Don Eppes smiled without meaning to as he passed the large table in his family's house. Ahead of him, Charlie's notes lay scattered across it, already taking up more of the table than seemed possible given that he'd been in town for less than a full day. Behind him, Don could hear his father moaning about a fumbled play in a bowl game with too long of a name.
Yelling at referees who wouldn't hear didn't seem, to Don, to be particularly good for one's health, yet Alan was in good spirits. He was recalcitrant about staying in the guest house, and although Don had been encouraged when Alan had wanted to "drive by and look at" a senior center fifteen minutes out of time, it turned out he just wanted to see the parking lot design.
That's civil engineers for you, Don thought, shaking his head.
He glanced down at the table: Charlie had been scribbling something on one page: EB talk: defn's, examples first? Ask B. mention SAT, cliques...
Someone knocked at the door. "I'll get it!" Alan snapped, as if as much to convince Don that his hearing hadn't gone than in a gesture of hospitality. Or maybe to take him off the quarterbacks' ineptitude. Whatever the case, he opened the door to let Amita in—she'd been catching up with some of her California friends to open her vacation.
"Hey," said Alan.
"You're still awake?" Don gaped. "Charlie crashed a while ago."
Amita laughed. "I'm more used to intercontinental flights than he is. Jet lag has never really been a problem for me."
"Lucky you," said Don.
"Well, if you need to stay up any later, there's coffee in the kitchen," Alan nodded.
"Coffee'd be great, thanks," Amita smiled appreciatively.
A few minutes later, they were all watching the game, the Eppes somewhat more intently than Amita. Trying to be conversational, Don asked, "So what's new in Cambridge?"
"Everything," she gushed. "Though nothing, really, it's just all different for me. Overwhelming, there's so many things I'm not used to—but it's really exciting."
"Don't want to be rude, but should I even bother to ask what you're...studying? Teaching?"
She laughed. "I actually taught algebra last term—not quite the kind of algebra you might remember but it doesn't matter. Teaching a couple graduate seminars when we start back up again. I'm excited about those, hoping to show some new applications."
"Do either of you get to use any of the stuff you worked on for the FBI?" Alan asked.
"Probably not, it'd be a hassle to get clearance. But it's okay, I've been reading a lot of new articles as well. Private-sector stuff."
"Same kind of things Charlie's working on?"
"Oh no, he's doing the whole cognitive-emergence stuff still. I can follow most of it, but at the end of the day we talk about things that aren't work."
"Seriously?" Don gaped. "You're a better influence on him than I thought."
Amita blushed. "Speaking of influences, how's Robin?"
Don sighed. "She's had a rough few months on the job."
"I'm sorry to hear that."
Don nodded. "Me too."
"What happened?" said Alan. "I thought you said she was working an open-and-shut case."
"The Williams one?" said Don. "Yeah. That was the problem. Got the stupid thing open, but it didn't shut."
The others did not follow up. Don glanced at the TV, but it had gone to a commercial break. After a quick glance to decide that he did not need a new razor, he took a long sip of beer, and sighed. "I assume she's going to blame the crime shows. She always blames the crime shows."
"Huh?" said Alan.
"Oh, crime shows, you know, on TV."
"Yeah, yeah," he said irritatedly, "I rely on you to keep me posted, you're much more interesting."
Don blushed. "But according to Robin, because of all the high-tech forensic things people see on crime shows, they get unrealistic standards, as jurors. They expect us to have DNA, or do some exotic tests much more quickly than is possible, even when there's a witness to tell them what happened!" He glanced at Amita, who was almost smiling. "What? I know witness testimony can be unreliable, so does Robin, but that doesn't explain—stop laughing!"
"Sorry!" Amita blushed. "You just reminded me of Charlie."
"That heated?" he said, sipping beer again.
The game had started back up, but Amita was paying little attention. "He made me—okay, not made, I volunteered to listen to a presentation he gave to some secondary schoolkids—they're like high schoolers—a few days ago."
"Oh? I think I saw notes about that on the table."
"Probably. Anyway, it was just funny because we also got to a part about witnesses."
"Witnesses? In math? I thought you said you weren't carrying over any of our work."
"I wasn't," she giggled. "Here, let me show you."
"Oh, you've done it now," Alan muttered, as Amita strode over to the table.
"Sue me, I want to see how she's going to try and pull this one off," said Don.
"I heard that," said Amita, grabbing a scratch piece of paper. At least, Don hoped it was scratch...
"Okay, so look at this," she said, scribbling down (x + y)(x'+z)(z'+y). "If you wanted this equation to be a positive number, how could you define x, y, and z?"
Don squinted. "What are those...apostrophes?"
"They have to do with changing functions, right? I saw this before, it's about speeds," said Alan.
"Yeah," Amita giggled, "that is usually it, except here, it's...oh, never mind. The point is, if you don't know what these letters stand for...you could try putting in different numbers, to see if they worked. But that would take a while."
"What is this? What does the equation represent?"
"Nothing, nothing," said Amita, "really. But if I just told you to figure out this..."
(1+1) x (0+1) x (0 + 1)
"...you know how to do that, right?"
"That's just two...times one, doesn't do anything...times one. Is that a trick question?" asked Don.
"No, no. It's two, right?"
"So...I mean I haven't gone into the primes. The apostrophes, what they mean. But when I ask you just to do the math with the numbers right there, it's a lot easier than trying to figure out that first puzzle, right?"
"Is that the same as the first puzzle?" said Don. "The ones represent the numbers, the zeroes represent the numbers with the apostrophes?"
"Yeah. Yeah," said Amita excitedly. "I mean it's not the same. This way is easier, you see?"
"Yeah. But the kind of math you guys do, that's not solving problems this easy, right?"
"No. But there are a lot of problems that are—when you do it with computers, they work out to be about as hard as either those first kind of problems, with the letters. Or the second kind that are just arithmetic. So when I just gave you the numbers, the ones and zeroes—we call that a "witness.""
"A witness?" Don laughed. "That tells you exactly what's happening. Nice. And people just ignore them?"
"Er, no. People get all worried about these hard problems—"
"—like demanding the DNA evidence—"
"—when maybe, people think, no one's ever shown that a computer would take that much longer to do the hard kinds anyway, and it might be just as easy as—"
"—having a witness!" they laughed together.
Don glanced at the paper, then noticing it was the back side of the one he'd seen before. "Cliques and the SAT, huh?" he asked. "Stuff that's really relevant to high-schoolers. Good for him!"
Amita took a second, then laughed uproariously. "Don, we live in England! They don't take the SAT!"
"Well, excuse me," he said defensively.
"Oh it's not your fault at all—that was really funny—no, this is the SAT." She turned the paper back over. "It's just the name of the problem. And the clique problem is another thing, they're all examples of the same phenomenon. He didn't go into this much detail in the presentation, just listed the names of a couple examples. I think he did a good job at teaching at the right level, these are just a couple notes."
"Oh," Don blinked. "So what was the presentation about, then?"
"Oh, this is all part of this one big math—well, computer science—thing. It's called P versus NP."
After a long silence, Amita blinked. "Sorry?"
"Oh..." Don looked at his father, who was giving a small, wondering smile, to his sister-in-law, but not before an imperceptible raise of his eyes to the floor above where his brother was still asleep. "Nothing."