You’re sitting in a plastic chair, in a circle of people sitting in plastic chairs, in a bright hospital room with pale blue walls. There’s a TV mounted high on one of the walls, but it’s off right now.
“All right,” says the guy in one of the chairs. He’s the only one who’s wearing shoes. Not these little socks with rough patches on their soles, at least if you put them on right.
The guy says, “The past couple days here in group we’ve been talking about what? Choices, right? Choices. Now I’ve got something I want you to try. I’m going to shut up for the next ten minutes, and for that ten minutes I invite each of you to think about the thing I’m about to explain. And each of you, you need to shut up, too, or else it’s not fair to the others. Okay?”
He waits until everybody, including you, says okay, or at least nods.
“All right, so here’s the thing. We’ve all had moments in our lives where we were faced with a choice. And we made our decision, and that choice sent our life down a certain path. And one thing led to another, and finally, well, here we all are.” He looks around the circle, his gaze pausing on each person. When he looks at you, you stare right back at him and he gives you this little smile he does sometimes. Then he finishes looking around the circle, and then he shakes his head and says, “Here we all fucking are.”
Everybody chuckles. This guy is all right. He’s told you that his drug of choice, back when he wasn’t the one wearing shoes to group, was meth. Normally you can’t stand tweakers. But he’s all right.
“So,” he says, “here’s what we’re going to do for the next ten minutes. Each of us is going to think back to some choice we once made, some decision that at the time made sense, but that ever since, we’ve wished we could do over. All right? Now, I invite you to sit here and take yourself, in your head, back to that moment. But this time, this time you get to do it over. This time you make a different choice. And for the next ten minutes—maybe close your eyes, if you like—for the next ten minutes you get to watch how your life goes, step by step by step, after this different choice. Just follow it out slow and easy, okay? All right? Give it its fair chance. All right, here we go. I’m shutting up now for ten minutes.”
You look around the circle. Most of the others are doing the same. A few have closed their eyes.
What the hell. You close your eyes.
If you ask Paul’s friend to let you both spend the night on the floor of his apartment, go to section 304.
If that strikes you as too obvious—too predictable—and instead you’re curious about how free will and determinism can coexist, go to section 132.
You pick an empty table and set down your tray, still thinking about your dialogue with the professor. As you’re taking the second bite from your burger, the redhead from class sits down opposite you.
“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.”