by Yoko Ogawa
"Root!" I interrupted. "Is that any way to act?" But the Professor didn't seem to notice his outburst.
"A problem isn't finished just because you've found the right answer. There's another way to get to 55; wouldn't you like to find it?"
"Not really…," said Root, sulking.
"All right, here's what we'll do. The radio is old, and it may take them a while to get it working again. So how about a contest to see whether you can find another way to get the sum before the radio is fixed?"
"Okay," said Root. "But I don't see how I'm going to do it. What other way is there besides just adding them up?"
"Who'd have guessed you're such a quitter," the Professor scolded. "Giving up before you've even tried."
"Fine. I'll try. But I can't promise I'll figure it out before the radio's done. I've got a lot of other stuff to do."
"We'll see," said the Professor, and he rubbed Root's head as he always did. "Oh!" he said suddenly. "I've got to make a note." He took a sheet of paper, wrote out their agreement, then clipped it to his lapel. There was something smooth and controlled in the way he held the pen and wrote the note, so different from his usual clumsy manner.
"But you have to promise to finish your homework before the game comes on; and to turn it off during dinner; and not to disturb the Professor while he's working." Root nodded grumpily as I listed each condition.
"I know," he said, "but it'll be worth it. The Tigers are good this year, not like last year and the year before when they were in last place. They even won their first game against the Giants."
"Is that right? Hanshin's having a good year?" the Professor said. "What's Enatsu's ERA?" The Professor looked back and forth between us. "How many strikeouts does he have?" Root waited for a moment before answering.
"They traded Enatsu," he said at last. "That was before I was born, and he's retired now." A jolt shot through the Professor and then he was still.
I had never seen him so distressed. He had always calmly accepted the way his memory failed him, but this time was different. This time he couldn't ignore the facts. Seeing him this way, I even forgot to worry about Root, who had received a shock of his own at causing the Professor such pain.
"But even after they traded him to the Carp, he was the best in the league." I hoped this would reassure him, but this new information distressed him even more.
"The Carp? What do you mean? How could Enatsu wear anything but the Hanshin pinstripes?"
He sat down and rested his elbows on the desk, running his hands through his freshly cut hair. Tiny clippings fell on his notebook. This time it was Root who rubbed the Professor's head. He smoothed the mussed hair as if trying to undo the trouble he'd caused.
Root and I were quiet on the way home that evening. When I asked him whether the Tigers had a game, his answer was barely audible.
"Who are they playing?"
"Taiyo."
"You think they'll win?"
"Who knows."
The lights were out in the barbershop and the park was empty. The formulas the Professor had scratched in the dirt were hidden in the shadows.
"I shouldn't have said those things," Root said. "But I didn't know he liked Enatsu so much."
"I didn't know, either," I said. And then, though it was probably wrong of me, I added, "Don't worry, it will all be back to normal by tomorrow morning. In the Professor's mind, Enatsu will be the Tigers' ace again and he won't remember anything about the Carp."
The problem that the Professor had posed to Root proved to be almost as difficult as the one that Enatsu had presented for all of us.
As the Professor had predicted, the man at the repair shop said that he had never seen such an old radio and that he wasn't sure he could fix it. But if he could, he said, he would try to have it done in a week's time. So every day, when I got home from work, I spent my evening looking for another way to find the sum of the natural numbers from 1 to 10. Root should have been working on the problem, too, but perhaps because he was upset over the incident with Enatsu, he gave up almost immediately and left me to find a solution. For my part, I was anxious to please the Professor, and I certainly didn't want to disappoint him any more than we already had. But the only way to please him, I suspected, was through numbers.
I began by reading the problem aloud, just as the Professor had insisted Root do with his homework: "1 + 2 + 3 +… 9 + 10 is 55. 1 + 2 + 3 +…" But this didn't seem to be much help-except to show that a simple equation could conceal a terribly difficult problem.
Next I tried writing out the numbers from 1 to 10 both horizontally and vertically and grouping them by odds and evens, primes and non-primes, and so on. I worked on the problem with matches and marbles, and when I was at the Professor's house, I jotted down numbers on the back of any piece of scrap paper, always looking for a clue.
To find an amicable number, all you had to do was perform the same sort of calculation again and again. If you had enough time, you'd eventually succeed. But this was different. I was constantly starting off in a new direction, looking for another way to approach the problem, only to wind up at a dead end, confused. To be honest, I wasn't always even sure of what I was trying to do. At times I seemed to be going around in circles and at others almost backward, away from a solution; and in the end, I was often simply staring at the scrap paper.
I'm not sure why I became so absorbed in a child's math problem with no practical value. At first, I was conscious of wanting to please the Professor, but gradually that feeling faded and I realized it had become a battle between the problem and me. When I woke in the morning, the equation was waiting-1 + 2 + 3 +… 9 + 10 = 55-and it followed me all through the day, as though it had burned itself into my retina and could not be ignored.
At first, it was just a small distraction, but it quickly became an obsession. Only a few people know the mystery concealed in this formula, and the rest of us go to our graves without even suspecting there is a secret to be revealed. But by some whim of fate, I had found it, and now knocked at the door, asking to be let in. Though I had never suspected it, from the moment I'd been dispatched by the Akebono Housekeeping Agency, I had been on a mission toward that door…
"Do I look like the Professor?" I asked Root, my hand pressed to my temple and a pencil clenched in my fingers. That day, I had covered the back of every flyer and handbill in the house, but I'd made no progress.
"No, not a bit," Root said. "When the Professor's solving a problem, he doesn't talk to himself the way you do, and he doesn't pull out his hair. His body's there but his mind goes somewhere else. And besides," he added, "his problems are a lot harder!"
"I know! But whose problem is this anyway? Maybe you could stop reading your baseball books for a minute and help me."
"But you're three times as old as I am! And besides, it's a crazy problem anyway."
"Showing the factors was progress. That was thanks to the Professor, wasn't it?"
"I guess so," said Root, looking at my work on the backs of the advertisements and nodding as though he found everything in proper order.
"I think you're on the right track," he said at last.
"Some help you are!" I laughed.
"Better than nothing," he said, turning back to his book.
Since he was very small, he'd often had to console me when I came home from work in tears-when I'd been accused of stealing, or called incompetent, or had the food I'd made thrown away right in front of me. "You're beautiful, Momma," he'd say, his voice full of conviction, "It'll be okay." This was what he always said when he comforted me. "I'm a beauty?" I would ask, and he'd say, feigning astonishment, "Sure you are. Didn't you know?" More than once I'd pretended to be crying just to hear these words; and he'd always play along willingly.
"But you know what I think?" he said suddenly. "When you're adding up the numbers, 10 is odd man out."
"Why do you say that?"
"Well, 10's the only one with two places."
He was right, of cou
rse. I had analyzed the numbers in many ways, but had not thought about how each number was special, different. When I looked at them again, it seemed terribly strange that I'd never noticed how odd 10 looked lined up against the others-the only one among them that could not be written without picking up the pencil.
"If you got rid of ten, you'd have a number in the center spot, which might be good."
"What do you mean, 'center spot'?"
"You'd know if you came to the last Parents' Day. We were doing gymnastics-that's my best sport-and in the middle of the exercise the teacher said, 'Double lines, face center.' The guy in the middle held up his arms and the rest of us lined up facing him. There were nine of us, so the guy in fifth place was the center, and the lines were even. For 10 it doesn't work. If you add just one guy, you don't have a center."
So now I tried leaving 10 aside and lining up the rest of the numbers. I circled five in the center, with four numbers before it and four after. The 5 stood, arms proudly extended, enjoying the attention of all the others.
And at that moment I experienced a kind of revelation for the first time in my life, a sort of miracle. In the midst of a vast field of numbers, a straight path opened before my eyes. A light was shining at the end, leading me on, and I knew then that it was the path to enlightenment.
The radio came back from the repair shop on Friday, the twenty-fourth of April, the day the Tigers were scheduled to play the Dragons. We put it on the center of the table and sat around it. Root twisted the knobs, and the broadcast of the game crackled out from the static. The signal was weak, but there was no doubt it was the baseball game-and the first sign of life from the outside world that had made its way into the house since my arrival. We let out a little cheer.
"I had no idea you could get baseball on this radio," said the Professor.
"Of course! You can get it on any radio."
"My brother bought it for me a long time ago, for practicing English conversation. I thought it would only pick up English."
"So you've never listened to the Tigers?" Root said.
"No, and I haven't got a TV, either…," murmured the Professor, as if confessing something awful. "I've never seen a baseball game."
"I don't believe it!" Root blurted out, nearly shouting.
"I know the rules, though," the Professor said, a bit defensively. But Root was not to be appeased.
"How can you call yourself a Tigers fan?"
"But I am-a big fan. When I was in college, I went to the library at lunch to read the sports pages. But I did more than just read about baseball. You see, no other sport is captured so perfectly by its statistics, its numbers. I analyzed the data for the Hanshin players, their batting averages and ERAs, and by tracking the changes, even miniscule shifts, I could picture the flow of the games in my head."
"And that was fun?"
"Of course it was. Even without the radio, I could keep every detail fixed in my mind: Enatsu's first victory as a pro in 1967-he beat the Carp with ten strikeouts; the game in 1973 when he pitched an extra-innings no-hitter and then hit a walk-off home run himself." Just at that moment, the announcer on the radio mentioned the name of the Tigers starting pitcher, Kasai. "So when is Enatsu scheduled to pitch?" the Professor asked.
"He's a little farther on in the rotation," Root answered without missing a beat. It surprised me to see him acting so grown-up. We'd promised that where Enatsu was concerned, we'd do anything to keep up the illusion. Still, it made us uncomfortable to lie to the Professor, and it was hard to know whether it was really in his best interest. But we could not bear to upset him again.
"We can tell him that Enatsu's back in the dugout, or that he's throwing in the bullpen," Root had said.
Since Enatsu had retired long before Root was born, he'd gone to the library to find out about him. He learned that he had a career record of 206 wins, 158 losses, and 193 saves, with 2,987 strikeouts. He'd hit a home run in his second at bat as a pro; he had short fingers for a pitcher. He'd struck out his great rival, Sadaharu Oh, more than any other pitcher, but he'd also surrendered the most home runs to him. In the course of their rivalry, however, he'd never hit Oh with a pitch. During the 1968 season, he set a world record with 401 strikeouts, and after the 1975 season (the year the Professor's memory came to an end), he'd been traded to the Nankai Hawks.
Root had wanted to know more about Enatsu, so he would seem more real to both of them as they listened to the cheers on the radio. While I had been struggling with the "homework" problem, he had been seeing to the Enatsu problem. Then one day, as I was flipping through a copy of Baseball Players Illustrated that he'd brought home from the library, I was stunned to find a picture of Enatsu, and see on his uniform the number 28. When he'd graduated from Osaka Gakuin and joined the Tigers, he'd been offered the three available numbers: 1, 13, and 28. He'd chosen 28. Enatsu had played his whole career with a perfect number on his back!
That evening, after dinner, we presented our solution. We stood before the Professor, pen and paper in hand, and bowed.
"This is the problem you gave us," said Root. "Find the sum of the numbers from 1 to 10 without adding them." He cleared his throat and then, just as we'd arranged the night before, I held the notebook while he wrote the numbers 1 to 9 in a line, adding 10 farther down on the page. "We already know the answer. It's 55. I added them up and that's what I got. But you didn't care about the answer."
The Professor folded his arms and listened intently, as if hanging on to Root's every word.
"So we decided to think about 1 to 9 first, and forget about 10 for right now. The number 5 is in the middle, so it's the… uh…"
"Average," I whispered in his ear.
"Right, the average. We haven't learned averages yet, so Momma helped me with that part. If you add up 1 through 9 and divide by 9 you get 5… so 5 × 9 = 45, that's the sum of the numbers 1 to 9. And now it's time to bring back the 10."
5 × 9 + 10 = 55
Root took the pen and wrote the equation on the pad.
The Professor sat studying what he had written, and I was sure then that my moment of inspiration must look laughably crude to him. I'd known from the start that I would never be able to extract something sublime and true from my poor brain cells, no chance of imagining something that would please a real mathematician.
But then the Professor stood up and began to applaud as warmly and enthusiastically as if we had just solved Fermat's theorem. He clapped for a long time, filling the little house with his approval.
"Wonderful! It's magnificent, Root." He folded Root in his arms, half crushing him.
"Okay, okay. I can't breathe," Root mumbled, his words nearly lost in the Professor's embrace.
He was determined to make this skinny boy with the flat head understand how beautiful his discovery was, but as I stood watching Root's triumph, I secretly felt proud of my own contribution. I looked at the line of figures Root had written. 5 × 9 + 10 = 55. And even though I'd never really studied mathematics, I knew that the formula became more impressive if you restated it in abstract form:
It was a splendid discovery, and the clarity and purity of the solution was even more extraordinary in light of the confusion it had emerged from, as if I'd unearthed a shard of crystal from the floor of a dark cave. I laughed quietly, realizing that I'd praised myself adequately, even if the Professor's compliments had been directed elsewhere.
Root was finally released, and we bowed again like two scholars who had just finished their presentation at an academic conference.
That day, the Tigers lost 2-3 to the Dragons. They had taken a two-run lead on a triple by Wada, but the Dragons responded with back-to-back home runs and won the game.
4
The Professor loved prime numbers more than anything in the world. I'd been vaguely aware of their existence, but it never occurred to me that they could be the object of someone's deepest affection. He was tender and attentive and respectful; by turns he would caress them or prostrate hi
mself before them; he never strayed far from his prime numbers. Whether at his desk or at the dinner table, when he talked about numbers, primes were most likely to make an appearance. At first, it was hard to see their appeal. They seemed so stubborn, resisting division by any number but one and themselves. Still, as we were swept up in the Professor's enthusiasm, we gradually came to understand his devotion, and the primes began to seem more real, as though we could reach out and touch them. I'm sure they meant something different to each of us, but as soon as the Professor would mention prime numbers, we would look at each other with conspiratorial smiles. Just as the thought of a caramel can cause your mouth to water, the mere mention of prime numbers made us anxious to know more about their secrets.
Evening was a precious time for the three of us. The vague tension around my morning arrival-which for the Professor was always our first encounter-had dissipated, and Root livened up our quiet days. I suppose that's why I'll always remember the Professor's face in the evening, in profile, lit by the setting sun.
Inevitably, the Professor repeated himself when he talked about prime numbers. But Root and I had promised each other that we would never tell him, even if we had heard the same thing several times before-a promise we took as seriously as our agreement to hide the truth about Enatsu. No matter how weary we were of hearing a story, we always made an effort to listen attentively. We felt we owed that to the Professor, who had put so much effort into treating the two of us as real mathematicians. But our main concern was to avoid confusing him. Any kind of uncertainty caused him pain, so we were determined to hide the time that had passed and the memories he'd lost. Biting our tongues was the least we could do.
But the truth was, we were almost never bored when he spoke of mathematics. Though he often returned to the topic of prime numbers-the proof that there were an infinite number of them, or a code that had been devised based on primes, or the most enormous known examples, or twin primes, or the Mersenne primes-the slightest change in the shape of his argument could make you see something you had never understood before. Even a difference in the weather or in his tone of voice seemed to cast these numbers in a different light.