“Sorry. The building on the left.”
“Yes?” said Caitlin.
“Look at the end of the name.”
“Oh! What the heck is that?”
“It’s a maple leaf. Where they’d have the apostrophe in the name in the States, they’ve got a maple leaf here. Applebee’s and Denny’s do the same thing: A-p-p-l-e-b-e-e, maple leaf, s, and D-e-n-n-y, maple leaf, s.”
“This is one wack-job country you got here, Matt.”
He laughed again. “We make it work somehow. I mean, it’s a small thing for English Canada, and it makes French Canada happy, so why the heck not? Yeah, the cloning of Tim Horton is kinda crazy, I’ll give you that. But all the maple leaves are cool.”
They went into the Hortons, and Matt read the menu to her, explaining what kinds of sandwiches they offered—she could have read it herself, given time, but there were people in line behind them. She ordered chicken salad on a whole-wheat bun, a chocolate glazed donut, and a Coke. He ordered sliced turkey on a regular bun and a small coffee.
Caitlin opened her wallet—and found herself pausing to stare. She still had her bills folded in distinctive ways so that she could tell a five from a ten from a twenty by touch. But now she could read the large, clear numerals on the Canadian bills—not to mention see that the five was blue, the ten purple, and the twenty green. Would wonders never cease?
Realizing she was holding up the line, Caitlin handed over a ten, took her change, and then followed Matt to a table in a corner—one of those modular ones with chairs attached to it. “So,” she said, after some chitchat that she had to admit was pretty lame, “do you—um, do you have a girlfriend?” She was amazed at how dry her mouth had suddenly become.
She was surprised to see him appear—hurt, perhaps? Like maybe he thought she was teasing him. But at last he said simply, “No.”
She looked away, in case she was making him uncomfortable, and pleased herself by the figurative and—at that precise moment, literal—truth of her reply: “I’m not seeing anyone, either.”
He took a bite of his sandwich, and she took a bite of hers. She was afraid to say anything else, but—
But she was Barbara Decter’s daughter, for Pete’s sake! And her mother had told her, years ago, when Caitlin had asked about her parents’ relationship, that she had asked her father out the first time, and, eighteen months later, that it had been her, not him, who had popped the big question.
So, hell, she wouldn’t even be here if her mother had been too shy to make the first move—and the second, and the third, and…
“Um,” she said, and “ah,” and then, disappointing herself with the quality of her rhetoric, she let loose with another “um.” Online she was fearless—she was Calculass! But here, in the real world, she was just Caitlin, and sometimes, especially when having to deal with people stuff, she felt more like her father’s daughter than her mother’s. She took a deep breath and tried to summon the strength of her alter ego. Then she looked down at her sandwich, and, when she forced the words out they came in a rush, without any pauses: “So would you like to go out sometime?”
Caitlin, of course, counted the seconds.
One. Two. Three.
She resisted the urge to look up him, afraid of the expression she might see.
Four. Five. Six.
“You want to go out with me?” he said, at last, sounding stunned.
She did lift her gaze. “Yes, silly.”
“I, uh, I thought you were going with Trevor. I, um, I mean, didn’t he take you to the dance?”
“Were you there?”
“Me?” He seemed astounded at the suggestion. “No.”
“Trevor’s a jerk,” she said. “And, no, I’m not going out with him. So, how ’bout it? Wanna go out sometime?”
“Well,” he said, and “um,” and, at last, “yes.”
“Great,” said Caitlin. She paused, waiting for him to make a suggestion, but when he didn’t she said, “There’s an awesome series of free public lectures at the Perimeter Institute. Have you ever been to any of those?”
“No. I’ve tried. The tickets are impossible to get. They go like that.” He snapped his fingers as he spoke the final word.
“I’ve got an in. My dad is on the lecture committee there.”
“Your dad works at PI?”
“Uh-huh. He studies quantum gravity.”
“Cool!”
Caitlin smiled. Who’d have thought her dad would turn out to be cool?
Suddenly, Braille dots flowed in front of her eyes. If I may be so bold, Caitlin, you should inquire about what he hopes to do after high school.
Caitlin wanted to ask what the hell Webmind was doing, but there was no way to do so with Matt right there. Still, it did seem like a good way to keep the conversation going, so she posed the suggested question.
“I’m going to do computer science.”
Ask him where.
“Where?”
“Here,” he said. “There’s nowhere better than the University of Waterloo.”
“Really? I’ve always had my heart set on MIT.”
“Well,” said Matt, “you should check out what’s here, too.”
Ask him what his favorite color is.
Caitlin couldn’t stand it anymore. “What are you doing?” she said into the air.
I read all of Project Gutenberg, Webmind replied at once, including the play Cyrano de Bergerac. I thought I’d lend a hand.
“Sorry,” said Matt. “I, um, I always eat my sandwich that way.”
Caitlin had too little experience with watching people eat to be able to identify whatever Matt had done that was unusual. “Ah,” she said, and smiled at him. “That’s okay. It’s cute.”
twenty-five
Caitlin had heard her mom use the phrase “nonzero-sum” from time to time. She knew it was a term from her mother’s field of expertise, game theory. Webmind had already read everything on Wikipedia about game theory, but that didn’t mean he actually understood what “nonzero-sum” meant. Nor, if she was really honest with herself, did Caitlin, and yet this notion of nonzero-sum games was stuck in her mind: win-win situations in which everything could be made better.
Her mother had been having her own conversations with Webmind all day long while Caitlin was at school. Once Caitlin got home and had checked her email and so forth, she went across the hall to her mother’s office and told her about that poor Australian girl who had committed suicide, and about how she’d told Webmind that he should intervene in nonzero-sum situations.
Her mom looked horrified. “It just… just watched her kill herself? It didn’t try to stop her?”
“He, Mom. He didn’t know what to do, what to think. We need him to understand what to do the next time, and not just with teen suicides, but in any nonzero-sum situations. Can you help us?”
Her mother’s face moved through several expressions but then settled on one that Caitlin had seen before: the take-charge, supermotherscan-do-everything face. “Yes, I’ll help it—help him—learn to help the rest of us. That’s something I definitely want in on.”
“Thanks,” replied Caitlin. “But, I mean, I know—we know—what nonzero-sum is; we get that. But there must be a lot more to game theory than just that.”
“Oh… a bit,” said her mother. Caitlin realized she was still coming to grips with the magnitude—the importance—of what she was about to do.
“So, could you explain it to us? I remember hearing you say once that game theory really isn’t just about mathematics, but about human psychology.”
“That’s right,” her mother said. “In fact, the hottest branch of game theory right now is called ‘behavioral game theory.’ ”
“Well, Webmind certainly needs to understand human behavior better.”
So everyone keeps saying, Webmind sent to her eye.
“Okay,” said her mom. “Let’s go downstairs.”
Her mother got a clipboard, some pens, and some
paper, and the two of them went to the dining room, which had a big table. There was normally one chair on each side of the table, but Caitlin’s mom moved hers to be next to Caitlin’s.
“Webmind is listening, right?” asked her mom.
The word Yes flashed in Caitlin’s vision, and she repeated it.
“Okay,” her mom said. “Do you know what the prisoner’s dilemma is?”
Caitlin thought, How to pick up the soap in the shower? But what she said was, “No.”
Her mother seemed to consider for a moment, then: “Okay, let’s do it like this: say you and Bashira both get in trouble at school. Say Principal Auerbach has said that he thinks you guys have hacked into the school’s computer and changed your grades—just like in WarGames, right? And he talks to each of you separately. He says to you, ‘Okay, look, Caitlin, I admit I haven’t got enough evidence to actually prove you did this, but I can suspend each of you for a week just because, well, because I’m the principal.’ ”
Caitlin nodded, and her mother went on. “But the principal’s real interest is in making sure this never happens again, so he adds that if you’ll say Bashira did it and explain how it was done, you get off scot-free—no suspension at all—and he’ll suspend Bashira for three weeks. Oh, except for this: if you say Bashira did it, and Bashira says you did—that is, if you each blame the other—then you’ll both get suspended for two weeks. Got that? You can end up with no suspension, one week’s worth, two weeks’ worth, or three weeks’ worth. And you know he’s going to make the same offer in private to Bashira. What do you do?”
Caitlin didn’t hesitate. “I clam up; I don’t say a word.”
“But if Bashira fingers you, you’ll get three weeks of suspension.”
“But she won’t,” Caitlin said firmly.
Her mother seemed to consider this. “Okay, okay, let’s say it’s not you and Bashira for the moment. Let’s say it’s just two random guys—um, Frank and Dale. What should you do if you’re Frank?”
Caitlin suppressed a smile. Frank was the name of her mother’s first husband, who had come and gone long before she’d been born, and Dale, she knew, was the former head of the Economics Department at the University of Houston—someone her mother had famously not gotten along with. Picking truly random people was as hard as generating really random numbers, it seemed.
Still, the math was easy. “I rat out Dale,” Caitlin said.
“Why?”
“Because it’s the best thing for me. If he doesn’t rat me out, I get away without any punishment, instead of having a one-week suspension. And if he does rat me out, then I’m still better off, because then I only get a two-week suspension, instead of the three weeks I’d have gotten by keeping my mouth shut. No matter what he does, I cut a week off my punishment by ratting him out.”
“And what about Dale? What should he do?”
Caitlin frowned. “Well, I guess he should rat me out, too.”
“Why?”
“The same reasons: no matter what I do, he gets one week less suspension by turning me in.”
Her mother smiled—but whether at Caitlin’s brilliance or at the thought of both Frank and Dale being punished, she couldn’t say. “Exactly,” her mom said, and she started to draw on the paper. “If we make a chart with Frank’s possible moves—we call them ‘defecting’ or ‘cooperating’—on the x-axis and Dale’s possible moves—the same things, defect or cooperate—on the y-axis, we get what’s called the payoff matrix: a table with a score for each possible outcome, see?” She pointed at one of the squares in the matrix. “Even though the best possible outcome—one week’s punishment—occurs when you both cooperate, the math says you should both defect. Granted it doesn’t give you personally the best possible outcome, but it does give you the best outcome you can reasonably expect given that the other player will selfishly act in his or her own interests.”
Caitlin frowned again. If game theory was all about people being selfish, it wasn’t going to help her accomplish what she wished with Webmind; she needed a way to make it want to act altruistically.
“Now,” her mom went on, “that’s a simple game: each player only got to make one move. But most games involve a series of turns. Consider a dollar bill—”
“We’re in Canada now, Mom,” Caitlin said, teasing. “They don’t have dollar bills.” She knew the Canadian one-dollar coin was called a loonie, because it had a picture of a loon—a kind of waterfowl—on the tails side. She also knew that the two-dollar coin was called a toonie. She thought a much more clever name would have been “doubloon,” but nobody had asked her.
“Fine,” her mother said, smiling. “Consider a dollar coin, then—and consider a bunch of people at a party. Now, I’ve actually tried this myself, and it really works. Announce to the group at the party that you’re going to auction off the dollar—highest bidder gets to keep it. But, unlike normal auctions, there’s one special condition: the second-highest bidder also has to pay up whatever his or her highest bid was—but gets nothing for it. Got that?”
Caitlin nodded.
“How much, on average, do you think the dollar sells for?”
She lifted her shoulders. “Fifty cents?”
“Nope. The average is $3.40.”
“That’s crazy!” said Caitlin.
“Loony, even,” her mother replied. “But it’s true.”
“Why do people bid so high?”
“Well, remember, the second-highest bidder has to pay the auctioneer, too, so…” She trailed off, clearly wanting Caitlin to figure it out for herself.
She tried to do so. The first bidder presumably bid a penny to start—which would net him a ninety-nine-cent profit. But then as soon as a second bidder offered two cents, the first bidder probably figured that offering three cents was still a good deal: he’d net ninety-seven cents in profit.
And so it would continue, until—
Ah!
Until one bidder bid ninety-nine cents—which would still give him a one-cent profit. But the previous bidder, whose bid might have been, say, ninety-eight cents, was now looking at losing that much and getting nothing in return. And so he would bid a dollar—thereby breaking even, at least. But then the guy who had bid ninety-nine cents faced a dilemma: he either walked away and lost ninety-nine cents, or he bid, say, $1.01—which would cut his losses to just a penny.
And so, indeed, it would escalate, with bids going higher and higher, until the utter ridiculousness of the situation finally caused all but one of the bidders to drop out.
Caitlin said as much to her mom, who smiled encouragingly. “That’s right, dear. Now, can you think of what the optimal strategy would be—and no cheating by having Webmind tell you.”
Caitlin considered for a second then: “Make an opening bid of ninety-nine cents. No one else would have any motive to bid against you, because the best they could do, if they outbid you by one cent, is break even, and if they bid more, they’d lose money. You’d end up being the only bidder, and you’d still make a profit, even if it’s only a penny.”
“That’s right,” her mother said again, “assuming all the potential bidders were rational and that their only motive was profit. But here’s where simple math fails to account for reality—there’s a psychological element that Webmind will need to understand.”
“Yes?”
“Suppose it was your worst enemy who had just bid ninety-nine cents. You might bid, say, $1.98, just so he’d be out almost a buck—and you’d still be out less than he was.”
“Wow,” Caitlin said. “That’s nasty.”
“I’ve seen this game get very ugly at parties,” her mom said. “I’ve seen couples who arrived together leave separately after playing it.”
“Ah, okay, then I’ve got a question for you, Mom. What would you wish for if you knew that your worst enemy would get double what you got?”
“Hmmm. A million—no. Um, I don’t know.”
“To be blind in one eye,” Caitlin
replied.
“God!” said her mother. “But, um, yes, that’s an example of what I’m trying to get at: it’s possible for people to value outcomes differently. Do you remember when your father taught you how to play chess?”
They had a special chessboard with Braille characters on the heads of each piece. “Sure.”
“And remember how he used to let you win?”
Caitlin raised her eyebrows. “Say what?”
“Um, dear, he—”
“I’m just kidding, Mom.”
She smiled. “Well, why did he let you win?”
“I dunno. I guess, ’cause if he didn’t, I wouldn’t have wanted to play anymore. I wouldn’t have come back for another game.”
“That’s right. What he valued most was not him winning, but rather you winning. In other words, you both wanted the same thing, and even though it cost him—in the sense of losing the game—to let you win, he was happy when you did.”
“I get it,” Caitlin said. “But, in the dollar auction, people don’t want to play anymore after a certain point, too, right? And I bet it’s not just that it’s ridiculous that causes them to finally stop bidding. It’s also boredom: I mean, even if you were bidding in ten-cent increments, instead of penny increments, it would still take thirty-four bids to get the $3.40 you mentioned. But if I was writing a pair of computer programs to play that game, they’d keep playing forever—because the only way you lose money is if you stop bidding.”
She paused, and then a big smile came to her face. “Or, to put it in terms like in that movie Dad and I watched, the only losing move is not to go on playing.”
“Good point,” her mom said. “Now, can you think of any real-life examples of things like the dollar game?”
Caitlin was trying to do just that when Schrödinger crossed her field of view, moving absolutely silently. “Evolution,” she said.
“Yes, exactly!” said her mom. “But why?”
“Evolution is an arms race, right?” said Caitlin. They’d talked about this in biology class. “Predators keep getting faster and stronger, so prey keeps getting faster and better able to defend itself. Gazelles evolved the ability to run fast in response to lions doing the same thing. The game goes on and on forever—because whoever stops upping the ante dies. Again, the only losing move in evolution is not to play.”
Watch w-2 Page 17
