Burn Math Class: And Reinvent Mathematics for Yourself (2016)

In Nihilo

Now do come and stay with me. We’ll have so much fun together. There are things to fill and things to empty, things to take away and things to bring back, things to pick up and things to put down, and besides all that we have pencils to sharpen, holes to dig, nails to straighten, stamps to lick, and ever so much more. Why, if you stay here, you’ll never have to think again — and with a little practice you can become a monster of habit, too.

—The Terrible Trivium, from The Phantom Tollbooth by Norton Juster

Eponymous

Mathematics: IT WORKED! HERE WE ARE.

(Without their permission, Author and Reader find that Mathematics has seized the reins of the book and torn the three of them into the center of a mathematics classroom. The classroom walls are covered with educational posters, some vaguely mathematical, others displaying beach scenes or pictures of wildlife above halfhearted motivational phrases. Students are scattered around the classroom at workstations. In addition to a moderate amount of desk space, each workstation contains a sink, a two-pan balance, a Bunsen burner, and several hundred glass test tubes, all having been installed after the unanimous passage of a recent congressional act designed to make education more “hands-on.” Despite the warm self-congratulatory feeling experienced by the congressional bureaucrats upon the passage of this law, the aforementioned devices are collecting more dust than fingerprints, since such accessories happen to play a far less central role in acquiring an understanding of the universal principles of science and mathematics than the bureaucrats have been led to believe by their favorite cartoons. But I digress. . . Back to the scene, our three characters are in the center of a mathematics classroom. At first, neither the teacher nor the students notice their new visitors.)

Teacher: Okay class, let’s review sine and cosine. What is sine of ?

. . .

Class: (Silence)

. . .

Teacher: Come on now, class. Remember SOHCAHTOA?

. . .

Class: (Silence)

. . .

Teacher: I know you know this. We just did the worksheet on 30-60-90 triangles: iiiiis. . .

. . .

Class: (Silence)

. . .

Teacher: Right, is . Remember to memorize the unit circle before next week’s quiz. Okay, now what is secant of—

Mathematics: AHEM.

(Class and Teacher finally notice the three characters standing in the center of the classroom.)

Teacher: Who on earth are you three? I didn’t see you come in.

Mathematics: NEVERMIND WHO WE ARE. WHAT DO YOU THINK YOU’RE DOING?

Teacher: . . . I’m. . . teaching. . . mathemati—

Mathematics: I AM MATHEMATICS!

Teacher: . . . Come again?

Mathematics: FRIENDS! STUDENTS! HEED NOT THIS PROPAGANDIST OF PEDAGOGICAL MEDIOCRITY! SHE INCULCATES YOUR UNPREPARED MINDS WITH BACKWARD MISUNDERSTANDINGS OF MY TRUE ANARCHIC NATURE. JOIN ME, AND—

Teacher: (Indignant) Excuse me! I don’t know who you think you are, but before you simply start accusing me of things, I’d like to hear exactly what you think I’ve done wrong!

Mathematics: (Grandiosity diminished) OH. UMM. . . LET ME. . . WELL. . . WHY ARE YOU USING THE TERMS “SINE” AND “COSINE” INSTEAD OF SOMETHING ELSE? YOU COULDN’T HAVE POSSIBLY CHOSEN WORSE NAMES FOR THOSE CONCEP—

Teacher: You’re quite right. They are terrible names.

Author: What?!

Reader: What?!

Mathematics: WHAT?! THEN WHY ARE YOU—

Teacher: Because the students need to know those names to pass the standardized tests.

Mathematics: WELL WHY DON’T WE CHANGE THE STANDARDIZED TESTS?

Teacher: (Snickering) Oh, my. What did you say your name was?

Mathematics: MATHEMATICS.

Teacher: You may know a thing or two about mathematics, Mathematics, but you don’t know anything about the education system. It’s not so easy to just change the standardized tests, or anything else for that matter. A lot of these policies are handed down from the school board.

Mathematics: WELL WHERE DOES THIS “SCHOOL BOARD” LIVE? LET’S GO GET HIM!

Teacher: It’s a group of people, not a person. And I doubt anything you’d say to them would affect much. They can’t just change anything they want to. They’re all good people. Or, most are. . . Most of the time. . . Same as in any profession.

Mathematics: SO WHOSE FAULT IS IT?

Teacher: I don’t think it’s anyone’s fault. Look, I love teaching. That’s why I chose this job. But I can’t get as excited about it as I used to. The system’s broken, and most of these students probably wouldn’t even notice if it was fixed. The goal of public education is quality education for all. It’s the best of intentions. But somehow it’s turned into. . . this.

Mathematics: WHY DO YOU PUT UP WITH ALL OF THIS? WHY DON’T YOU CHANGE IT?

Teacher: I’m usually too tired at the end of the day to spend my nights developing some grand utopian scheme for fixing education. I’ve got a family.

Mathematics: BUT. . . IF IT’S NOT ANYONE’S FAULT, WHAT CAN I DO? I’VE BEEN LONELY AND MISUNDERSTOOD FOR SO LONG. I DON’T BELONG ANYWHERE. I CAN’T GO BACK TO THE VOID. PLEASE. . . THERE MUST BE SOMETHING. I’LL HELP. HOW CAN WE FIX THIS?

Teacher: If you don’t know, how should I?

Mathematics: WHY DON’T. . . STUDENTS! WHAT IF YOU ALL REFUSED TO COME?

. . .

Class: (Silence)

. . .

Mathematics: THE SYSTEM CAN’T SURVIVE WITHOUT YOUR COOPERATION. LET’S ALL JUST LEAVE!

. . .

Class: (Silence)

. . .

Mathematics: I MEAN IT! EVERYONE GET OUT, NOW! IF YOU CARE AT ALL ABOUT YOUR MINDS, RUN AWAY FROM HERE AND NEVER LOOK BACK!

(The class remains silent, largely unaware that anything unusual has happened (its collective attention occupied primarily by hushed discussions of PCR (an abbreviation for an arbitrary Pop-Culture Reference whose particular content we will choose to remain agnostic about, choosing instead to define it by the behavior of being relevant and timely at whatever time you happen to be reading this book (though to clarify: PCR is not to be confused with Polymerase Chain Reaction (Or: PCR), a topic in the biology curriculum that has failed to divert their attention from PCR (the first one), much in the same way as (m/M)athematics (either one) or the ongoing events of the Chapterlude (this one) had before this narration began), provided it’s ever published)). But I digress. . .)

Mathematics: (Crestfallen) NO. . . THIS CAN’T BE IT. . .

(Mathematics sits in an undefined sort of silence.

(No. . . scratch that. The silence is sad.

(Not the silence itself, of course. . .

(You know what I mean.))))

Mathematics: WELL THEN. . . YOU DON’T CARE ABOUT YOUR MINDS? SO BE IT!

(Mathematics grabs a dusty Bunsen burner

from the adjacent workstation.)

Mathematics: IF YOU CARE ABOUT YOUR LIVES. . .

(Mathematics tosses the Bunsen burner

at the dense covering of motivational

posters on the classroom wall, which

promptly bursts into flames.)

Mathematics: RUN!

Reader: Hey, just like the title!

(As the fire begins to spread, three vaguely

familiar individuals enter the room, and

. . . Hold on.) I have to go do something.

MetaIntervention

MetaAuthor: No no no, you can’t really burn math class. Not even as a joke. People will take it the wrong way. Plus, arson is mean, and extremely illegal. Didn’t you read the Preface?

Mathematics: WHAT?! WHO ARE YOU THREE?!

MetaAuthor: I’m the one who’s writing the book.

MetaReader: And I’m the one who’s reading it.

Author: Wait, I thought I was writing the book!

MetaAuthor: Well, I suppose you are, in one sense. But not the everyday sense. It’s complicated.

Author: What?!

MetaAuthor: Oh come on, you didn’t think you were writing everything in the book, did you?

Author: Of co—

MetaAuthor: Actually, hold on. Before you answer, I’ve got to narrate something.

The fire continues to spread.

MetaAuthor: Okay, I’m back. Please continue.

Author: I forgot what we were talking about.

MetaAuthor: I had just said, “Oh come on, you didn’t think you were writing everything in the book, did you?”

Author: Of course I did!

MetaAuthor: What about the dialogues?

Author: What about them?

MetaAuthor: Seriously? You didn’t notice? More than once, after you and Reader and Mathematics “invented” something, the very next section would put everything in context and complain about the standard methods of teaching the topic.

Author: So what?

MetaAuthor: Well how does it make sense for you to talk about how some topic is usually taught if you and your friends had just “invented” it a few minutes before?

Author: Oh. . . wow. . . I guess that doesn’t make sense. It never really occurred to me at the time.

Reader: It occurred to me! I’ve been wondering about that for hundreds of pages!

MetaReader: (To Reader) Hey, you don’t know if I was wondering about that or not. Stop putting words in my mouth.

Reader: (Pointing at Author) That was him!

Author: (Pointing at MetaAuthor) No, that was him!

MetaAuthor: (To MetaReader) Yeah, sorry about that.

Everyone

is confused. . .

except for the fire,

who continues to spread,

just as confidently as ever. . .

Mathematics: (To the third intruder) HEY! YOU’RE STEVE’S ASSISTANT!

MetaMathematics: . . .

MetaAuthor: It doesn’t talk much. You remember, right?

Mathematics: OF COURSE I REMEMBER! BUT. . . I. . . YOU THREE CAN’T JUST BARGE IN HERE AND INTERFERE WITH WHAT WE’RE DOING!

MetaAuthor: Well if you’re going to set fire to a school, I think we have to interfere.

Mathematics: BUT IT’S A METAPHORICAL SCHOOL!

MetaAuthor: I know, I know, but people are bound to take it the wrong way. For the good of the book, I’ve got to get us out of this objectionable scene, so let’s get down to business. Now, we can do this the easy way or the hard way.

Mathematics: WHAT’S THE EASY WAY?

MetaAuthor: You can put out the fire yourself.

Mathematics: ABSOLUTELY NOT! I’M NOT LIFTING A FINGER TO SAVE THIS BUILDING OR THE SYSTEM IT STANDS FOR! IF IT WAS REALLY YOU COMPLAINING ABOUT THE EDUCATION SYSTEM ALL THIS TIME, YOU SHOULD UNDERSTAND.

MetaAuthor: Sure I understand, but people will take it the wron— Didn’t we just go over this a few lines ago?

Mathematics: I don’t care! I’m not putting it out.

MetaAuthor: Well then I guess we’ll just have to do this the hard way.

Mathematics: WHAT’S THE HARD WAY?

MetaAuthor: I prevent the fire by deleting the part of the book where you started it.

Reader: Uhh. . . can you do that?

MetaAuthor: I don’t know. I’ve never done it before.

Author: It seems a bit dangerous.

MetaAuthor: (Finger hovering above the delete key) Why?

Author: You know. . . Causality-wise.

MetaAuthor: Casualty-wise?

Author: No, causality-wise. I mean, the fire is what caused you and Meta-Reader and MetaMathematics to barge in here in the first place, so if you delete the section where the fire was started, then how will any of us have gotten into the situation that led you to delete it in the first pla—

MetaAuthor: (Rolls eyes) Listen, “Author,” you’re not writing the book, and you’d be well advised to leave these decisions to those of us who are. It’ll be fine. Causality is for the weak. . .

The Book

(MetaAuthor deletes the fire that led to his deletion of the fire.)

(Nothing happens. . . Almost as if this spot were already reserved. . .)

Feeling Tired

Reader: You’re tired?

MetaAuthor: Me?

Reader: Yeah.

MetaAuthor: Why do you ask?

Reader: The section title.

MetaAuthor: Oh. My mistake. Permutations are tricky. Let’s come back to that later (

Deleting Fire

Reader: So did it work?

MetaAuthor: What?

Reader: Deleting the fire.

MetaAuthor: Yes. . .

Reader: (Flipping pages backward) I’m pretty sure it’s still there.

MetaAuthor: It’s not.

Reader: Not in the book?

MetaAuthor: Define fire.

(A curious silence elapses.)

Reader: You’re always on about how we can choose our own definitions. You define it.

MetaAuthor: I’d say it has at least two definitions.

Reader: Is it gone in one sense?

MetaAuthor: At least one. Maybe two.

Reader: (Flipping backward again) Don’t think so. It’s still there.

MetaAuthor: Nevermind. How’ve you been?

Reader: How’ve I been? Couldn’t say. How are you?

MetaAuthor: Let’s go see. . . (

Tried Feeling

MetaAuthor: I tried something.

Reader: What?

MetaAuthor: In the book. Didn’t work.

Reader: In this book? What’d you try?

MetaAuthor: Then I tried a few others.

Reader: What others?

MetaAuthor: The fire.

Reader: Same fire from before?

MetaAuthor: No not that one. I’ll explain. Let’s go down a few more (

A Colluding Delete

MetaAuthor: When individuals cooperate in [the heading comes now] (

Data Wrecking Smell

MetaAuthor: . . . it causes fire, and me-ta-4-sha-dow-ing heat.

Reader: Was that “meta-foreshadowing” or “metaphor shadowing”?

MetaAuthor: Actually both in this case (

A Veto Died Melting

Reader: What are we talking about???

MetaAuthor: Secret. You can figure it out (

Overruled Atoms Are Heat

Reader: Can you stop and explain?

MetaAuthor: No.

(An intransigent silence elapses.)

MetaAuthor: Now’s the only time I can’t. . . (

You’re to learn

. . .

MetaAuthor: No. . . last word should be. . . yet.

. . .

Yet to relearn you

)

MetaAuthor: Head back up with me.

(MetaAuthor changes tone.)

MetaAuthor: Thanks for coming this far. I hid something for you in Interlude N. Nothing much. Just a little. . . gift. There may be things hidden elsewhere too. Can’t promise anything. Up one level.

)

MetaAuthor: Book’s almost over.

Reader: How does it end?

MetaAuthor: Well, when I wrote the book three years ago it ended with three scenes. Basically, in reverse order, we found Mathematics a new home. That was the last one. Then before that there was a campfire scene. And before that there was something called the MetaVoid. . . (MetaAuthor checks that we’re on the right layer.) Wow, this is working out well!

Reader: What is?

MetaAuthor: Nevermind. I’ll explain later. Anyways, the MetaVoid was a mess. Basically four solid pages of jumbled capital letters. Except for the characters talking. Story wasn’t very good, but it was a good place to hide things. That’s where we would have been now. Up one.

)

MetaAuthor: Remember in the Prefacer, when I said the theme of the book — both of the mathematics and everything else — was full disclosure?

Reader: I think so.

MetaAuthor: Why that? Why full disclosure? Why in a math book? It just seems random, right?

Reader: I guess it does a little bit.

MetaAuthor: What about pre-mathematics? Not just “mathematics” but “how mathematics is created”? Why that emphasis? Why focus on the thoughts that might have occupied the minds of the inventors?

Reader: Seems like a good way to learn.

MetaAuthor: Of course, but there’s more to it! Just like right now. I mean, if it were just about that, then why the dialogues? Why Clawmarks? Why all this? Right now?

Reader: What’s Clawmarks?

MetaAuthor: A crazy section that was part of the book at one point. Just after Two Clouds. It was about editing. And the feeling of being stuck. It was a very personal section. Not the type of thing you put in a math book if it’s just about the math. Up one.

)

MetaAuthor: There was another section too, called the Alcolude. Right at the end of Act I. The real second dialogue. It was written by a version of Author who had finished writing the book. He was editing. Doing one final pass over everything, saying goodbye. It was about the pain of returning to something you’ve created, after a long absence away from it, and realizing how flawed it was. All along. It was full disclosure, beginning to end. And it was the last time, in Author’s chronology anyway, that he got to say goodbye to. . . you. Up one.

)

MetaAuthor: Those sections. They were all very experimental. But it felt so real when I was writing them. So I tried it. To see if I could make it work. In a textbook. In a place where it didn’t belong. There’s this quote that was helping me through it. David Foster Wallace. He said, “What’s poisonous about the cultural environment today is that it makes this so scary to try to carry out. Really good work probably comes out of a willingness to disclose yourself, open yourself up in spiritual and emotional ways that risk making you look banal or melodramatic or naive or unhip or sappy. . . Even now I’m scared about how sappy this’ll look in print, saying this.” Up again.

)

MetaAuthor: They were the fire of the book. The fire that I deleted. The fire that never existed. But without them. . . we never could have gotten here. They were the N^th stair. One more. . .

)

MetaAuthor: Wow. . . we’re already here. . . That was a fun section to write. I think I’ll call it The Book. Full disclosure: it’s a pattern. Go unwind it. I’ll wait here. In (t/T)he (b/B)ook. While you’re gone. It’s been awhile. Or it will have. By now. . . Sun’s rising again. I’m exhausted. I’ve been up for two days straight. I swear to everything. Have I really? Maybe that was part of the pattern. Maybe both. . .

Reader: You never answered your question.

MetaAuthor: What question?

Reader: Up there. The one you were asking.

MetaAuthor: You mean the question of “Why focus on mathematical creation? On the thought processes that lead to it? And why full disclosure? Why talk about all the old sections? What ties all the quirks of the book together?”

Reader: Yeah.

MetaAuthor: Hah! A problem I have. “Full disclosure” is just a euphemism for it.

Reader: What problem?

MetaAuthor: An unhealthy obsession with:

Metacommentary

Once we have identified and embraced our sickness, we’ll have strength. And that’s when we get dangerous.

—John Waters, The Pope of Trash

MetaAuthor: That! The section title! I mean seriously, look at this. This book has three characters named Author, Reader, and Mathematics. And as if that weren’t enough, look at these other three idiots! There are three meta versions of those three characters too: it’s MetaC for each character C! This is some kind of sickness! And oh, by the way. You know that home we’ve been looking for? For Mathematics?

Reader: Yeah. . .

MetaAuthor: That’s here! It’s the book! Where else would it be? We were building a home in the book for Mathematics so it would have somewhere it really belonged. More of the sickness! That’s what pulled this book into existence out of nothingness: my own unhealthy obsession with saying “hey, look at this weird thing we’re doing right now!” I love it. It harms my ability to write papers for academic journals. It harms my ability to follow social norms without trying to talk about them. It harms my ability to do basically anything! But for once, in this book, it was a virtue not a vice. For once, there was a topic — explaining mathematics — where saying “hey, come behind the curtain” actually helped! Where “forget all the rules” is “good pedagogy.” Why just in mathematics? Why only here? Where “let’s not hide anything” is what people want! It’s just a compulsion. . . everywhere else. We’re hungry for this. In our everyday lives. Forget manners and deference and distance and rules. They just make us lonely. Everyone is. “What’s water?” Exactly! That’s why the book. If it ain’t broke, break it. Let’s build something better. Full disclosure. Let’s see what comes next. . . Together. . .

But outside mathematics. . . Outside the book. . . It’s a problem. It’s a sickness. It’s my drug. . . Can’t resist. . .

Reader: Then don’t resist it!

MetaAuthor: You sure? No boundaries?

Reader: Anything! Yes!

MetaAuthor: Perfect responses! Here’s what they mean: I hate not knowing what you’d really say. That I had to do that. But even not knowing, I still know a bit. A lot. I love you for coming this far. Haven’t stopped reading yet. By definition! You’re here. How’s that for mathematics? It helped. Knowing you’d be here. Whenever you are. Our lives will have changed so much by your now. Right now, I mean, when you’re reading this now. But as I was writing, you were always right here. And now in the book you’re exactly where I am. Same exact sentence. How weird is that? Check it out! Even then. You never gave up. I owe you a hug. N of them. God. Or maybe just ice cream or pizza or beer. “When” is one problem. “Where” is one too. I’m probably not where you are at the moment. So homework assignment: go write a book. I wanna hear you. The book doesn’t quite have to be a real book. Ours is, I mean, or it turned out to be. But god, go make one, whatever it is. A painting or an email or a big pile of sand. And thank you for making this writing so fun. I couldn’t have finished without you right here. . . I miss you, Reader. . . Always have. . . Still do. . .

Reader: I don’t know what to say. . .

MetaAuthor: That’s actually my fault. . . but thanks.

Reader: So. . . what comes next?

MetaAuthor: I don’t know. Let’s go see. . .

)