Authors: Yôko Ogawa
Tags: #Fiction, #Humorous, #Psychological, #Sports
"Have you ever heard of triangular numbers?" the Professor
said, pointing at the radiation sign on the door of the X-ray room.
It was shaped like a triangle.
"No," I said. He sounded calm now, but I could tell that he was
still a little shaken.
"They're truly elegant," he said, beginning to draw dots on the
back of a questionnaire that he'd picked up in the lobby.
"What do you make of these?"
"Well, let's see. It looks like neatly stacked firewood, or maybe
rows of beans."
"That's right, the point is they're 'neatly' arranged. One in the
first row, two in the second, three in the third.... It's the simplest
way to form a triangle." I glanced at the dots on the page. The
Professor's hand was trembling slightly. The black marks seemed
to float up in the half-light. "So then, if we total up the number of
dots in each triangle, we get 1, 3, 6, 10, 15, and 21. And if we write
these as equations:
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15
1 + 2 + 3 + 4 + 5 + 6 = 21
"In other words, a triangular number is the sum of all the natural
numbers between 1 and a certain number. Then, if you put two
of these triangles together, things get even more interesting. Why
don't we look at the fourth one, 10, so we don't have to draw too
It wasn't particularly cold in the hall, but the trembling in his
hand had grown worse and the dots had slightly smudged. His
whole being seemed concentrated in the tip of his pencil. A few of
the notes on his suit were smeared with blood and now illegible.
"Look at this. When you put two of the four-row triangles together,
you get a rectangle that is 4 dots high and 5 dots wide; and
the total number in the rectangle is 4 × 5 or 20 dots. Do you see
that? And if you divide that in half, you get 20 ÷ 2 = 10, or the sum
of the natural numbers from 1 to 4. Or, if you look at each line of
the rectangle, you get:
"And once you know that, you can use this relationship to figure
out the tenth triangle—the sum of the numbers from 1 to
10—or the hundredth or any other. For 1 to 10 it would be:
"And for 1 to 100,
"And 1 to 1000,
"And 1 to 10,000...."
The pencil rolled out of his hand and fell at his feet. The Professor
was crying. I believe it was the first time I saw him in tears,
but I had the feeling that I'd seen these emotions many times before.
I placed my hand on his.
"Do you understand?" he said. "You can find the sums of all
the natural numbers."
"Just by lining up the dots in a triangle. That's all there is to it."
"Yes, I see that now."
"But do you really understand?"
"Don't worry," I told him. "Everything's going to be all right.
How can you cry, look at these beautiful triangular numbers."
Just then the door to the examination room opened and Root
"See!" he said, giving his bandaged hand a wave. "I'm fine."
Leaving the clinic, we suddenly realized that we were starving,
so we decided to eat out. Since the Professor hated crowds, we
went to the emptiest restaurant in the arcade near the station
and had a bowl of curry and rice. There were almost no other
customers, so we might have guessed that the curry wouldn't be
particularly good; but Root, who almost never ate out, was delighted.
He also seemed pleased to have such a dramatic bandage
(for a relatively minor injury), as if he were the hero of
some great battle.
"I won't be able to help with the dishes or even take a bath for
a while," he said, a bit full of himself.
The Professor carried him home on his back, and Root was less
worried about being seen now that it was dark. Perhaps he was
just being considerate of the Professor. Whatever the reason, he
climbed on without objection and rode happily. A thin sliver of
moon hung above the row of sycamores glowing under the street
lamps. A pleasant breeze was blowing, our stomachs were full,
and Root's hand would heal. I felt a great sense of contentment.
My footsteps fell in with the Professor's, and Root's tennis shoes
swung back and forth in time.
After seeing the Professor home, we headed back to our apartment.
For some reason Root was suddenly in a bad mood. He went
straight to his room and turned on the radio, and refused to answer
when I called to tell him to take off his bloodstained clothes.
"Are the Tigers losing?" I asked. He was standing at his desk,
glaring at the radio. They were playing the Giants. "They lost yesterday,
didn't they?" Still no answer. The announcer informed us
that the score was tied 2-2 in the bottom of the ninth, with Nakata
and Kuwata locked in a pitchers' duel. "Does it hurt?" I asked.
He bit his lip and kept his eyes on the radio. "If it hurts, take the
medicine the doctor gave us. I'll get you some water."
"No," he said.
"You really should," I coaxed. "You don't want it to get infected."
"I said it doesn't hurt."
He clenched his bandaged fist and rapped it against the desk,
using his good hand to hide the tears welling up in his eyes. This
clearly had nothing to do with the Tigers.
"Why are you doing that?" I said. "They just finished stitching
you up. What am I supposed to do if you start bleeding again?"
Tears streamed down his cheeks now. I tried to check whether
blood was soaking through the bandage, but he brushed my hand
away. Cheers erupted from the radio—a two out single.
"Are you mad because I went out and left you with the Professor?
Or are you embarrassed because you couldn't handle the
knife? Or because you made a mistake in front of the Professor?"
He'd fallen silent again. Kameyama was up at bat.
Kuwata has been nearly unhittable.... He's struck out his last
two at bats ... will it be another fastball? ... Here's the windup
The cheers rose again and again, drowning out the announcer,
but Root seemed indifferent. He sat perfectly still as the tears continued
to roll down his cheeks.
I realized I had seen two men cry this evening. I had, of course,
seen Root's tears countless times before—as an infant, when he'd
wanted to be held or fed; and later, during tantrums, or when he
lost his grandmother. And, for that matter, at the moment he came
into this world. But these tears were different, and no matter how
I tried to wipe them away, they seemed to flow from a place I
could never reach.
"Are you mad because the Professor couldn't dress the wound
properly?" I asked at last.
"No," said Root. He stared at me for a moment and then he
spoke so calmly it seemed as though he had completely regained
control of himself. "I'm mad because you didn't trust him. I'll
never forgive you for that."
Kameyama hit the second pitch into right center, and Wada
scored from first to end the game. The announcer was shouting
and the roar of the crowd swept over us.
The next day, the Professor and I recopied his note tags. "I wonder
where all this blood came from," he said, checking himself for
"Root, my son, hurt his hand with a knife—but it wasn't serious."
"Your son? That's terrible! It looks like it bled all over."
"No, he's just fine, thanks to you."
"Really? I helped?"
"Of course. How do you think the blood got on you?"
I pulled the notes from his suit one by one. Most were covered
with an incomprehensible scrawl of math symbols—as though few
things other than numbers were worth remembering.
"And when you finished helping Root, you taught me something
important in the waiting room."
"You taught me about triangular numbers, and the formula for
finding the sum of the natural numbers from 1 to 10—something
I could never have imagined, something sublime." I held out the
most important note. "Shall we start with this one?"