The John Green Collection

by Green, John

  Colin,

  I hate to fulfill the Theorem, but I don’t think we should be involved romantically. The problem is that I am secretly in love with Hassan. I can’t help myself. I hold your bony shoulder blades in my hands and think of his fleshy back. I kiss your stomach and I think of his awe-inspiring gut. I like you, Colin. I really do. But—I’m sorry. It’s just not going to work.

  I hope we can still be friends.

  Sincerely,

  Lindsey Lee Wells

  P.S. Just kidding.

  Colin wanted to be all-the-way happy, he really did—because ever since he saw the steepness of the curve with Lindsey, he’d been hoping that it’d be wrong. But as he sat there on the bed, the note in his still-shaky hands, he couldn’t help but feel that he would never be a genius. For as much as he believed Lindsey that what matters to you defines your mattering, he still wanted the Theorem to work, still wanted to be as special as everyone had always told him he was.

  • • •

  The next day, Colin was feverishly trying to fix the Theorem while Hassan and Lindsey played Hold ’Em poker for pennies in the Pink Mansion’s screened-in porch. A ceiling fan blew the warm air around without really cooling it. Colin was half paying attention to the game while scribbling graphs, trying to make the Theorem account for the fact that Lindsey Lee Wells was, quite clearly, still his girlfriend. And then poker finally clarified the Theorem’s unfixable flaw.

  Hassan shouted, “She’s all in for thirteen cents, Singleton! It’s a huge bet. Should I call?”

  “She does tend to bluff,” Colin answered without looking up.

  “You better be right, Singleton. I call. Okay, turn ’em over, kid! Gutshot Dolly has trip Queens! It’s a hell of a hand, but will it beat—A FULL HOUSE?!” Lindsey groaned with disappointment as Hassan flipped over his hand.

  Colin knew nothing about poker except that it was a game of human behavior and probability, and therefore the kind of quasi-closed system in which a Theorem similar to the Theorem of Underlying Katherine Predictability ought to work. And when Hassan turned over his full house, Colin all of a sudden realized: you can make a Theorem that explains why you won or lost past poker hands, but you can never make one to predict future poker hands. The past, like Lindsey had told him, is a logical story. It’s the sense of what happened. But since it is not yet remembered, the future need not make any fugging sense at all.

  In that moment, the future—uncontainable by any Theorem mathematical or otherwise—stretched out before Colin: infinite and unknowable and beautiful. “Eureka,” Colin said, and only in saying it did he realize he had just successfully whispered.

  “I figured something out,” he said aloud. “The future is unpredictable.”

  Hassan said, “Sometimes the kafir likes to say massively obvious things in a really profound voice.”

  Colin laughed as Hassan returned to counting the pennies of victory, but Colin’s brain was spinning with the implications: if the future is forever, he thought, then eventually it will swallow us all up. Even Colin could only name a handful of people who lived, say, 2,400 years ago. In another 2,400 years, even Socrates, the most well-known genius of that century, might be forgotten. The future will erase everything—there’s no level of fame or genius that allows you to transcend oblivion. The infinite future makes that kind of mattering impossible.

  But there’s another way. There are stories. Colin was looking at Lindsey, whose eyes were crinkling into a smile as Hassan loaned her nine cents so they could keep playing. Colin thought of Lindsey’s storytelling lessons. The stories they’d told each other were so much a part of the how and why of his liking her. Okay. Loving. Four days in, and already, indisputably: loving. And he found himself thinking that maybe stories don’t just make us matter to each other—maybe they’re also the only way to the infinite mattering he’d been after for so long.

  And Colin thought: Because like say I tell someone about my feral hog hunt. Even if it’s a dumb story, telling it changes other people just the slightest little bit, just as living the story changes me. An infinitesimal change. And that infinitesimal change ripples outward—ever smaller but everlasting. I will get forgotten, but the stories will last. And so we all matter—maybe less than a lot, but always more than none.

  And it wasn’t only the remembered stories that mattered. That was the true meaning of the K-3 anomaly: Having the correct graph from the start proved not that the Theorem was accurate, but that there’s a place in the brain for knowing what cannot be remembered.

  Almost without knowing it, he’d started writing. The graphs in his notebook had been replaced by words. Colin looked up then and wiped a single bead of sweat from his tanned, scarred forehead. Hassan turned around to Colin and said, “I realize the future is unpredictable, but I’m wondering if the future might possibly feature a Monster Thickburger.”

  “I predict it will,” Lindsey said.

  • • •

  As they hustled out the door, Lindsey shouted, “Shotgun,” and Colin said, “Driver,” and Hassan said, “Crap,” and then Linds ran past Colin, beating him to the door. She held it open for him, leaning up to peck his lips.

  That brief walk—from the screened-in porch outside to the Hearse—was one of those moments he knew he’d remember and look back on, one of those moments that he’d try to capture in the stories he told. Nothing was happening, really, but the moment was thick with mattering. Lindsey laced her fingers in Colin’s hand, and Hassan sang a song called, “I love the / Monster Thickburger at Ha-ar-dee’s / For my stomach / It’s a wonderful paar-ty,” and they piled into the Hearse.

  They’d just driven past the General Store when Hassan said, “We don’t have to go to Hardee’s, really. We could go anywhere.”

  “Oh good because I really don’t want to go to Hardee’s,” Lindsey said. “It’s sort of horrible. There’s a Wendy’s two exits down the interstate, in Milan. Wendy’s is way better. They have, like, salads.”

  So Colin drove past the Hardee’s and out onto the interstate headed north. As the staggered lines rushed past him, he thought about the space between what we remember and what happened, the space between what we predict and what will happen. And in that space, Colin thought, there was room enough to reinvent himself—room enough to make himself into something other than a prodigy, to remake his story better and different— room enough to be reborn again and again. A snake killer, an Archduke, a slayer of TOCs—a genius, even. There was room enough to be anyone— anyone except whom he’d already been, for if Colin had learned one thing from Gutshot, it’s that you can’t stop the future from coming. And for the first time in his life, he smiled thinking about the always-coming infinite future stretching out before him.

  And they drove on. Lindsey turned to Colin and said, “You know, we could just keep going. We don’t have to stop.” Hassan in the back leaned forward between the seats and said, “Yeah. Yeah. Let’s just keep driving for a while.” Colin pressed down hard on the accelerator, and he was thinking of all the places they might go, and all the days left in their summer. Beside him, Lindsey Lee Wells’s fingers were on his forearm, and she was saying, “Yeah. God. We could, couldn’t we? We could just keep going.”

  Colin’s skin was alive with the feeling of connection to everyone in that car and everyone not in it. And he was feeling not-unique in the very best possible way.

  (author’s note)

  The footnotes of the novel you just read (unless you haven’t finished reading it and are skipping ahead, in which case you should go back and read everything in order and not try to find out what happens, you sneaky little sneakster) promise a math-laden appendix. And so here it is.

  As it happens, I got a C-minus in pre calc despite the heroic efforts of my eleventh-grade math teacher, Mr. Lantrip, and then I went on to take something called “finite mathematics,” because it was supposed to be easier than calculus. I picked the college I attended partly because it had no math requirement. But then
shortly after college, I became—and I know this is weird—kind of into math. Unfortunately, I still suck at it. I’m into math the way my nine-year-old self was into skateboarding. I talk about it a lot, and I think about it a lot, but I can’t actually, like, do it.

  Fortunately, I am friends with this guy Daniel Biss, who happens to be one of the best young mathematicians in America. Daniel is world famous in the math world, partly because of a paper he published a few years ago that apparently proves that circles are basically fat, bloated triangles. He is also one of my dearest friends. Daniel is pretty much entirely responsible for the fact that the formula is real math that really works within the context of the book. I asked him to write an appendix about the math behind Colin’s Theorem. This appendix, like all appendices, is strictly optional reading, of course. But boy, is it fascinating. Enjoy.

  —John Green

  (the appendix)

  Colin’s Eureka moment was made up of three ingredients.

  First of all, he noticed that a relationship is something you can draw a graph of; one such graph might look something like this:

  According to Colin’s thesis, the horizontal line (which we call the x-axis) represents time. The first time the curve crosses the x-axis corresponds to the beginning of the relationship, and the second crossing indicates the conclusion of the relationship. If the curve spends the intermediate time above the x-axis (as is the case in our example), then the girl dumps the boy; if, instead, the curve passes below the x-axis, that means that the boy dumps the girl. (“Boy” and “girl,” for our purposes, contain no gender-specific meaning; for same-sex relationships, you could as easily call them “boy1” and “boy2” or “girl1” and “girl2.”) So in our diagram, the couple’s first kiss is on a Tuesday, and then the girl dumps the boy on Wednesday. (All in all, a fairly typical Colin-Katherine affair.)

  Since the curve crosses the x-axis only at the beginning and end of the relationship, we should expect that at any point in time, the farther the curve strays from the x-axis, the farther the relationship is from breakup, or, put another way, the better the relationship seems to be going. Here’s a more complicated example, the graph of my relationship with one of my ex-girlfriends:

  The initial burst came in February when, all in a matter of hours, we met, a blizzard started, and she totaled her car on an icy highway, breaking her wrist in the process. We suddenly found ourselves snowed in at my apartment, she an invalid doped up on painkillers, and me distracted and intoxicated by my new jobs as nurse and boyfriend. That phase ended abruptly when, two weeks later, the snow melted, her hand healed, and we had to leave my apartment and interact with the world, whereupon we immediately discovered that we led radically different lives and didn’t have all that much in common. The next, smaller spike occurred when we went to Budapest for vacation. That ended, moments later, when we noticed that we were spending about twenty-three hours of each romantically Budapestian day bickering about absolutely everything. The curve finally crosses the x-axis somewhere in August, which is when I dumped her and she threw me out of her apartment and onto the streets of Berkeley, homeless and penniless, at midnight.

  • • •

  The second ingredient in Colin’s Eureka moment is the fact that graphs (including graphs of romantic relationships) can be represented by functions. This one will take a bit of explaining; bear with me.

  The first thing to say is that when we draw a diagram like this,

  each point can be represented by numbers. That is, the horizontal line (the x-axis) has little numbers marked on it, as does the vertical line (the y-axis). Now, to specify a single point somewhere in the plane, it’s enough to just list two numbers: one that tells us how far along the x-axis the point lies, and the other that tells us where it’s situated along the y-axis. For example, the point (2,1) should correspond to the spot marked “2” on the x-axis and the spot marked “1” on the y-axis. Equivalently, it’s located two units to the right and one unit above the location where the x- and y-axes cross, which location is called (0,0). Similarly, the point (0,–2) is located on the y-axis two units below the crossing, and the point (–3,2) is situated three units to the left and two units above the crossing.

  Okay, so functions: a function is a kind of machine for turning one number into another. It’s a rulebook for a very simple game: I give you any number I want and you always give me back some other number. For instance, a function might say, “Take the number and multiply it by itself (i.e., square it).” Then our conversation would go something like this:

  ME: 1

  YOU: 1

  ME: 2

  YOU: 4

  ME: 3

  YOU: 9

  ME: 9,252,459,984

  YOU: 85,608,015,755,521,280,256

  Now, many functions can be written using algebraic equations. For example, the function above would be written

  which means that when I give you the number x, the function instructs you to take x and multiply it by itself (i.e., to compute x2) and return that new number to me. Using the function, we can plot all points of the form (x,f(x)). Those points together will form some kind of curve in the plane, and we call that curve the “graph of the function.” Consider the function f(x) = x2. We can plot the points (1,1), (2,4), and (3,9).

  In this case, it might help to plot the additional points (0,0), (–1,1), (–2,4), and (–3,9). (Remember that if you take a negative number and multiply it by itself, you get a positive number.)

  Now, you can probably guess that the graph will be a curve that looks something like this:

  Unfortunately, you’ll notice that this graph doesn’t do a particularly good job of representing relationships. The graphs that Colin wants to use for his Theorem all need to cross the x-axis twice (once for when a couple starts dating, and once for the dumping), whereas the graph we drew only touched it once. But this can easily be fixed by using slightly more complicated functions. Consider, for example, the function f(x) = 1-x2.

  This graph is quite familiar to Colin—it’s a graph of a short relationship in which he’s dumped by the girl (we know that the girl dumps Colin because the graph is above the x-axis between the first kiss and the dumping). It’s the graph that tells an outline of the story of Colin’s life. Now all we need to do is figure out how to modify it so as to flesh out some details.

  One of the great themes of twentieth-century mathematics has been the drive to study everything in “families.” (When mathematicians use the word “family,” they mean “any collection of like or related objects.” E.g., a chair and a desk are both members of the “furniture family.”)

  Here’s the idea: a line is nothing more than a collection (a “family”) of points; a plane is simply a family of lines, and so forth. This is supposed to convince you that if one object (like a point) is interesting, then it will be even more interesting to study a whole family of similar objects (like a line). This point of view has come to completely dominate mathematical research over the last sixty years.

  This brings us to the third piece of Colin’s Eureka puzzle. Every Katherine is different, so each dumping that Colin receives at the hands of a new Katherine is different from all the previous ones. This means that no matter how carefully Colin crafts a single function, a single graph, he’ll only ever be learning about a single Katherine. What Colin really needs is to study all possible Katherines and their functions, all at once. What he needs, in other words, is to study the family of all Katherine functions.

  And this, at last, was Colin’s complete insight: that relationships can be graphed, that graphs come from functions, and that it might be possible to study all such functions at once, with a single (very complicated) formula, in such a way that would enable him to predict when (and, more importantly, whether), any prospective Katherine would dump him.85

  Let’s give an example of what this might mean; in fact, we’ll talk about the first example that Colin tried. The formula looks like this:

  In explaining this
expression, I certainly have a lot of questions to answer: first off, what on earth is D? It’s the Dumper/Dumpee differential: you can give anybody a score between 0 and 5 depending on where they fall on the spectrum of heartbreak. Now, if you’re trying to predict how a relationship between a boy and girl will work out, you begin by taking the boy’s D/D differential score and subtracting from it the girl’s D/D differential score and calling the answer A. (So if the boy is a 2 and the girl is a 4, you get D = −2.)

  Now, let’s see what effect this has on the graph. In the example I just gave where the boy gets a 2 and the girl gets a 4, so that D = −2, we have

  whose graph looks like this:

  As you can see, the relationship doesn’t last too long, and the girl ends up dumping the boy (a situation Colin is quite familiar with).

  If, instead, the boy was a 5 and the girl was a 1, we’d have D = 4, so that

  which has the following graph:

  This relationship is even shorter, but it seems even more intense (the peak is remarkably steep), and this time the boy dumps the girl.

  Unfortunately, this formula has problems. For one thing, if D = 0, that is, if they’re equal Dumpers or Dumpees, then we get

  whose graph is just a horizontal line, so you can’t tell where the relationship begins or ends. The more basic problem is that it’s patently absurd to suggest that relationships are so simple, that their graphs are so uniform, which is what Lindsey Lee Wells eventually helps Colin to figure out. And so Colin’s final formula ends up being far more subtle.