Once Upon a Prime, page 8
Back to “Foundations of Literature,” then. Queneau suggests that literary texts could be created subject to specific literary axioms. Instead of points and lines, we could talk about words and sentences. Having created a set of axioms, your new literary form will consist of texts that satisfy those axioms. The two geometric axioms we had earlier, says Queneau, would then become the following:
1. Given two distinct words in the text, there is always a sentence in the text containing those two words.
2. Given a sentence in the text, any two words in the text uniquely determine that sentence.
As Queneau points out, the text describing the axioms does not itself satisfy the axioms, and that’s fine—the definition of (say) a rhyming couplet is not necessarily itself a rhyming couplet, though naturally I now want to think of one that is.
Let me show you a truly strange “geometry.” It’s called the Fano plane, named for the Italian mathematician Gino Fano, who discovered it. (In fact, at least two other anticipatory plagiarists had independently discovered it before him, though I don’t think he was aware of this.) The Fano plane contains precisely seven points, and precisely seven “lines”—in my picture they are shown as six straight lines and a circle. Each line consists of exactly three points.
The Fano Plane
This object is breathtakingly symmetrical. Every pair of points lies on exactly one line and every pair of lines meets in exactly one point. Every line contains precisely three points and every point lies on precisely three lines. It’s beautiful. Yes, there are about a million applications of this structure, everything from cryptography to lottery tickets, from set theory to experiment design. There’s also a link to a picture that may be more familiar—the classic Venn diagram showing all the possible intersections between three sets: the seven regions of the diagram correspond to the seven points of the Fano plane. But the reason I love the Fano plane has nothing to do with the applications. It’s purely down to its symmetrical simplicity.
As a tribute to Queneau and the Oulipo, I have created a new axiomatic literary form, which I have christened “Fano fiction.” The rules for Fano fiction are simple. Each text uses a vocabulary of exactly seven words (our “points”) and consists of exactly seven sentences (our “lines”), each of which contains exactly three words. Each pair of words appears in exactly one sentence, and any pair of sentences has exactly one word in common. I’ve also required of myself that each sentence should observe the traditional grammatical rule of having a verb in it. With only twenty-one words in total, it’s going to have to be a pretty spare narrative. My inaugural work of Fano fiction is encapsulated in the Fano plane diagram on the following page.
The story tells how you, a talent agency employee, were advised that it’s best to get hold of the next big talent, and book her fast. A T-shirt line she endorsed flew off the shelves, and there was a bidding war for her autobiography. You encouraged her to write the follow-up volume without delay, and to top her best previous achievements. She did so well that you could sell your share of the proceeds and retire a millionaire. And here’s the Fano fiction version:
“Book top act!
Best book fast!”
Top sold fast.
Next, book sold.
“Act fast—next!
Next: top best!”
Best act: sold.
All I need to do now is sit back and wait for my Nobel Prize in Literature.
I said at the end of the last chapter that the members of the Oulipo take the use of constraints to extremes. Do they go too far down that route? One accusation sometimes leveled at their work is that the constraints imposed serve only to create clever puzzles. The first response to this objection is that there’s no reason something can’t be clever and great art at the same time. But more important—and this is a point Oulipians themselves have reminded critics of from time to time—the Oulipo is a workshop of potential literature. Its purpose is to provide possible structures, not necessarily to provide the literature itself. As Raymond Queneau said, “We place ourselves beyond aesthetic value, which does not mean that we despise it.”
The fact that many terrible sonnets have been written in the course of history does not imply that the concept of the sonnet is inherently bad; there is some boring, arid constrained writing, just as there are boring, arid novels. But there are also fantastic, imaginative, creative, exciting works of constrained writing—Perec, Calvino, Queneau, and others have produced art that we are still talking about. So that’s my defense of the Oulipo. Everyone will have their own personal sense of the boundary between art and artifice, but I truly think there’s something Oulipian to suit every taste.
4
Let Me Count the Ways
The Arithmetic of Narrative Choice
Have you ever played one of those story apps on your phone that require you to make a choice at the end of each “scene”? I can almost hear the brain cells dissolving as my daughter decides whether her character should go to the prom with Chad or with Kyle. Naturally, I can’t help but wonder how many ways through such games there are, and how many scenes have to be written. Many books, plays, and even poems give us a choice of how to read them. Mathematics can help us to understand the implications. Imagine an interactive story in which at the end of each page you pick one of two options, each of which takes you to a different page. On the face of it, you’d need two different second pages, but then four different third pages, eight fourth pages, and so on. Incredibly, even if you make only ten choices in the whole book, it would need to be more than two thousand pages long! This obviously can’t be how such books are constructed.
In this chapter, we’ll look at the mathematics of narrative choice. We’ll learn how to write a play in which the audience gets to decide what happens next without the actors’ having to learn hundreds of scenes, and we’ll explore what happens when you write a story in the shape of a Möbius strip.
* * *
We saw in Chapter 2 some playful examples of graphs representing the plots of stories. But there is a different kind of graph that can be used in plays, books, or other forms of literature in which the creators make available more than one path through the text. This can be done by directing the reader in various ways, or by giving the reader (or theatergoer) choices at key points, or by introducing randomness. The graphs I’m talking about are networks with points, or vertices, joined by edges that represent some sort of link between the points, like the interval graphs I showed you in the last chapter. The example I gave there was a subway map. For these kinds of maps, what we care about is the connections, not exact distances or accurate geographical location. Another graph that’s very important in today’s world is one in which each vertex is a web page, and we join two pages when one includes a link to the other. These kinds of graphs represent the connectedness of the Internet and help to determine how highly pages are ranked in search engines. Pages with lots of links are higher up the list. Finally, if you have ever played Six Degrees of Kevin Bacon, you’ll know that we can also represent the connectedness of society with a graph in which every person is a vertex and two people are linked if they have appeared in (or directed or otherwise been involved with) the same movie.
I’m now going to show you a graph that was devised by Oulipo member Paul Fournel, along with Jean-Pierre Enard. It’s called a theater tree, and it was created to help write interactive plays. The idea is that at the end of each scene, the actors ask the audience to choose between two possible plot developments. A masked man walks onto the stage at the end of a scene, say. The audience are asked: Is this man the king’s illegitimate son, or is he the queen’s lover? The audience’s choice determines the scene to be played next. This is fun for the audience, but think about the poor actors (not to mention the poor set builders, costume designers, and prop wranglers): every time there is another choice, the number of scenes the actors have to learn goes up, and it goes up dramatically. If the audience makes four choices in total, then they will see five scenes (a choice at the end of Scenes 1 to 4, and then the final Scene 5). But how many scenes do the actors have to learn? There’s one Scene 1. Then the audience makes a choice, and so there would be two versions of Scene 2. Then there’s another choice, so these two Scene 2s bifurcate into four Scene 3s, then eight Scene 4s, and finally sixteen Scene 5s. If you add this up, you get thirty-one scenes. (Is this ? Yes, it is.) The scene structure can be shown in a graph, working down from Scene 1 at the top to all the possible Scene 5s at the bottom:
Here’s where Fournel and Enard come in. They used the fact that there are other graphs that start from a single vertex (Scene 1) and still have a choice of two paths below each vertex but have fewer vertices in total. This means that the audience can still experience an interactive play with five choices, but the actors will be a lot happier.
Let’s look at Fournel and Enard’s suggested graph—the theater tree. As you can see, there are only fifteen scenes:
How does this work? In the theater tree, we start at the top with Scene 1, then work down, making our choice at each point. But whereas in the original play we had four different versions of Scene 3, the theater tree manages to have just two. How? Well, the writer has to ensure that whichever version of Scene 2 is played, by the end of the scene it’s possible to choose between the same two options for Scene 3. For example, if the audience decided at the end of Scene 1 that the masked stranger was the king’s son, then in their Scene 2 a new person, the queen’s lover, could dramatically appear. Meanwhile, for those who said the stranger should be the queen’s lover, their Scene 2 could introduce the king’s son. This way, in either case, the decision at the end of Scene 2 can be “Should the king’s son and the queen’s lover fight a duel, or should they turn out to be old friends?” At the end of Scene 4, the audience again is given a choice: “Do you want a happy ending, or a tragic ending?” In order for the four Scene 4s to resolve to just two endings, the final scene is split into a bridging scene—5a (in gray)—and a conclusion—5b (in black). Counting up all the scenes and half scenes, we arrive at a total of fifteen.
In both these setups, the audience sees five scenes. How many possible plays are there for the audience? The answer is the total number of paths. In both cases, the answer is sixteen. This is because each choice splits the play universe in two. With one choice, there are two plays. With two choices, you get four plays; with three choices it’s eight, and with four choices it’s sixteen. Paul Fournel pointed out that creating sixteen separate five-scene plays would require writing eighty scenes. Even the inefficient version of an interactive play improved on this with thirty-one scenes. But the theater tree is even better. Graph theory has reduced the performers’ workload by sixty-five scenes: an impressive 81 percent.
I wondered whether it was possible to do even better. The answer is yes, but with a caveat. If you went to see an interactive play created using the theater tree, your experience—four choices made, five scenes—would be indistinguishable from one created using the larger 31-scene tree. At least, it would be if you saw it only once. If you went back the next day for another go, there’s a good chance you’d see some of the same scenes, even if you picked different options. The illusion of the full tree works for only a single viewing—which is fine, of course. During that single viewing you would not feel that your choices were illusory in any way. However, here is a more efficient tree that still gives the audience four choices:
This time, I’ve deployed the same trick that the theater tree uses to prevent the need for four different Scene 3s, but I’ve applied it to every scene. It requires that each time a choice is made, by the end of the resulting scene the choice has to turn out to have been irrelevant. Should two people fight or turn out to be friends? The scene that follows must somehow make both things true, whichever the audience picked, so that subsequent choices are not constrained. This is because at each point, only two scenes are available, so both have to make sense, whatever the sequence of choices. If the audience votes for a fight, then maybe the characters start fighting, but it emerges that they are friends who have had a disagreement. If the audience wants them to be friends, then fine, they greet each other as friends but an argument ensues that results in a fight. It would likely become fairly obvious as an audience member in a play like this that your choices are not really having any effect. My graph may be more efficient, but it will likely lead to a worse play than a theater tree would.
I’m not aware of vast numbers of productions of theater-tree plays. But there have certainly been interactive TV shows, one example being 2018’s Bandersnatch, part of the Black Mirror series on Netflix. It has 150 minutes of footage ingeniously put together to create 250 segments. Choices made by the viewer determine which segments are played, and in what order. There are reportedly more than a trillion paths through the story, each lasting on average ninety minutes. Such shows would be prohibitively expensive to make unless efficient graphs are used. Without them, every choice doubles the number of scenes that must be written and filmed, so that, as I said at the start of this chapter, even ten choices over eleven scenes would require more than two thousand scenes (the exact number is ). The analogue of the hyperefficient but boring graph in which there are just two versions of each scene after the first would require twenty-one scenes—but viewers would soon smell a rat. The best solutions will be somewhere between these two extremes.
There is a form of literature that uses just this kind of combination of free choice and hidden structure, but on a vastly more ambitious scale. I’m talking about the “choose your own adventure”–style books that many of us had as kids. They were very popular in the 1980s, then fell out of favor as computer games started to be able to create the same kind of experience. But now they are having a bit of a revival. If you’re not familiar with this genre, basically you, the reader, are a character in the book: you are thrown into events, and you have to decide what to do at regular intervals. If you want to investigate that mysterious cave you just found, turn to page 144. If you want to take the path to the castle, turn to page 81. If instead you want to cross the bridge and fight the troll, turn to page 121. Sometimes randomness is introduced—you may need to roll dice to determine whether you beat the troll in the fight you decided to pick with it. If you win, go to page 94; if you lose, go to page 26. Reading these books involves potentially hundreds of choices (unless you foolishly choose to get into an argument with a troll, in which case you’re likely a goner after only a few pages). The arithmetic of choice tells us straightaway that many pages must appear on several narrative paths. Otherwise, in a book with 100 choices, even if there are just two options each time, the book would be pages long. Even if each page were just a tenth of a millimeter thick, it would take the light from your flashlight (I assume you are reading the book under the covers because your parents told you to go to sleep hours ago) 26.8 billion years to get from the first page to the last. In reality, a scaled-up version of something like the theater tree has to be used.
To find out more, I needed to talk to an expert. For my ninth birthday, I was given a book called The Warlock of Firetop Mountain, the first volume in the wildly successful Fighting Fantasy series of interactive books in which “You are the hero.”1 The book came out in 1982, and it was written by Ian Livingstone and Steve Jackson. Since these names have been etched on my brain for over forty years, I was delighted when Sir Ian, as he is now known, agreed to speak to me about how he constructs his branching narrative adventure stories. As well as being the co-creator of the Fighting Fantasy series, which has sold more than twenty million books worldwide, he’s also a gaming legend—co-founder of Games Workshop, which brought Dungeons & Dragons to the UK, and of Eidos Interactive, publisher of the Tomb Raider games.
When we meet, Sir Ian explains that he creates each book using a flowchart, done by hand, and he shows me the original chart for Deathtrap Dungeon (Puffin, 1984). He starts with a basic path and then gradually adds branch points—places where decisions are made. Very little is predetermined. “We know the overall story arc, but what happens along the way is an iterative process.” For example, “You might decide you want an iron door, then you think, ‘Well, how do we get in here? Is it open? No, I want it to be locked, there’s something important in there.’ So we need a key.… You then go back earlier in the story and add a box to a room that they’ve been in, and the key is in the box.” Each event or decision is numbered at random, and those numbers are then crossed off a master list (the Fighting Fantasy books all have four hundred sections, or “references”). There are many story strands in play, but there are always what Sir Ian calls pinch points, at which you go back to a node that gives important information and brings the story back into one passageway again. These pinch points are vital in preventing an exponential increase in the number of possible choices.
As you go along with the writing, you have to keep checking that there is definitely at least one successful path through the book, as well as making sure there aren’t any loops from which there’s no escape. And then there’s the question of difficulty. There’s great skill in designing the book so that the challenge is at the right level—not enough monsters to fight, and it’s too easy; too many, and the reader becomes dispirited. “Oh, no, not another army of the undead,” you sigh. Sir Ian’s books are carefully calibrated to avoid either extreme. He does have fun with readers, though. “My joy is always trying to lure people to their doom,” he jokes. “The petals along the floor where they fall on the poison spikes.” He also enjoys the occasional red herring, “littering the dungeon with useless objects that they pick up, and then they miss the important items.”
