Catherine Asaro - Nebula Awards Showcase 2013

“Hi,” says the redhead. “I’m Kerry.”

You never finish the burger.

The two of you talk about how free will differs from unpredictability. How predetermination doesn’t equate to constraint. How fists can’t have free will because they don’t have brains, but how brains are overrated.

Kerry is a year ahead of you—a junior—and a math major. (Kerry’s the one who introduced the term equate into your conversation.)

You try not to be obvious about letting your gaze wander over what you can see of Kerry’s body. You’d like to see more.

Then Kerry makes a stupid claim about the contrast Boethius drew between fatalism and divine omniscience.

If you steer the conversation back to the part about how brains are overrated, go to section 138.

If you get frustrated as you keep trying to explain why Kerry’s claim is stupid, go to section 155.

You and Kerry have been spending all your evenings together at the library, and afterward at the Rathskeller or just wandering campus talking. But so far things haven’t gotten past holding hands and kissing. Pretty intense kissing, true, but come on.

Apparently math majors are shy.

Tonight, though, the two of you are rolling around on your bed, and many items of clothing have been removed. A few minutes ago you almost blurted out something about hoping that Boethius’s God was looking someplace else, but you suppressed the impulse.

As you yank off a sock, Kerry suddenly pulls away and says, “Do you have any… I mean, because I don’t, not with me… .”

You don’t either, but right at this instant you’re not really up for a Philosophical Dialogue. “I’ll get some tomorrow,” you say, and you reach for Kerry’s shoulder.

“Wait.” Kerry eyes you reappraisingly.

If you say, “Just this one time,” go to section 160.

If you offer an apologetic smile and sigh, and then, deliberately but gently, you put the sock back onto its foot, go to section 144.

You listen to the morning’s birdsongs. Kerry’s dorm is on the edge of campus, by the arboretum, so mornings are louder here than in your room. There’s one bird who keeps hitting this little arpeggio with a syncopation on the last note that you’re trying to memorize, so you can try it out later on guitar.

You’re also trying to memorize how Kerry looks asleep. Just because you think that will make a good memory.

Eventually the alarm buzzes, and you two have to get out of bed.

A little later, you face each other over breakfast trays. (The first time you shared breakfast, you discovered that you both like oatmeal—with raisins, and definitely no brown sugar—and that neither of you can stand breakfast sausage.)

Kerry asks, “Figure it out yet?”

You’ve been teaching Kerry some basic music theory, and in return you’re learning about set theory. Last night Kerry gave you a challenge: Suppose you’re given some arbitrary sets. It doesn’t matter how many or what’s in them. Maybe one contains all the even numbers, while another contains red fire trucks, and a third includes the contents of your pants pockets on the morning of your fourteenth birthday. Whatever. Now prove that, without having to know exactly what’s in each set, there is some other set that has at least one element in common with each of the given sets—but which isn’t simply the union of all of them, as if you’d dumped all of the original sets into one big bag.

You did, in fact, figure this out, last night while you were brushing your teeth. But then the two of you got distracted by other, more entertaining, challenges.

“All right,” you say. “I pick one element from each of the sets you give me. My new set is defined as the set containing precisely those elements. Ta-dah.”

Orange juice in hand, Kerry nods. “Very good.”

You grin, but Kerry’s not finished.

“So who gave you permission to pick an element from each of those sets? There’s nothing in the basic rules of set theory—the axioms—that says you can do that.”

You frown. “Of course you can. It’s obvious.”

Kerry raises an eyebrow.

“Fine,” you say. “I choose the smallest element in each set—that’s well-defined, right?”

“What if one of the sets consists of all fractions bigger than zero? What’s the smallest fraction?” Kerry reaches for your toast, which you’ve been neglecting.

Annoyed, you start to offer a counterproposal. But you catch yourself as you see its flaw. Which suggests a different solution—but no, that doesn’t work, either… .

Finally Kerry says, “It does seem natural that you should be able to pick elements out of sets. But it turns out that there’s no way to prove that you can do that, in general, based on the axioms of set theory. Most mathematicians agree with you that it should be allowed, though, so they add a new rule that specifically says you can do it. The Axiom of Choice.”

Now you’re annoyed again. “Then why didn’t you tell me that up front? If this Axiom of Choice is simply one of the rules, why are we even discussing it?”

Kerry leans forward, one elbow skidding almost into a puddle of spilled coffee. “It’s not one of the rules. Not one of the most basic, defining ones, anyway. You can build up a complete, self-consistent system of mathematics that doesn’t include the Axiom of Choice. If you add it in, you end up with a slightly different system. One that includes a lot of new, interesting results, most of which feel right. So most mathematicians are fine with proofs that depend on the Axiom of Choice.”

You glance at your watch. You’ll both be late for class if you don’t pick up your trays and get going. But a corner of Kerry’s argument looks loose to you.

“So,” you say, “you can do math either with this axiom or without it?”

“Right.” Kerry stands up.

You remain in your seat. “Then, each mathematician has to choose whether or not to use the Axiom of Choice.”

Kerry pauses and stares at you.

And then, slowly, Kerry nods, and slides the two trays in your direction. As if presenting you an award.

“I guess,” says Kerry, “that says something about the rules of the higher system. The one in which we live.”

If you stack both trays and carry them away, go to section 147.

If you push back Kerry’s tray and grumble about hypocritical mathematicians, go to section 170.

That night, after you get under the covers, Kerry approaches the bed, naked.

“Tonight,” says Kerry, “I want you to lie completely still. Got it? Now pay attention. Here’s my hand. And here’s my mouth. And here—” Kerry takes a step back, so you can get a really good look, “—is the rest of me.”

Kerry draws out the moment.

“Choose.”

If

“Okay, that’s ten minutes.”

You open your eyes to a circle of people sitting in plastic chairs, in a bright room with pale blue walls.

“So,” says the guy with shoes. “Who wants to share something from their experience?”

If after a few seconds you raise your hand, go to section 511.

If it strikes you that group is bullshit, go to section 550.

One of the counselors is standing in your room, looking Very Serious.

“We can’t do this without you,” she says. She’s in her forties, you guess, her dark hair braided and wrapped up on top of her head. You’ve decided that the lilt in her voice comes from Jamaica.

You lie completely still.

She sighs. “You only get to keep your bed if you’re an active participant in ward activities. Do you understand me? If you’re going to stay here, then you have to get yourself up and out of this room, and interact with the others.”