This man may be envious of me, Tengo began to think after a certain point. He’s jealous—either of me as a person or of the life I’m leading. But does a father really feel jealousy toward his own son? As a child, Tengo did not judge his father, but he could not help feeling a pathetic kind of meanness that emanated from his father’s words and deeds—and this he found almost physically unbearable. Often he felt that this man was not only envious of him, but that he actually hated something in his son. It was not that his father hated Tengo as a person but rather that he hated something inside Tengo, something that he could not forgive.

Mathematics gave Tengo an effective means of retreat. By fleeing into a world of numerical expression, he was able to escape from the troublesome cage of reality. As a little boy, he noticed that he could easily move into a mathematical world with the flick of a switch in his head. He remained free as long as he actively explored that realm of infinite consistency. He walked down the gigantic building’s twisted corridor, opening one numbered door after another. Each time a new spectacle opened up before him, the ugly traces of the real world would dissipate and then simply disappear. The world governed by numerical expression was, for him, a legitimate and always safe hiding place. As long as he stayed in that world, he could forget or ignore the rules and burdens forced upon him by the real world.

Where mathematics was a magnificent imaginary building, the world of story as represented by Dickens was like a deep, magical forest for Tengo. When mathematics stretched infinitely upward toward the heavens, the forest spread out beneath his gaze in silence, its dark, sturdy roots stretching deep into the earth. In the forest there were no maps, no numbered doorways.

In elementary and middle school, Tengo was utterly absorbed by the world of mathematics. Its clarity and absolute freedom enthralled him, and he also needed them to survive. Once he entered adolescence, however, he began to feel increasingly that this might not be enough. There was no problem as long as he was visiting the world of math, but whenever he returned to the real world (as return he must), he found himself in the same miserable cage. Nothing had improved. Rather, his shackles felt even heavier. So then, what good was mathematics? Wasn’t it just a temporary means of escape that made his real-life situation even worse?

As his doubts increased, Tengo began deliberately to put some distance between himself and the world of mathematics, and instead the forest of story began to exert a stronger pull on his heart. Of course, reading novels was just another form of escape. As soon as he closed their pages he had to come back to the real world. But at some point Tengo noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of mathematics. Why should that have been? After much deep thought, he reached a conclusion. No matter how clear the relationships of things might become in the forest of story, there was never a clear-cut solution. That was how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within.

The older he became, the more Tengo was drawn to this kind of narrative suggestion. Mathematics was a great joy for him even now, as an adult. When he was teaching students at the cram school, the same joy he had felt as a child would come welling up naturally. To share the joy of that conceptual freedom with someone was a wonderful thing. But Tengo was no longer able to lose himself so unreservedly in a world of numerical expression. For he knew that no amount of searching in that world would give him the solution he was really looking for.

When he was in the fifth grade, after much careful thinking, Tengo declared that he wanted to stop making the rounds with his father on Sundays to collect the NHK subscription fees. He told his father that he wanted to use the time for studying and reading books and playing with other kids. Just as his father had his own work, he had things that he had to do. He wanted to live a normal life like everybody else.

Tengo said what he needed to say, concisely and coherently.

His father, of course, blew up. He didn’t give a damn what other families did, he said; it had nothing to do with them. We have our own way of doing things. And don’t you dare talk to me about a “normal life,” Mr. Know-it-all. What do you know about a “normal life”? Tengo did not try to argue with him. He merely stared back in silence, knowing that nothing he said would get through to his father. If that was what Tengo wanted, his father continued, that was what he would get. But if he couldn’t listen to his father, his father couldn’t go on feeding him anymore. Tengo should get the hell out.

Tengo did as he was told. He packed a bag and left home. He had made up his mind. No matter how angry his father got, no matter how much he screamed and shouted, Tengo was not going to be afraid—even if his father raised a hand to him (which he did not do). Now that Tengo had been given permission to leave his cage, he was more relieved than anything else.

But still, there was no way a ten-year-old boy could live on his own. When class was dismissed at the end of the day, he confessed his predicament to his teacher and said he had no place to spend the night. He also explained to her what an emotional burden it had been for him to make the rounds with his father on Sundays collecting NHK subscription fees. The teacher was a single woman in her mid-thirties. She was far from beautiful and she wore thick, ugly glasses, but she was a fair-minded, warmhearted person. A small woman, she was normally quiet and mild-mannered, but she could be surprisingly quick-tempered; once she let her anger out, she became a different person, and no one could stop her. The difference shocked people. Tengo, however, was fond of her, and her temper tantrums never frightened him.

She heard Tengo out with understanding and sympathy, and she brought him home to spend the night in her house. She spread a blanket on the sofa and had him sleep there. She made him breakfast in the morning. That evening she took him to his father’s place for a long talk.

Tengo was told to leave the room, so he was not sure what they said to each other, but finally his father had to sheathe his sword. However extreme his anger might be, he could not leave a ten-year-old boy to wander the streets alone. The duty of a parent to support his child was a matter of law.

As a result of the teacher’s talk with his father, Tengo was free to spend Sundays as he pleased. He was required to devote the morning to housework, but he could do anything he wanted after that. This was the first tangible right that Tengo had ever won from his father. His father was too angry to talk to Tengo for a while, but this was of no great concern to the boy. He had won something far more important than that. He had taken his first step toward freedom and independence.

Tengo did not see his fifth-grade teacher for a long time after he left elementary school. He probably could have seen her if he had attended the occasional class reunion, to which he was invited, but he had no intention of showing his face at such gatherings. He had virtually no happy memories from that school. He did, however, think of his teacher now and then and recall what she had done for him.