Page 17 of Middlegame

“Cool,” Dodger says, and sits cross-legged on the ground, backpack in her lap. She unzips it and pulls out her notebook, opening it and looking at the page like she’s trying to read it. She’s not: she’s giving him a chance to see.

The paper is covered in squiggles, mathematical symbols, and a dismaying number of letters. There aren’t many numbers. That’s the thing with Dodger: she seems to think numbers are irrelevant to the process of doing math. What’s scarier is she seems to be right. She still helps with his math, but hers has progressed to college level and beyond. Half her local library’s reference section is stored under her bed in photocopies that swallow the bulk of her allowance every week. What feels like half his local library’s reference section is there with it, copied by hand in California as he read it, uncomprehending, in Massachusetts.

“I don’t know what that is,” he says.

“That’s okay. I didn’t expect you to.” Dodger taps the top of the page, where she’s transcribed an equation. She’s discovered gel pens recently. Her math papers are a rainbow explosion of figures, symbols, and confusing results. “This is a really famous problem by a man named Monroe. There’s a reward for solving it. Like, a lot of money. People have been trying for sixty years, and no one’s been able to figure it out.”

“And you have?”

“I have.” Dodger smiles. For the moment, she is still; for the moment, she’s at peace. Roger sometimes feels like he’s the only one who gets to see her that way, and he knows how lucky he is to have that, even as he wishes there was someone else she trusted this much. He’s very far away. They may never meet. They may not even be in the same world—because once you say “I have a friend who talks in my head, and I’m pretty sure she’s real, she knows things I don’t know, and I guess that’s what real looks like,” it’s not such a leap to say “I think she’s in another dimension”—and if she ever gets really hurt, he’s not going to be able to do anything to help her. He can imagine calling the police and trying to make them understand that his imaginary friend who isn’t imaginary has fallen and broken her leg. He’d go to the nuthouse so fast that they’d probably leave his shoes behind like in a cartoon.

“Can you tell me the answer?”

“No.” There’s no rancor in her reply: she knows he wouldn’t understand, like he knows she wouldn’t understand if he started trying to explain the etymology of the words they’re both using. They shore up one another’s limits. That means knowing where those limits are. “But if I send this in, if I show my work and send this in . . .” Her fingers skitter across the page like water bugs across the surface of the pond, hesitant and proprietary all at once.

“They’d give you the money?”

Dodger smiles serenely. He can feel it. “They’d have to. I did the work, and the rules say anyone can enter, anyone can do the work and enter. It’s a lot of money, Roger.”

“How much?”

“Ten thousand dollars.”

For a moment, Roger is silent, staggered by the size of the figure. Ten thousand dollars is a lot of books, a lot of photocopies; it’s the sort of money even adults only dream about. For Dodger, it could mean her own home computer, one of those fancy ones that does math faster than a calculator, even faster than her; it could mean the tools she’s shown him in her scientific catalogs, the ones that would let her figure out the way the universe is made.

“I was thinking, if I send it in, and they give me the money . . . I could say you were my pen pal. That we met last year at chess camp. If you sent me a couple letters, it would be a way for me to have your address that wouldn’t look weird, you know?” She sounds suddenly shy, like she can’t believe she’s saying this out loud. “Ten thousand dollars is a lot of money. I bet my parents would be okay with spending part of the prize on plane tickets, if it was so I could visit a friend. We could come to Cambridge. Me and my parents. Daddy says the East Coast has a lot of history he’d love to see, and Mom likes anything he likes, and I could meet you. You could meet me. For really real, not just like this.”

Roger is silent. Roger is reeling. This is moving so fast, and what if he sends her a letter and it never gets there? They’ve talked about this before, about the possibility that they’re in different dimensions, talking through some sort of wormhole or cosmic hiccup. About the chance that trying to make contact—because it would be easy to pass a phone number or an address along their mental link, it would be so easy—would sever that bond and leave them both on their own.

Roger has gotten better at making friends in the past two years. He knows the words they want to hear from him, and he’s no longer so scared of rejection, because he knows Dodger will always be there; if the kids in his class say he’s not worth their time, that won’t render him eternally alone. He’s not sure he could hold on to that confidence if he lost her. And Dodger . . .

He’s not in her head all the time. She has class and baths and stuff, and so does he; sometimes they have to walk solo. But he’s never dropped in to find her talking to anyone else about anything that feels like friendship, and when he’s asked, she’s never been willing to answer. It doesn’t feel like she has any friends but him. That’s a little scary.

“Roger?” she whispers.

“Are you sure?” He shakes his head. She can’t hear it, but he needs to move. If he opens his eyes, he’ll lose her. He’s had a lot of practice at doing things with his eyes closed. “What if . . . Remember when we were talking about wormholes and stuff? What if that was true?”

“I don’t think sending a letter could violate quantum entanglement,” she says. “If you send it and it doesn’t get here, we’ll know we’re not in the same dimension, and we don’t have to try doing this again. But don’t you want to meet me for real?”

He does not. What they have is strange and fragile and it’s the best thing in his world, but it’s also terrifying and weird. It’s not normal. Dodger doesn’t seem to care whether people think she’s normal. Roger does. He likes it when people treat him like everybody else, like he’s just a smart kid and not some sort of circus freak. What if meeting her makes their connection go away and suddenly he’s a lopsided genius again, taking remedial math classes while he argues with college professors about verb tenses? Or what if it’s like on Star Trek, where touching somebody who reads minds makes it worse, and they can never turn off the connection between their thoughts again?

He’s been quiet too long. Dodger’s hand flashes into her frame of vision as she reaches up and wipes her eyes; she’s crying. He didn’t answer when she asked if he wanted to meet her, and now she’s crying. “Dodge—”

“Forget it.” She slams the notebook, wrinkling the pages. There are glittering stars drawn on the cover, fidget-constellations marching from margin to margin in silver and purple ink. Somehow that little reminder that she is a person when he’s not around, that she’s not an imaginary friend he can take or leave at will, makes it worse. “It was a stupid idea, okay? I’ll use the money to go to Disney World or something. Roller coasters are like math you can ride.”

“I’m sorry.”

“You should go now, Roger. It’s family game night, isn’t it?” She wipes her eyes again as she stands. “Maybe I can get Dad to play chess with me. You don’t like watching that, anyway.”

Roger doesn’t say anything. He’s learned to recognize Dodger’s moods: there’s no getting through to her when she’s this upset, and maybe that’s good, because it means he has time to figure out what to say to make her stop crying. It’s not that he doesn’t care about her—he loves her, the way he assumes he’d love a sister—but sometimes changing things isn’t the right thing to do. Sometimes changing things means throwing the whole world out of alignment.

“Well?” she demands.

“I’ll come back at bedtime,” he says, and opens his eyes on his own bedroom ceiling. The California afternoon is gone, replaced by the snow outside his window and the gray-and-brown wallpaper he picked out for himself the last time his mother decided to redecorate.

Carefully, he sits up, checking his body for tingles and numbness. He’s not out of his body when he’s visiting Dodger, but he’s less connected to it than a person is supposed to be. He can forget about it, if he’s gone long enough. Sometimes he snaps back into his own skin and discovers he’s been lying wrong on his arm for an hour, and then everything buzzes and stings while it’s waking up. He’s had to bite his lip more than once to keep from whimpering and attracting the attention of his parents. His mom has already expressed concerns that he might be narcoleptic. He’s had to plead with her not to have him tested, claiming he just gets headaches sometimes.

(That’s not entirely false: he does get headaches sometimes, and the school nurse has seen enough of them that she was happy to explain to his parents that no, there’s nothing wrong with him, it’s just that kids work their brains too hard and make them hurt sometimes. As long as it’s nothing worse than the occasional nap in a dark room in the middle of the day, there’s nothing for them to worry about. Roger doesn’t like the way she looks at him—with pity, like he’s halfway to becoming an invalid, like she’s trying to protect what remains of his childhood by refusing to refer him to a doctor—but it’s kept his parents from probing any deeper, so he supposes he’s grateful.)