Forever Changes (3 page)

English looked tolerable, and history looked completely horrible, not to mention boring as hell, but at least she got to sit with Mel and Steph in those classes. They were in her gym class, too, but she decided she was probably going to have to get another “Special Circumstances” note to get out of it.

Finally, right before lunch, it was time for AP Calculus.  Deciding she needed a boost if she was going to be able to concentrate, Brianna stood at her locker and washed a handful of Funyons down with a swig of ice-blue Gatorade.

This made her the last one into class, but, fortunately Mr. Eccles didn’t seem to notice.   He was a big fat guy with wild, wispy hair on the sides and almost no hair on the top.  He was wearing a  hideous red paisley shirt. Standing in the front of the room with a half smile and a big gut,  he looked kind of like the Buddha statue next to the register at the Jade Garden restaurant.

“As surely everyone is aware,” the teacher began, “one James Doubt graduated from this school and went on to great fame in the National Football League.  Many is the student who hopes to follow in Mr. Doubt’s footsteps. And yet, in the twenty-four years I have been a teacher here, approximately thirteen senior football players graduate each year, and of those, exactly one has achieved success in the National Football League, making the odds of success in that area—”

“About point three percent,” Brianna found herself saying, because she’d  reflexively started solving the problem.  There was a pause.  She caught a dirty look from Lisa Stiehm.

“Absolutely correct, Ms. …” Mr. Eccles said as he looked at his grade book.

“Brianna Pelletier,” Brianna said.

“Correct, Miss Pelletier.  Now, in the same time period, at least a hundred students have gone on to be engineers, doctors, scientists, and computer professionals due to their pursuit of mathematics.

“So your presence in this class shows that you understand the importance of mathematics to your future. But on your way to The College of Your Choice,”  Eccles continued, as Brianna winced, “we are going to ponder the infinite, tame the unknowable, imagine the unimaginable, and make sense of that which is senseless.”

Brianna felt cold.  She liked math in part because it gave her brain something to do
besides
pondering the infinite.

“Now, in any math class, we deal with facts, and fuzzy abstraction and uncertainty simply disappear in the reality of numbers.  Correct?”

Brianna nodded. Exactly.  Besides the fact that she was good at it, what Brianna liked about math was that everything made sense.  There was always an answer, even if it was hard to find, and you could prove it was right.  It was like there was an itch in her brain that she could scratch by doing a math problem.

“I am sorry to inform you that the castle of mathematics that we’ve convinced you is a solid thing made of stone is actually a dreamlike structure made entirely of, say, Mashmallow Fluff.

Mr. Eccles pointed up at the number line on top of the blackboard.  “Consider the number line, an imaginary line full of numbers, which are—what?  Simply ideas.  You can have two
of
something, but can you ever hold the number two in your hand?  No.  But, as you know, the number line extends forever.

“And you also know that prime numbers, like integers, never stop.   It’s not as easy to find the next one, but there are always more.  So there are an infinite number of prime numbers.

“Here, then, are two infinities.  One is all integers.  The second, only those integers which are prime.  Which of these infinities is larger?”  The class was silent.  It was kind of screwed up that you could have two different-sized infinities, even though you really couldn’t.  Mr. Eccles looked like he was going to wait for an answer, so Brianna raised her hand.  “Ms. Pelletier?”

“The question doesn’t make sense.  Infinity is like forever, so infinity is just infinity.  You can pair them up. One with two, two with three, three with five, four with seven, five with eleven”–and here she paused because a lot of the snobs in this class were looking at her like she was nuts– “I mean … until forever. You can match each integer with a prime. So they’re the same.”

“Yes!” Mr. Eccles yelled, and Brianna smiled.  “Infinity is infinity! Or is it?  To paraphrase Mr. Orwell, some infinities are more equal than others. If we try to pair up each integer with a real number as Ms. Pelletier has done with the integers and the primes, well, we run into trouble.  It turns out it can’t be done.  So
those
infinities are not the same.

“Now this is, as we said when I was your age, really freaky, man. Indeed, it appears to have driven a mathematician named Cantor quite mad.” People laughed.  “It’s very hard to make yourself think about it.  But fortunately, we stand upon the shoulders of giants, and the ability of Liebniz and Newton to wrap their minds around things that are simply unimaginable to most of us brings us the calculus.

“It turns out that this discipline borne of things imaginary and difficult to think about is very good at describing the world.

“Indeed, without this structure of abstractions, this castle of marshmallow fluff that is mathematics—and I do apologize, it is getting close to lunchtime, and I too feel pangs of hunger–we could never do something as concrete as lifting a 747 off the ground.

“Thus, you see, mastery of mathematics makes you incredibly powerful, for you become a concretizer of abstractions.  Presented with ideas so foreign to our experience that they can only just barely be contemplated, the mathematician smiles and tames them with rules, indeed, brings order from chaos.  Is this not, my friends, the very definition of creation?  This is not simply an adventure, it is
the
central adventure of human existence, and I am pleased to be able to share it with you.  Questions?” He smiled as he said this, knowing he had completely messed with their minds.

He’d messed with Brianna’s, too, but in a good way.  Because all that infinity stuff did freak her out, but she really liked what he said about mastering it with math.  It was exciting.  Brianna knew most of these kids from her other math classes, and she knew a bunch of them were probably pretty annoyed right now. Like the fat guy said, they liked math because it was real.

Brianna pictured the number line on top of the board continuing forever in both directions, shooting off the edge of the earth, a tangent to the sphere. She was flying next to it, through space, past the planets, just going and going and going, shooting along the number line forever, counting integers and primes and never stopping.

Brianna zoomed back from space when she saw Adam raise his hand. She knew he was going to ask his dorky music question.  She wanted to shake him—she was patient with Melissa and Todd and everybody else who didn’t get math like she did, but she got frustrated with how Adam seemed completely clueless about acting in a way that didn’t make people want to punch him.  She winced as Mr. Eccles called on him.

“Yes.  A question, Mr. …?”

“Pennington.”

“Yes, Mr. Pennington.  You wish to stump me with Zeno’s paradox?  I assure you that we will deal with, and hopefully dismiss, Zeno’s paradox in time. Meanwhile, your homework for this evening is a simple review set of problems which you can find on page twenty-four of your textbook.”

This was Mr. Eccles’ way of saying don’t ask me any questions, but Adam didn’t get it.  “Actually, I just wanted to know if you were really in a band.  My cousin said you played bass for the Electric Prunes or something.”

You could always get teachers off-track by asking them something about themselves, and Brianna pondered the fact that if Adam only had the good sense to do that near the beginning of class someday, maybe after they’d already lost ten minutes to a fire drill, then people would actually like him for it.  But he had to ask when they’d already been dismissed five minutes early for lunch.

“Mr. Pennington, I would
love
to discuss those days, but right now I believe the collective growl from  your classmates’ tummies would drown out my answer.  My clue to you is fourteen.  All right, everyone, please depart from my sight and fill those rumbling bellies of yours.”

As she stopped at the desk at the front of the room to pick up the textbook that looked like it weighed as much as she did, Brianna asked Mr. Eccles, who was pulling out what looked like a Fluffernutter from his drawer, “So what’s Zeno’s paradox?”

His face lit up.  “Ms. Pelletier, you’ve delayed feeding your belly in order to feed your mind.  Wonderful and admirable.  As you can clearly see”—he patted his gigantic gut—“it has, unfortunately, been years since I did the same.  And, indeed, I am quite hungry right now, so you will forgive me if I take a small bite of my sandwich …”  He bit into the fluffernutter, which made Brianna hungry. “… Ahh, that’s better.  Now, Zeno posed to Socrates a paradox which I will now paraphrase.   On your way to the cafeteria, you will, at some point, have traveled half of the distance to the cafeteria.  Correct?”

“Um, sure.”

“And from that halfway point, you will eventually reach a point half of the remaining distance to the cafeteria. And from that point, you will reach a point half of the remaining distance.  And so on and so on, to infinity, actually.  For if you continue to travel half the distance, you will, of course, never reach the cafeteria  at all, but merely continue to cut the remaining distance in half forever.

“Thus Zeno appears to have proven that you can never reach the cafeteria from here, which is undoubtedly news to those of your classmates already standing amid the pungent smells of”– he rooted in his desk and pulled out a photocopied calendar with the lunch menu on it– “sloppy joes.  With Tater Tots.”  He smiled. “It’s quite easy to refute Zeno by simply walking to the cafeteria, but proving him wrong by means of mathematics is far trickier.”

“Okay.  Thanks!” Brianna said, suddenly feeling self-conscious that she was chatting with a teacher after class.  She grabbed her book, stuffed it into her bag, threw an embarrassed,“See you tomorrow” over her shoulder, and bolted from the room.

When she got to the caf, Melissa and Stephanie were already eating.  “Where were you?” Stephanie asked.

“Calc.  Hey, when do we get to sign out for lunch?”

“Not till next week,” Melissa replied.

“Too bad. I would kill you for a Fluffernutter,” Brianna said.

Melissa laughed.  “I love you too, Bri.  Good to know I come second to a sandwich.  Just out of curiousity, does widdle Bwi need the crusts cut off, or would a regular Fluffernutter do?”

“Shut up.” Brianna sat down and contemplated her turkey and cheese sandwich.  She took out the knife and the small Tupperware of mayo that Dad packed.  She cut the sandwich down the middle, then thought for a minute about telling Stephanie and Melissa that she could make this sandwich last forever, that if she could eat half the sandwich every day, she would never ever finish it.   Then she thought better of it, spread the mayo, and started to eat.

At the end of the day, Brianna hiked up to the third floor where the ninth grade lockers were.  She really just wanted to go home, but she felt like a good mentor would check in on her mentee.  As she passed the door to the second floor, she thought she saw Todd down by the sophomore lockers.  He had been up at his parents’ camp in New Hampshire all summer, and she had no illusions that he was being faithful to her or anything, because they weren’t really boyfriend/girlfriend, but she still thought he might call when he got back.  Then again, she hadn’t called him.

Up on the third floor, she waded through the sea of short, loud boys punching each other and squealy, jittery girls hugging because it had been a whole forty-five minutes since they’d seen each other.  Had she ever been like them?

Well, no.  Most ninth grade girls have the beginnings of an adult body, Brianna thought.

She found Ashley, who was also skinny but already sporting a b-cup—how unfair was that?—at her locker with a couple of her friends.

“How was it?” Brianna asked.

“Hey!” Ashley said, “Bri!  It was cool, I guess. Oh, sorry, Bri, this is Sarah, Keri, and Caitlin.”

“Hi,” Brianna said, as she looked at three identical little blonde girls she would never be able to tell apart.

“Do you need a ride home?” Brianna asked Ashley.

“Oh … well, my mom’s picking us up,” Ashley said.

“Okay.  Well, I gotta go—Melissa’s probably panicking about pre-calc already, so I should probably go calm her down,” Brianna said, suddenly feeling stupid.  She’d thought she was doing Ashley this big favor, but it turned out Ashley didn’t need her at all.

Ashley didn’t need her, but Melissa certainly did.  Brianna’s phone rang as she was walking down the stairs.

“Where are you?” Melissa sounded desperate.

“I’m heading downstairs.  Where are you?”

“I’m waiting by your car.”

“I’ll be right there.”  Brianna got out to her car, and when she got there, Melissa hugged her and lost it.

“I should just drop out right now and go to Blaine and rent a chair next to my mom at the salon, because I’m going to fail math and not get into any college anywhere.”

Brianna patted her back.  “Okay, Mel, okay.  You’re not going to fail. I’ll help you, it’ll be fine.”

“It’s not gonna be fine!  Oh my God, he was so mean … it was like I wandered into Chinese class or something. I completely didn’t get it.”

“Okay.  We got you through Algebra 2, right?”

“Yeah.”

“So we’ll get through this too.”

“Okay.”

“I need food, though. Let’s go get a snack and look at your homework.”

Before school the next day, Melissa and Brianna had to hear again about how Stephanie was going to dump Kevin this time, but at least Stephanie had the good sense to buy all chocolate munchkins.  In homeroom, Adam came up to her and said, “Hey, Brianna, it’s Love!”

People were looking over at them and smirking.  Brianna wanted to crawl under the desk. “Um, what do you mean?”

“The band that Eccles was in!  It’s called Love!  They were this sixties band. I’ve been doing research on these psychedelic bands—the Electric Prunes, the Strawberry Alarm Clock, the Chocolate Watchband, Moby Grape.”

“You’re making this up, right?”

“I swear to God, they were real bands!  Anyway, they’ve all had like a million people in them, but none of them seemed to be Mr. Eccles.  But then I found this one called Love, and they have this big song called “7 and 7 Is.”

“Um, yeah?”

“Remember when he said ‘my clue is fourteen’?  7 and 7 is?  Get it?”

“Well, okay, maybe.”

“So I look at this Web site, and guess what the second guitarist’s name is?”

“Eccles?”

“Yeah!  Well, sort of.  I mean, they spelled it E-C-H-O-L-S, but I don’t know if that was  a mistake, or if he changed his name for the band or something.  Dare me to ask him about it?”

“Well, if you want.”

Adam started digging through his bag. “Here,” he said, handing Brianna a CD,  “I downloaded a bunch of Love songs for you.” Adam blushed.  “I mean, you know, songs by the band Love. I burned you a copy.”

“Thanks, Adam,” Brianna said, smiling as she took the CD and put it into her bag.  She wondered briefly if his making  her a CD  meant anything.  She hoped not.  He was her only ally in calc class, and she didn’t want anything messing that up.

Brianna refined the timing of her walking and snacking and arrived in class two minutes early.  She had a fluffernutter in her bag because she’d been craving one so bad after yesterday that she’d called Dad at work to ask him to bring home fluffernutter supplies.

Eccles went over the homework, and then started back in on the mind-blowing stuff.  “Critical to our work in this class are quantities we shall refer to as infinitesimals.  These are quantities which are infinitely small.  Now what could I possibly mean by this?”

He waited for a hand to go up, but nobody budged.  Nervous and uncomfortable, Brianna reached up to scratch the side of her head.

This, apparently, was a mistake. “Ms. Pelletier, as I know you only slightly, I don’t know whether you were raising your hand or gathering steam for a head scratch, but, nonetheless, you can handle my question, yes?.”

“Okay,” she said, and paused for a minute.  She wanted to make sure she said exactly what she meant to say.  She saw some of the other kids smirking, but she wasn’t going to open her mouth until she had it right. Finally, she answered, “Well, between zero and one there have to be an infinite number of points that match up to fractions where the denominator keeps getting bigger.  So like something like one over two times ten to the 500
^th
or whatever is going to be really really small, almost zero.”

“Yes, Ms. Pelletier, indeed.  As the integers grow infinitely large, fractions grow infinitely small, and as we follow those fractions toward zero, we will reach a point so close to zero that it is, for many purposes, zero, except when we don’t want it to be.”

The rest of the class looked about as baffled by that as Brianna was.

Everyone was silent, and Eccles seemed to savor the confusion, and just as he was about to speak, Brianna felt that familiar tickle in her throat.  She tried to fight it, but the tickle got worse and worse, and she had to let one cough out, one tiny little cough so small that most people probably wouldn’t even register it.  Unfortunately, letting that cough out led to more coughing, which led to more coughing, and pretty soon she was hunched over her desk, face red, knowing she had to go to the bathroom and hawk one into the sink.  Still coughing, she got to her feet, looked at Eccles, who nodded, and left the room.

It took her another minute to stop coughing, and another couple to fight back the post-tussive emesis, which is what the doctors called it when she coughed so much she puked.  She stood over the toilet for a minute, willing herself not to vomit. After getting it under control,  she splashed some water on her face and went back to class.

Everybody was trying to solve a problem when she got back, so she took out her notebook and started working.

By the time class was almost over,  when everybody was trying to pack up and get down to lunch, Adam did it again.  His hand shot up, and Eccles kind of sighed and said, “Mr. Pennington?”

“Did you play guitar in a band called Love?”

“Mr. Pennington, in my youth I did a number of regrettable things, and so there are several years for which I have only the foggiest memories.  I certainly remember something about playing guitar, but beyond that, it is all somewhat of a purple haze.”  He gave this big grin, and then said, “Don’t forget your homework, which is on the board, and have a wonderful remainder of your day.”

Adam was right next to her as soon as she walked out of the classroom.

“It’s totally him!  Did you hear that?”

“Yeah, but it sounded inconclusive to me.”

“I think he’s just messing with me.  You’re not gonna forget being in a band like that.”

“No, I guess not.”  Brianna conceded.

They walked in silence for a minute, and  Adam, kind of randomb ly busted out with, “I’m going to MIT next month for an interview and an info session.”

“My Dad’s on my butt about going to one,”  Brianna told him.

Silence erupted again, and she couldn’t stand it. “Is that where you want to go?”

“Absolutely,” Adam said, his face lighting up.  “I really, like … well, no offense or anything, but I really hate Blackpool and Blackpool High, and I really want to go somewhere with a bad football team where nobody calls you a fag and punches you for being smart.”

Brianna looked at him and saw that he was blushing.  He was keeping a straight face, but his voice had kind of cracked when he said that.  “Oh.” She said. “Um, is that like a funny exaggeration?”

He looked at her like she was the stupidest person on earth.  “No.” His smile came back, and he said, “Anyway, you should really go, even if it’s just to get your dad off your back.  Here,”  he said, digging a pen and a notebook out of his bag and scrawling a date and time on a piece of paper. “Here’s when I’m going. Myabe I’ll see you there.” They finally reached the ground floor, where Adam added, “Though I think I’d stand a better chance at MIT if we had a normal teacher who just told us how to solve stuff that’s on the AP and didn’t try to mess with our minds all the time. All that stuff about which infinity is bigger makes it harder.”

“I dunno,” Brianna said as they reached the cafeteria doors (“Take that, Zeno!” she thought.), “I actually kind of like that stuff.  Well, there’s Steph and Mel.” Though they were math and alphabetical order buddies, Brianna and Adam inhabited very different places in the rigid social seating chart of the cafeteria.

“See you,” Adam said.  “Tell me what you think of the CD,” he said, walking away.

“I will!” Brianna said.  She watched as Pete, a football player Stephanie had hooked up with last year, bumped into Adam.  She wondered if it was an accident.

As she sat down at the table, Melissa said, “Hey Bri, your boyfriend’s cute!” She and Stephanie laughed.

“You just never get tired of that joke, do you?” Brianna said as she sat down.

When she got up to throw her trash away, twelve minutes later, she saw Mr. Eccles, on cafeteria duty, standing next to the garbage cans.  The can was nearly full, and Brianna stuffed her lunch bag gingerly into a spot where it looked like it might not topple the trash overflowing from the top.

“Ah,” Eccles said, “sometimes I like thinking of the stacking of trash in the can as a function with an as-yet-undiscovered limit. I believe, Ms. Pelletier, that your bag has brought us an infinitesimal distance from the limit of this particular function.  When Mr. Teague there arrives with his mini Chips Ahoy wrapper, I think this particular function will become undefined.”

“I guess we’ll see,” Brianna said. She coughed, thankfully only once, and then walked away, turning back only as she heard the sound of garbage falling on the floor.  Jim Teague was standing there looking stupid, and Eccles was grinning. “It’s all math!” he called out to her.

Brianna rolled her eyes, but, as she headed out of the cafeteria, she wondered if everything really was math, or if there were some things that couldn’t be plotted or predicted.