Infinity + One
Page 36
It was Finn’s turn to shake his head. “I don’t know, Bonnie. No matter how many words we get, there’s always going to be the last one, and one word is never enough.”
“I would have told her I loved her,” Bonnie whispered. “And I would have told her to save me a mansion next to hers.”
“A mansion?” Finn asked gently.
“There’s a song we always sang in church. “My Father’s House has Many Mansions.” Ever heard it?”
“No.”
“My Father’s house has many mansions, if it were not so, I would have told you,” she sang the line softly.
“Maybe God lives in the Grand Hotel,” Finn murmured, wanting to sit up and beg her to sing the rest. Instead, he folded his arms beneath his head and pretended that her voice didn’t make him feel things he didn’t want to feel and make him consider things he refused to consider.
“What’s the Grand Hotel?” she asked.
“It’s a little paradox about infinity—Hilbert’s paradox of the Grand Hotel.”
“What’s a paradox?”
“Something that contradicts our intuition or our common sense. Something that seems to defy logic. My dad loved them. Most of them are very mathematical.”
“So tell me about the Grand Hotel. Tell me the paradox.” The tears had faded from her voice, and Finn eagerly proceeded, wanting to keep them at bay.
“Imagine there’s a hotel with a countably infinite number of rooms.”
“Countably infinite?”
“Yeah. Meaning I could count the rooms, one by one, even if the counting never ends.”
“Okay,” she said drawing the word out, like she wasn’t sure she understood, but wanted him to keep talking.
“And all those rooms are filled,” Finn added.
“So infinite rooms, and all are full.”
“Uh-huh. Pretend someone comes along and wants to stay at the Grand Hotel. There’s an infinite number of rooms, so that should be possible, right?”
“Yeah, but you said all the rooms are occupied,” she countered, already confused.
“They are. But if you have the person in room one move to room two, and the person in room two move to room three, and the person in room three move to room four, and so on, then you just cleared out some space. You have an empty room—room one.”
“That makes no sense.”
“Sure it does, you can’t find the end of infinity. There is no end. So if you can’t tack space onto the end of infinity, you have to create space at the beginning.”
“But you said all the rooms are filled.”
“Yes. And they will still be filled,” Finn said, as if this were completely reasonable.
“So if ten people come along and want to stay at the Infinity Hotel . . .” her voice trailed off, waiting for him to fill in the rest.
“Then you have the person in room one move to room eleven, and the person in room two move to room twelve, and the person in room three move to room thirteen, and so on, clearing out ten rooms.”
She laughed quietly. “That makes no sense whatsoever. Eventually someone’s not going to have a room.”
“There are infinite rooms.”
“Yeah, yeah, yeah. And infinite people,” she muttered, as if her mind were a little blown.
“That’s why it’s called a paradox. In a lot of ways, infinity makes no sense. It’s impossible to get your mind around that type of vastness,” Finn said thoughtfully. “But no one argues with infinity. We just accept that it’s beyond visualization.”
“I don’t know about that . . . I frequently argue with Infinity.” Bonnie rubbed her face against his leg as if she liked the feel of him beside her.
“Ha ha,” Finn said dryly, wondering if he should pull away. He probably should. But he didn’t.
“Do you think heaven is filled with countably infinite rooms filled with countably infinite people?” she asked.
Maybe Bonnie wondered if Minnie was in her own heavenly room. Maybe Fisher was there too, in a room near Minnie’s. Maybe they had found each other the way Finn and Bonnie had, Finn mused to himself. And then he swallowed a groan at his romantic thoughts. He was getting delusional. And it was all Bonnie’s fault.
“I don’t know, Bonnie Rae,” he said.
“People in Appalachia have been singing that song since the dawn of time. They’re hoping there are infinite rooms and that the rooms are all mansions.”
“That’s kind of sad.” The cynic in Finn didn’t like the thought of people singing about mansions that didn’t exist. It felt like buying lottery tickets to him—a huge waste of emotion and energy.
“Yeah. I guess so. But it’s hopeful too. And sometimes hope is the difference between life and death.”
Finn had no answer for that.
“Hey!” she said suddenly, her voice rising with her epiphany. “I know how we can make some room at the Infinity Hotel without making everyone move. I’ve officially solved the paradox. Call it Bonnie Rae’s Solution.”
“Oh yeah?”
“Yeah. We’ll all double up. Problem solved. You wanna double up, Infinity Clyde?” Finn was sure if he could see her face she would be waggling her eyebrows. She liked to tease. And she was damn good at it.
Yeah. He wanted to double up. Instead he decided to poke back a little. “The problem is, when people double up, they start to multiply.”
“I would have told her I loved her,” Bonnie whispered. “And I would have told her to save me a mansion next to hers.”
“A mansion?” Finn asked gently.
“There’s a song we always sang in church. “My Father’s House has Many Mansions.” Ever heard it?”
“No.”
“My Father’s house has many mansions, if it were not so, I would have told you,” she sang the line softly.
“Maybe God lives in the Grand Hotel,” Finn murmured, wanting to sit up and beg her to sing the rest. Instead, he folded his arms beneath his head and pretended that her voice didn’t make him feel things he didn’t want to feel and make him consider things he refused to consider.
“What’s the Grand Hotel?” she asked.
“It’s a little paradox about infinity—Hilbert’s paradox of the Grand Hotel.”
“What’s a paradox?”
“Something that contradicts our intuition or our common sense. Something that seems to defy logic. My dad loved them. Most of them are very mathematical.”
“So tell me about the Grand Hotel. Tell me the paradox.” The tears had faded from her voice, and Finn eagerly proceeded, wanting to keep them at bay.
“Imagine there’s a hotel with a countably infinite number of rooms.”
“Countably infinite?”
“Yeah. Meaning I could count the rooms, one by one, even if the counting never ends.”
“Okay,” she said drawing the word out, like she wasn’t sure she understood, but wanted him to keep talking.
“And all those rooms are filled,” Finn added.
“So infinite rooms, and all are full.”
“Uh-huh. Pretend someone comes along and wants to stay at the Grand Hotel. There’s an infinite number of rooms, so that should be possible, right?”
“Yeah, but you said all the rooms are occupied,” she countered, already confused.
“They are. But if you have the person in room one move to room two, and the person in room two move to room three, and the person in room three move to room four, and so on, then you just cleared out some space. You have an empty room—room one.”
“That makes no sense.”
“Sure it does, you can’t find the end of infinity. There is no end. So if you can’t tack space onto the end of infinity, you have to create space at the beginning.”
“But you said all the rooms are filled.”
“Yes. And they will still be filled,” Finn said, as if this were completely reasonable.
“So if ten people come along and want to stay at the Infinity Hotel . . .” her voice trailed off, waiting for him to fill in the rest.
“Then you have the person in room one move to room eleven, and the person in room two move to room twelve, and the person in room three move to room thirteen, and so on, clearing out ten rooms.”
She laughed quietly. “That makes no sense whatsoever. Eventually someone’s not going to have a room.”
“There are infinite rooms.”
“Yeah, yeah, yeah. And infinite people,” she muttered, as if her mind were a little blown.
“That’s why it’s called a paradox. In a lot of ways, infinity makes no sense. It’s impossible to get your mind around that type of vastness,” Finn said thoughtfully. “But no one argues with infinity. We just accept that it’s beyond visualization.”
“I don’t know about that . . . I frequently argue with Infinity.” Bonnie rubbed her face against his leg as if she liked the feel of him beside her.
“Ha ha,” Finn said dryly, wondering if he should pull away. He probably should. But he didn’t.
“Do you think heaven is filled with countably infinite rooms filled with countably infinite people?” she asked.
Maybe Bonnie wondered if Minnie was in her own heavenly room. Maybe Fisher was there too, in a room near Minnie’s. Maybe they had found each other the way Finn and Bonnie had, Finn mused to himself. And then he swallowed a groan at his romantic thoughts. He was getting delusional. And it was all Bonnie’s fault.
“I don’t know, Bonnie Rae,” he said.
“People in Appalachia have been singing that song since the dawn of time. They’re hoping there are infinite rooms and that the rooms are all mansions.”
“That’s kind of sad.” The cynic in Finn didn’t like the thought of people singing about mansions that didn’t exist. It felt like buying lottery tickets to him—a huge waste of emotion and energy.
“Yeah. I guess so. But it’s hopeful too. And sometimes hope is the difference between life and death.”
Finn had no answer for that.
“Hey!” she said suddenly, her voice rising with her epiphany. “I know how we can make some room at the Infinity Hotel without making everyone move. I’ve officially solved the paradox. Call it Bonnie Rae’s Solution.”
“Oh yeah?”
“Yeah. We’ll all double up. Problem solved. You wanna double up, Infinity Clyde?” Finn was sure if he could see her face she would be waggling her eyebrows. She liked to tease. And she was damn good at it.
Yeah. He wanted to double up. Instead he decided to poke back a little. “The problem is, when people double up, they start to multiply.”
