We all walked over, tentatively, expectantly, after silently p
icking up our bags. Some mysterious mechanism had already lit the lamps on the lower level, because light shone up through the enormous hole without our having done anything.
We descended cautiously, ready for whatever might happen, but nothing did. We reached the bottom of the ramp and found ourselves in a huge, frigid esplanade, even bigger than the one we'd seen up above and best described as gleaming. Everything glowed as if the servants had just finished cleaning or, better yet, as if a speck of dust had never found its way in there. The floor was made of forged, polished bronze, like the mirrors Fernanda and I had taken. Thick, black-lacquered columns held not only receptacles that were already lit but a ceiling as well, also made of bronze that stretched away from our heads the farther we walked. The floor was on a slight incline, barely perceptible, causing the space to expand until it was colossal, truly magnificent. We continued walking, following an imaginary straight line. The air was very cold. At some point I turned back to look at the ramp, but couldn't see it anymore. I did, however, discover a town, or something that looked like a town, on our right, with its walls, towers, flagpoles, and the roofs of its houses and palaces. It was just like a real one, only smaller, as if little people or children lived there. A bit farther on, to the left, I saw another, and then many more. After a while we crossed one of those arched Chinese bridges over a small river whose waters were actually liquid mercury, brilliant silver, flowing smoothly within its banks. The children rushed to reach into the current and touch the strange, fascinating metal that slipped through their fingers, forming little silver balls in the palms of their hands, but I wouldn't let them dawdle, and they reluctantly rejoined the group.
Lao Jiang bent over a small stone stela on the floor to read the inscription.
“We've just left the province of Nanyang and are entering Xianyang,” he said, chuckling. “It can't be far, then, to the prefecture of Hanzhong.”
“We've crossed Everything Under the Sky already?” Master Red asked, using the expression commonly used among the Chinese to refer to their country.
“Well,” Lao Jiang said quite enthusiastically, “they likely put the ramp near the capital, the center of power for both the real empire above as well as this little Zhongguo, Tianxia or Everything Under the Sky. This is an exact replica. It's like a giant map with magnificent models and these astonishing rivers of mercury.”