Pass/Fail (2012) (12 page)

So he sat quietly in class, paying attention to the lecture but not too much attention, taking notes like any other student. His mind was racing the whole time, trying to figure out what help Mr. Irwin could give him, but he forced himself to stay calm and not show anything on his face.

The lecture that day was on quantum mechanics and the uncertainty principle, a difficult subject even for the brightest students. As usual Mr. Irwin was breaking it down carefully so that everyone in the class could understand what he was talking about. “So you have the nucleus of a calcium atom, here,” he said, drawing a circle on the chalkboard with a couple pluses and zeros inside to represent protons and neutrons. “It’s pretty big. That is to say, you could only fit about a billion of them in this little dot.” He touched the chalk lightly against the board, leaving a tiny speck. A few of the students chuckled. “And that’s squeezing them in pretty tight.” He grinned for the class, giving them a second to write their notes. “Then you have electrons. In this case, twenty of them.” He drew twenty minus symbols outside the circle. Some were quite close to the nucleus but some were pretty far away. “And you want to know where they are. It would be a shame if one of them went missing. What would he have then?”

He was looking right at Jake.

Jake squirmed in his chair. “An ion,” he said, remembering the chemistry class he’d taken the year before. “A, um, a cation, because it would have a positive charge.”

“Yes, exactly! Great,” Mr. Irwin said. “And we can’t have that. So we want to keep track of our electrons. That might sound tough to do, since electrons are very small. As small as protons and neutrons are, you could fit almost two thousand electrons in the same space. But scientists are very clever people, and they’ve managed to find a way to detect even a single electron. And not just because they have remarkably good eyesight, either.”

Jake smiled. If he wasn’t so on edge he might have enjoyed this.

Mr. Irwin moved to stand directly next to Jake. He was facing the rest of the class but he put one hand down on the wooden surface of Jake’s desk. “So to keep track of your electrons you need to know two things. You need to know where they are, right? But electrons don’t stand still. They’re always moving. So knowing where they were a minute ago isn’t the only thing you want to know. You’d also like to know its momentum, so you know where it’s headed, where it’s going to be. That’s where Uncertainty comes in. It turns out you can know one of those things, or the other, but not both, because even looking at an electron changes it. You,” he said, laying a hand on Jake’s shoulder, “only get to ask one question—because to find out the position, you have to change the momentum. To find out the momentum, you have to change the position. You can test,” he said, and rapped the desk with his knuckles, “the position, but then you’ll only ever know where the electron was today.” He knocked on the desk again. “You’ll never know where it was originally going, or where it should have been tomorrow.”

The bell rang then. Mr. Irwin held up his hands in surrender. “More on this next time, when I’ll explain why it matters.” The students laughed as they jumped up and grabbed their books, in a hurry to get out in the hall.

Jake took his time. He was only slowly realizing that he’d just been given a secret message. There had been no special reason otherwise for Mr. Irwin to emphasize those two particular words.

The message was TEST TODAY.

Jake didn’t say a word as he got up and pulled his knapsack onto his shoulders, but he tried to meet Mr. Irwin’s gaze as he walked past, hoping to thank him if only with a quick look. The teacher, however, was busy studying some papers on his desk and didn’t look up.

Jake spent the rest of the school day psyching himself up. He could handle this test, he told himself. Knowing it was coming gave him a chance to prepare himself. Unfortunately there was no way for Mr. Irwin to tell him what the test might be, or how to pass it, but just knowing it was coming helped. Before, the tests had surprised him and caught him off his guard. Not this time.

At the end of sixth period the bell didn’t ring. Jake was in Ms. Holman’s English class at the time and like many of the other students he was watching the clock, waiting for the bell. It didn’t come at the appointed time, though, and Ms. Holman kept droning on about Chaucer. She didn’t even stop her lecture when she suddenly rushed back to her desk and sat down in her chair as if she was expecting something.

It only startled Jake a little when the PA crackled to life and told all the students to sleep. Like the kids around him, Ms. Holman slumped over in her chair and stared vacantly at the ceiling. She had known, of course, what was coming, and hadn’t wanted to fall down when the command came—that was why she rushed for her chair.

When the door of the classroom opened and a masked Proctor stepped inside, Jake didn’t even jump.

“Are you ready for your next test, Jake?” the Proctor asked.

“Yes,” Jake said, and for once he thought he was.

Chapter Twenty-Six

The Proctor led Jake through the school, back toward the teacher’s wing. They passed silently by classrooms where nothing stirred, where the sounds of lectures being taught were absent, past the cafeteria where students lay slumped over across the long white formica tables. Jake didn’t let it get to him. He’d been through this before and he knew they were only sleeping.

When they passed Ms. Baker’s Home Economics class, Jake glanced at the window inset into the door, expecting more of the same. He nearly shrieked in surprise, then, when someone came up to the glass and pressed a hand against the window, looking out.

It was Megan. Unlike everyone else, she hadn’t fallen asleep. Interesting.

She watched his face as he passed. When he was quite close she raised her eyebrows as if asking him a question, and he could guess what it was: did he need any help, did he want her to come along. He gave her a brief shake of the head. She mouthed the words “good luck” at him, and he smiled back.

The Proctor had never stopped walking or even slowed down. Jake jogged forward to catch up and soon they were at the back door of the school, by the guidance office. They stepped outside into bright desert sunlight and Jake saw they’d arrived at the location of the test.

Two Proctors stood back there, behind them only the dusty plain and the cloudless sky, almost painfully blue. They were dressed almost exactly like the Proctor who’d led him there, except for one detail. The one on the left wore a serge suit that was spotlessly white, and his mask was the same color. The Proctor on the left was dressed in black, with a black mask.

Each of them held a single pale blue envelope before them, as if they were presenting their calling cards. They didn’t move a muscle as Jake approached.

The Proctor in white spoke first, in a buzzing voice that was much higher in pitch than the typical Proctor timbre. “I speak only the truth,” he said.

Next the Proctor in black spoke in a deep bass rumble, distorted until it was nearly a growl. “I speak only the truth,” he said.

The Proctor in white turned to look at the Proctor in black. “He speaks only in lies,” he warbled.

“He speaks only in lies,” the Proctor in black said, looking across at the Proctor in white.

Which didn’t make any sense, of course. If they both spoke only the truth, then they had both told a lie about each other. If the both spoke only in the lies, they’d told the truth about each other. It was a paradox. Unless…

Jake understood, then. One of them always spoke the truth, and had told the truth about the other speaking lies. The other never told the truth, and had told a lie about the other being honest. The problem was, there was no way to tell which of them was honest and which was a liar.

“In my hands, I hold a PASS,” the Proctor in white said.

“In my hands, I hold a PASS,” the Proctor in black replied.

“He is holding a FAIL,” they both said, in unison.

So Jake had to decide which one had the PASS. It was that simple. Except one of them was lying. And he didn’t know which one.

Okay
, he thought.
I’m smart enough to do this. If I wasn’t smart enough to figure this out, they never would have picked me for the Curriculum in the first place.
It was a calming thought, which certainly beat the usual mind-numbing panic he felt when faced with an unexpected test.

Jake thought he should start by establishing some ground rules.

He turned to see if the mirror-faced Proctor was still there, and he was.

“Can I take both cards, and keep the one I like?”

“No,” the Proctor said. “You must choose one envelope.”

Jake had assumed as much but it never hurt to ask. After all, cheating was permitted “Can I ask them to open their envelopes and show me their cards before I make my choice?”

“No,” the Proctor said. “Once an envelope is open, it will count as your choice.”

Jake nodded. “Are there any automatic failure conditions to this test?”

“No,” the Proctor told him. “Unless you fail to choose.”

“Can I ask them questions?” he asked.

“Yes,” the Proctor said.

Jake rubbed his hands together. Easy, then. He could ask one of them whether he had blue hair or not, or whether the rain fell up, or whether the sky was green. If they answered yes or no it didn’t matter—either way it would establish whether the one he asked was honest or a liar. Then he would ask the honest one whether he held a PASS or a FAIL. Easy.

Way, way, too easy.

He started to open his mouth, to ask the Proctor in white whether he was wearing a purple shirt or not. Then a twinge of paranoia made him stop. He heard Mr. Irwin’s voice in his head, warning him there would be a test today. It had made a big difference, knowing that—he had walked into the test calm and collected, ready for just about anything. But what else had Mr. Irwin said? He’d been talking about the Uncertainty Principle, and how you could know one fact about a given particle but not two.

He had said, quite clearly, “You only get to ask one question.”

Jake rubbed at his chin for a while. Then he turned to face the Proctor in blue, behind him. “How many questions am I allowed to ask?”

The Proctor buzzed at him. “You may ask one of them one yes-or-no question. Asking a question of both at the same time, or asking a second question, will be taken as a refusal to choose an envelope, and this will result in an automatic failure condition.”

Jake’s heart jumped in his chest. If he had followed his original course of action, and asked two questions—but, he told himself slowly, he hadn’t. With Mr. Irwin’s help, he’d been smart enough to not make that mistake.

One question only. He could only ask one of them one question. That made his original strategy unworkable. He thought about what else Mr. Irwin had said, desperately looking for clues. The test seemed impossible. He had to ask which of them was holding the PASS—but then how would he know if they were lying or not?

“Please ask your question now,” the Proctor in blue said.

Chapter Twenty-Seven

Jake stared at the Proctors dressed in black and white as if he could tell which was honest and which was the liar just by some subtle difference in their clothing or the way they stood. It was useless, though. Other than the difference in color they were identical, as were the envelopes they held in their outstretched hands.

He should have asked Megan to come with him, he thought. Maybe she could see a way to solve this one where he couldn’t. He hadn’t wanted to get her involved, not if he didn’t have to—the tests were dangerous, and if the Proctors were willing to kill him he had no doubt they’d see her as completely expendable. They might even kill her just for trying to help him, even if cheating
was
permitted.

He started to sweat in the heat of the desert.

He could only ask one question, and it could only be answered by yes or no. And yet he had to get two pieces of information out of that simple answer: he had to figure out if the Proctor he spoke to was telling the truth or lying, and he had to learn whether that Proctor’s envelope was a PASS or a FAIL.

This was just like the Uncertainty Principle, he thought. You could determine a particle’s position or its momentum—but never both at the same time. Mr. Irwin had been trying to warn him how tricky this was going to be when he gave that lecture.

Jake silently thanked the teacher, though he wasn’t sure exactly what for. Mr. Irwin had managed to send Jake one secret message, why not two? Why couldn’t he have slipped the word “black” or “white” into his lesson plan? Unless maybe he didn’t know which of them would be the one holding the PASS. Maybe even the Proctor in blue didn’t know.

Jake closed his eyes and tried to remember everything else that Mr. Irwin had said to him recently, anything that might be useful. A lot of things came to him but they were warnings, not solutions. Then he recalled one thing. It wasn’t an answer, but maybe it would help.

Mr. Irwin had said that logic problems were fun, because there was always a clear answer.

Which maybe meant that this puzzle wasn’t like the Uncertainty Principle at all. It had to have a definite answer. Subatomic particles couldn’t ever be fully measured—you could only determine a probability of them being in a certain place, or possessing a certain momentum. But the blue envelopes weren’t subatomic particles. They didn’t follow the rules of quantum mechanics.

Which meant there might just be a way of learning two pieces of information at the same time. Jake thought about it. The answer to his question had to be simplicity itself: either a yes, or a no. But what if the question were complex? He worked through a number of possible questions in his mind, then finally hit on a solution.

It had to be phrased perfectly, though. Jake licked his lips, wiped his sweaty palms on his jeans, and then turned to one of the Proctors. It didn’t matter which one, and he was barely aware that he was addressing the Proctor in black.

“If,” he began, choosing each word carefully, “I were to ask him,” he went on, pointing at the Proctor in white, “whether or not he’s holding a PASS, what would his answer be?”