The Gift of Numbers aka The Housekeeper and the Professor

8

It was on the day of the Star Festival that the Tigers lost their seventh game in a row, 1-0 against Taiyo.

I'd had no trouble falling back into the rhythm of the job, despite my month away. And because of the Professor's memory problem, he immediately forgot my misunderstanding with his sister-in-law. For him, no trace of the trouble remained.

I transferred the notes to his summer suit, taking care to fasten them in the same positions, and I rewrote those that were torn or faded.

"In an envelope in the desk, second drawer from the bottom."

"Theory of Functions, 2nd edition, pp. 315-372 and Commentary on Hyperbolic Functions, volume IV, chapter 1, § 17."

"Medicine to take after meals in manila envelope, on the left in the sideboard."

"Spare razor blades next to the mirror above the sink."

"Thank for the cake."

Some of the notes were out of date-it had been a month since Root had brought the Professor a little steamed bun he had baked in his home economics class-but it seemed wrong to throw them out. I treated them all with equal respect.

As I read through them, I realized how hard it was for the Profossor to simply get through the day, and how carefully he hid the enormous efforts he made. I tried to work as quickly as possible and not to linger over the notes. When they were all reattached, his summer suit was ready.

For a few weeks, the Professor had been working on an extremely difficult problem, one that would pay the largest cash prize in the history of the Journal of Mathematics to the reader who solved it. Indifferent to money, the Professor took pleasure in the difficulty of the problem itself. Checks from the journal were left unopened on the hall table, and when I asked him if he wanted me to cash his prize money at the post office, he shrugged. In the end, I asked the agency to forward them to his sister-in-law.

Just by looking at the Professor, I could tell that the new problem was especially hard. The intensity of his thought seemed to be near breaking point. He would vanish into the study as though he were literally retreating into his mind, and I imagined that his body might actually vaporize into pure contemplation and disappear. But then the sound of his pencil scratching across the paper would break the stillness and reassure me-the Professor was still with us and was making some progress with the proof.

I tried to imagine how he could work through a problem like this over such a long period of time-he basically had to start again from the beginning every morning. To compensate for the loss of his thoughts from the day before, he had only an ordinary notebook and the scribbled notes that covered his body like a cocoon. Since the accident, math was his life, so perhaps it was also what led him to sit down at his desk each day and return to the problem in front of him.

I was considering all of this while making dinner when the Professor suddenly appeared. Usually, when he was wrestling with a problem, I hardly saw him. I wasn't sure whether I would be interrupting his thinking if I spoke to him, so I continued seeding the peppers and peeling the onions. He walked over, leaned against the counter, folded his arms, and stood there staring at my hands. I felt awkward with him watching me, so I went to get some eggs out of the refrigerator, and a frying pan.

"Did you need something?" I asked at last, no longer able to stand the silence.

"No, go on," he said. His tone was reassuring. "I like to watch you cook," he added.

I wondered if the problem had proven so difficult his brain had blown a fuse-but I broke the eggs into a bowl and beat them with my chopsticks. I went on stirring after the spices had dissolved and the lumps were gone, only stopping when my hand had grown numb.

"Now what are you going to do?" he asked quietly.

"Well…," I said, "next…, uh, I have to fry the pork." The Professor's sudden appearance had disrupted my usual routine.

"You're not going to cook the eggs now?"

"No, it's best to let them sit, so the spices blend in."

We were alone, Root was off playing in the park. The afternoon sun divided the garden into patches of shadow and dappled light. The air was still, and the curtains hung limply by the open window. The Professor was watching me with the intense stare he normally reserved for math. His pupils were so black they looked transparent, and his eyelashes seemed to quiver with each breath. He was gazing at my hands, which were only a few feet away, but he might have been staring off into distant space. I dusted the pork filets in flour and arranged them in the pan.

"Why do you have to move them around like that?"

"Because the temperature at the center of the pan is higher than at the edges. You have to move them every so often to cook them evenly."

"I see. No one gets the best spot all the time-they have to compromise."

He nodded as if I had just revealed a great secret. The aroma of cooking meat drifted up between us.

I sliced some peppers and onions for the salad and made an olive oil dressing. Then I fried the eggs. I had planned to sneak some grated carrot into the dressing, which now proved impossible with the Professor watching me. He said nothing, but he seemed to hold his breath while I cut the lemon peel in the shape of a flower. He leaned in closer as I mixed the vinegar and oil, and I thought I heard him sigh when I set the piping hot omelet on the counter.

"Excuse me," I said at last, unable to control my curiosity. "But I'm wondering what you find so interesting."

"I like to watch you cook," he said again. He unfolded his arms and looked out the window for the spot where the evening star would appear. Then he went back to his study without a sound. The setting sun shone on his back as he walked away.

I looked at the food I had just finished preparing and then at my hands. Sautéed pork garnished with lemon, a salad, and a soft, yellow omelet. I studied the dishes, one by one. They were all perfectly ordinary, but they looked delicious-satisfying food at the end of a long day. I looked at my palms again, filled suddenly with an absurd sense of satisfaction, as though I had just solved Fermat's Last Theorem.

The rainy season came to an end, Root's summer vacation began, and still the Professor struggled with his proof. I was eagerly looking forward to the day he would ask me to mail it to the magazine.

The weather had turned hot. The cottage had neither airconditioning nor a cross breeze. Root and I tried not to complain, but we were no match for the Professor's stoicism. At noon, on the hottest day, he would sit at his desk with the doors closed, never removing his jacket-as if he were afraid that all the work he'd done on the proof would crumble if he slipped out of his coat. The notes on his suit had wilted, and he was covered in a painful-looking heat rash, but when I came in with a fan, or suggested a cold shower, or more barley tea, he would chase me out in exasperation.

Once his summer vacation started, Root would come with me to the cottage in the morning. Given my recent run-in with the widow, I thought it best not to increase the amount of time he spent with me at work, but the Professor wouldn't hear of it. He was absolutely convinced that a child on vacation had to be where his mother could watch over him. Root, however, much preferred to be at the park playing baseball with his friends or at the pool, so he was almost never with us.

On Friday, July 31, the proof was finished. The Professor didn't seem very excited, nor did he seem especially exhausted. He calmly handed me the pages, and I ran to the post office to be sure to catch the mail before the weekend. I watched as they stamped the envelope and put it in the bin; then, feeling both excited and relieved, I wandered home slowly, shopping along the way. I bought the Professor new underwear, some sweet-smelling soap, ice cream, jelly, and sweet bean paste.

When I reached home, the Professor no longer knew who I was. I checked my watch-it had only been an hour and ten minutes since I'd left. The Professor's eighty-minute timer had never failed before. His head had always been more accurate than any clock. I took off my watch and held it up to my ear.

"How much did you weigh when you were born?" the Professor said.

At the beginning of August, Root went camping for four nights. The trip was only for children over ten, and Root had been looking forward to it for a long time. It would be his first time away from me, but he showed no signs of fear. When I dropped him off at the bus, clusters of mothers and children were saying their good-byes. The mothers were all issuing last-minute instructions and warnings, and I had a few of my own for Root, telling him to wear his jacket and to hang on to his insurance card-but he never gave me a chance to finish. He was the first one on the bus, and he barely waved good-bye as they pulled away.

The first evening, I lingered at the Professor's, reluctant to go home to my empty apartment after I'd finished washing the dinner dishes.

"Would you like some fruit?"

"That would be nice," the Professor replied, turning to look at me from his easy chair. Though the sun would not be setting for some time yet, thick clouds had gathered, and the light in the garden was mottled, as though the world had been wrapped in lavender cellophane. A gentle breeze blew through the kitchen window. I cut up some melon and took it to the Professor. Then I sat down beside him.

"You should have some, too," he said.

"No, thanks. You go ahead."

He crushed the flesh of the melon with the back of his fork and began to eat, spraying juice on the table.

With Root at camp, there was no one to turn on the radio, the house was quiet. There was no sign of life from the widow's house, either. A single cicada cried for a moment and then fell silent.

"Have a little," he said, holding out the last slice.

"No, thanks. You eat it," I said, wiping his mouth with my handkerchief. "It was hot again today."

"Scorching," he said.

"Don't forget to use the medicine for your heat rash. It's in the bathroom."

"I'll try to remember," he said.

"They say it'll be even hotter tomorrow."

"That's how we spend the summer," he said, "complaining about the heat."

The trees suddenly began to tremble and the sky grew dark. The line of hills on the horizon, faintly visible just a moment before, disappeared in the gloom. There was a rumbling in the distance.

"Thunder!" we said together, as the rain began to fall in enormous drops. The pounding on the roof echoed through the room. I stood up to close the windows, but the Professor stopped me.

"Leave them," he said. "It feels good to have them open."

The curtains billowed in the breeze, letting the rain pour in on our bare feet. It was cool and refreshing, just as the Professor had said. The sun had vanished and the only light in the garden was the faint glow from the lamp above the kitchen sink. Small birds flitted among the drooping, tangled branches of the trees, and then the rain obscured everything. The smell of fresh garden soil filled the air as the thunder drew closer.

I was thinking about Root. Would he find the raincoat I'd packed? And should I have made him take an extra pair of sneakers? I hoped he was eating properly, and that he wouldn't go to bed with wet hair and catch a cold.

"Do you suppose it's raining in the mountains?" I said.

"It's too dark to see," said the Professor, squinting off at the horizon. "I suppose I'll need to get my prescription changed soon."

"Is the lightning over the mountains?" I said.

"Why are you so concerned about the mountains?"

"My son's camping there."

"Your son?"

"Yes. He's ten. He likes baseball and he's a bit of a handful. You nicknamed him Root, because his head is flat on top."

"Is that so, you have a son? That's fine," he said. As soon as Root was mentioned, the Professor cheered up, as usual. "It's a grand thing for a child to go camping in the summer. What could be better for him?"

The Professor leaned back and stretched. His breath smelled faintly of melon. A streak of lightning flashed across the sky, and the thunder rumbled louder than ever. The darkness and heavy rain could not obscure the lightning, and even after a burst had faded, it remained etched on my retina.

"I'm sure that one hit the ground," I said. The Professor grunted but did not answer. The rain splashed over the floor. As I rolled up his cuffs so they wouldn't get wet, his legs twitched as though I were tickling him.

"Lightning tends to strike high places, so the mountains are more dangerous than down here," he said. As a mathematician- a scientist-I thought he would have known more than I did about lightning, but I was wrong. "And the evening star was hazy this evening, which usually means the weather is taking a turn for the worse." There was none of the Professor's usual logic in his pronouncements on the weather.

As he spoke, the rain fell hard. The lightning flashed, the thunder rattled the windowpanes.

"I'm worried about Root," I said.

"Someone once wrote that worrying is the hardest thing about being a parent."

"His clothes are probably soaked, and he's there for four more days. He'll be miserable."

"It's just a shower. When the sun comes out tomorrow and it warms up, everything will dry out."

"But what if he gets struck by lightning?"

"The odds are very low," he said.

"But if he does? What if lightning strikes his Tigers cap? It's flat and shaped like the square root sign; it could attract lightning."

"Pointy heads are more dangerous," he said. "They're like lightning rods."

The Professor was usually the one to worry about Root, but this time he was determined to comfort me. A gust of wind twisted the trees, but as the storm raged on, the cottage seemed to settle into silence. There was a light in a window on the second floor of the widow's house.

"I feel empty when Root isn't here," I said.

I hadn't really been speaking to him, but the Professor murmured in reply, "So, you're saying that there's a zero in you?"

"I suppose that's what I mean," I said, nodding weakly.

"The person who discovered zero must have been remarkable, don't you think?"

"Hasn't zero been around forever?"

"How long is forever?"

"I don't know. For as long as people have been around-wasn't there always a zero?"

"So you think that zero was there waiting for us when humans came into being, like the flowers and the stars? You should have more respect for human progress. We made the zero, through great pain and struggle."

He sat up in his chair and scratched his head, looking utterly disheveled.

"So who was it? Who discovered zero?"

"An Indian mathematician; we don't know his name. The ancient Greeks thought there was no need to count something that was nothing. And since it was nothing, they held that it was impossible to express it as a figure. So someone had to overcome this reasonable assumption, someone had to figure out how to express nothing as a number. This unknown man from India made nonexistence exist. Extraordinary, don't you think?"

"Yes," I agreed, though I wasn't sure how this Indian mathematician would calm my worries about Root. Still, I had learned from experience that anything the Professor was passionate about was bound to be worthwhile. "So, a great Indian teacher of mathematics discovered the zero written in God's notebook, and, thanks to him, we can now read many more pages in the notebook. Is that it?"

"That's it exactly." He laughed. He took a pencil and notepaper from his pocket, as I'd seen him do a thousand times. The gesture was always refined. "Take a look at this," he said. "It's thanks to zero that we can tell these two numbers apart." Using the arm of the chair to write on, he scribbled down the numbers 38 and 308. Then he drew two thick lines under the zero. "Thirty-eight is made up of three 10s and eight 1s; 308 is three 100s, no 10s, and eight 1s. The tens place is empty, and it's the 0 that tells us that. Do you see?"

"I do."

"So, let's pretend there's a ruler here, a wooden ruler thirty centimeters long. What would be the mark all the way at the left here?"

"That would be zero."

"That's right. So zero would be on the far left. A ruler begins at zero. All you have to do is line up the edge of what you want to measure with the zero, and the ruler does the rest. If you started with 1, it wouldn't work. So it's zero that allows us to use a ruler, too."

The rain continued. A siren wailed somewhere; the thunder drowned it out.

"But the most marvelous thing about zero is not that it's a sign or a measurement, but that it's a real number all by itself. It's the number that's one less than 1, the smallest of the natural numbers. Despite what the Greeks might have thought, zero doesn't disturb the rules of calculation; on the contrary, it brings greater order to them. Try imagining one little bird sitting on a branch, singing in a clear, high voice. He has a pretty little beak and colorful feathers. You stare at him, enchanted; but as soon as you breathe, he flies away, leaving only the bare branch, and a few dried leaves fluttering in the breeze." The Professor pointed out at the dark garden, as if the bird had really just flown away. The shadows seemed deeper and longer in the rain. "Yes, 1 – 1 = 0. A lovely equation, don't you think?"

He turned toward me. A loud clap of thunder shook the room, and the light in the main house blinked off for a moment. I gripped the sleeve of his jacket.

"Don't worry," he said, reaching over to stroke my hand. "The square root sign is a sturdy one. It shelters all the numbers."

Needless to say, Root came home safe and sound when his camping trip was over. He brought the Professor a little figurine of a sleeping rabbit he had made from twigs and acorns. The Professor set it on his desk, and at its feet he attached a note: "A present from (the housekeeper's son)."

I asked Root whether the storm on the first day of his trip had caused problems, but he said they hadn't had a drop of rain. In the end, the only damage from the lightning had been done to a gingko tree at a shrine near the Professor's house.

The heat returned, and with it the buzzing of the cicadas. The curtains and the floor were dry by the next day.

Root's attention turned to the Tigers. He had apparently hoped they would be in first place by the time he got back; but things had not gone his way and they had fallen back to fourth after losing to the first-place Swallows.

"Did you cheer for them while I was gone?"

"Of course we did," said the Professor. Root seemed to suspect that his team's problems had been caused by the Professor's negligence.

"But you don't even know how to turn on the radio."

"Your mother showed me."

"Really?"

"Really. She even tuned in the game for me."

"But they don't win if you just sit there and listen."

"I know, and I truly did cheer for them. I talked to the radio the whole time. I prayed Enatsu would strike out the side every inning." The Professor did everything he could to placate Root.

Soon, we were back to our evenings in the kitchen listening to the radio. The receiver, which was perched on top of the dish cupboard, had worked very well since the Professor had it repaired; and the terrible static that occasionally drowned out the game was due to the poor location of the cottage rather than to the radio itself.

We kept the volume low until the game came on, so low you could barely hear it over the everyday sounds-my puttering in the kitchen before dinner, the motorbikes on the street outside, the Professor muttering to himself, or Root's occasional sneeze. Only when we all fell silent could we hear the music, which always seemed to be some nameless old song.

The Professor was reading in his easy chair near the window. Root was fidgeting at the table, working on something in his notebook. The previous title on the notebook-"Cubic forms with whole-number coefficients, No. 11"-had been scratched out and replaced with "Tiger Notes" in Root's handwriting. The Professor had given him a notebook he no longer needed to record data on the team. The first three pages were filled with incomprehensible equations and the later ones with other esoteric bits of information, such as Nakada's ERA or Shinjo's batting average.

I was kneading bread dough in the kitchen. We had decided to have fresh bread, something we hadn't had in a long while; topped with cheese or ham or vegetables, it would be our dinner. The sun had set, but the air was stifling, as though the leaves on the trees were breathing back the heat they had absorbed from the long, hot day. A warm blast of air blew in through the windows. The flowers on the morning glory Root had brought home from school had closed up for the night, and cicadas were resting on the trunk of the tallest tree in the garden, a grand old paulownia.

The fresh dough was soft and supple. The counter and floor were white with flour, as was my brow where I'd wiped the sweat with my sleeve.

"Professor?" said Root, his pencil poised above the page. Due to the heat, he wore a sleeveless T-shirt and a pair of shorts. He was just back from the pool and his hair was still wet.

"Yes?" said the Professor, looking up. His reading glasses had slipped to the end of his nose.

"What does 'Total Bases' mean?"

"It's the number of bases a player earns from a hit. So you'd score one for a single, two for a double, three for a triple, and…"

"Four for a home run."

"Right!" The Professor was delighted by Root's enthusiasm.

"You shouldn't bother the Professor when he's working," I said, dividing the dough into pieces and rounding them into little balls.

"I know," said Root.

The sky was clear, without a wisp of cloud. Sunlight filtered through the brilliant green leaves of the paulownia tree, dappling the ground in the garden. Root counted out the bases on his fingers as I lit the oven. Static crackled through the music on the radio and then faded again.

"But what about-" Root spoke up again.

"What about what?" I interrupted.

"I'm not asking you," he said. "Professor, how do you calculate 'Regulation at Bats'?"

"You multiply the number of games by 3.1, and discard everything after the decimal point."

"So you round down for.4 and up for.5?" Root asked.

"That's right. Let me have a look." He closed his book and went over to where Root was working. The notes on his jacket made a low, rustling sound. He rested one hand on the table and the other on Root's shoulder. Their shadows merged, with Root's legs swinging back and forth under the chair. I put the little loaves in the oven.

Soon, the music on the radio announced the start of the game. Root turned up the volume.

"Got to win today… got to win today… got to win today." It was his daily incantation.

"Do you suppose Enatsu will be starting?" the Professor said, taking off his glasses.

As we listened, I remembered the pristine pitcher's mound at the center of the infield, neatly rounded into a cool, damp, black mass awaiting the start of the game.

"Pitching today for the Tigers…"

Cheers and static drowned out the voice of the announcer. The smell of baking bread filled the room as we pictured the trail left by the pitcher's cleats on his walk out to the mound.