by Peter Turchi
While Perec exaggerates the power of the puzzle maker (the puzzle solver could instead choose to ignore the puzzle, set fire to it, or mash it into paste and feed it to hippos), the essential notion—that the composer keeps his audience in mind and anticipates their reactions—holds true, as does the notion that a dedicated puzzle solver is engaged in conversation with the composer.16 A puzzle presents a problem, and even if we pick one up for relaxation, we’re choosing to engage with difficulty or conflict. A puzzle whose solution is immediately apparent isn’t refreshing or enjoyable; it’s “too easy.” We feel neither exercised nor rewarded. The deception or distraction in a composition takes the place of the multiple possibilities, distractions, and arbitrariness of life. A fiction writer might not think she’s deliberately misleading her reader, but she is, almost undoubtedly, trying to get her reader to imagine the various things that could happen (as opposed to the more limited number of things that do happen), the choices her characters could make, all the possible stories that could follow from what’s been set in place. If we can’t imagine Elizabeth Bennet marrying Mr. Bingley or Mr. Collins—if Pride and Prejudice failed to help us anticipate what either of those marriages would do to Elizabeth—Jane Austen’s novel would lose much of its tension and dramatic interest.
The Chess Players, by Jonathan Wolstenholme
In addition to originality, invention, and conciseness, chess problem composers talk about illustrating one or more themes and, perhaps surprisingly, about aesthetic value. Marcel Duchamp famously said, “I have come to the conclusion that while all artists are not chess players, all chess players are artists.” To some people, it comes as a surprise to hear puzzle makers, problem composers, scientists, and mathematicians talk about art and beauty. While the first goal is to create a functional puzzle or problem, or—in math and science—to solve a problem, the next goal is to achieve a combination of clarity, economy, and—in the case of puzzles—cleverness. That combination of qualities makes a composition ingenious, surprising in its simplicity. In math, in physics, and in computer science, among other fields, there are ugly solutions and elegant ones.17
PATTERN RECOGNITION
In Speak, Memory, his autobiography, Nabokov describes his process for composing a chess problem, which serves as a metaphor for his composition of a novel:
Will Shortz, puzzle editor of the New York Times, has been creating puzzles for National Public Radio since 1987. He recalls as one of his favorites a puzzle in which he lists two things in an unstated category. The solver is required to name the one other item in the same category that comes between the first two alphabetically. To solve “Florida and Hawaii,” for instance, the solver would determine that the category is “United States” and then identify Georgia as the correct answer.
1. Thursday / Wednesday
2. Earth / Mars
3. Cleveland / Coolidge
4. Africa / Asia
5. Comet / Dancer
6. Neptunium / Niobium
7. Ecclesiastes / Exodus
8. Sagittarius / Taurus
9. Catcher / First base
10. Flush / Full house
11. Bashful / Dopey
12. Drummers drumming / Geese a-laying
“There are several reasons I like this puzzle,” Shortz says. “One is that it’s very accessible—anyone can try it. You don’t have to be a puzzle whiz. Second, it plays with your mind in a weird way. It’s kind of funny to think what comes between Thursday and Wednesday, for example, since we usually think of those things chronologically. And third, it’s completely different from any puzzle that’s come before it, at least as far as I know. I can’t think of any earlier puzzle with an alphabetical constraint like this.”
I would experience, without warning, a spasm of acute mental pleasure, as the bud of a chess problem burst open in my brain, promising me a night of labour and felicity. It might be a new way of blending an unusual strategic device with an unusual line of defence; it might be a glimpse, curiously stylized and thus incomplete, of the actual configuration that would render at last, with humour and grace, a difficult theme that I had despaired of expressing before; or it might be a mere gesture . . . suggesting new harmonies and new conflicts. . . .
It is one thing to conceive the main play of a composition and another to construct it. The strain on the mind is formidable. . . . This or that knight is a lever adjusted and tried, and readjusted and tried again, till the problem is tuned up to the necessary level of beauty and surprise. . . . Competition in chess problems is not really between White and Black but between the composer and the hypothetical solver (just as in a first-rate work of fiction the real clash is not between the characters but between the author and the world). . . .
But whatever I can say about this matter of problem composing, I do not seem to convey sufficiently the ecstatic core of the process . . . the event is accompanied by a mellow physical satisfaction, especially when the chessmen are beginning to enact adequately, in a penultimate rehearsal, the composer’s dream.
To solve this 3D grid sudoku by Thomas Snyder, place the digits 1–8 into the empty cells in the grid (a single digit per cell) so that each digit appears exactly once in each of the six outlined regions and the twelve “rows.” A “row” follows the opposite, parallel sides of each quadrilateral.
While other writers might not feel they are engaging in competition with their readers, to the extent that the writer means to lead her reader somewhere new, along a route that contains at least a few surprises, even the friendliest writer anticipates and makes use of the reader’s expectations. We all recognize the gap between conceiving “the main play of a composition,” or the essence of a story, and actually constructing it. Just as puzzle composers have many ways of conversing with puzzle solvers, writers have many different ways of conversing with their readers.
The puzzles Nabokov embedded in his novels for his readers to solve go well beyond plot, and in many cases they are never explicitly stated. His particular game-playing depends on a like-minded reader. But while Pale Fire might seem far removed from Bonfire of the Vanities, every novel and story and poem—every piece of written communication—relies on certain assumptions about the reader, and what he or she will recognize and understand.
Exploit pattern recognition: I magically produce four silver dollars, one at a time, with the back of my hand toward you. Then I allow you to see the palm of my hand empty before a fifth coin appears. As Homo sapiens, you grasp the pattern, and take away the impression that I produced all five coins from a hand whose palm was empty.
— TELLER
William Gibson’s Pattern Recognition begins as a novel about a woman consulting for a corporate client: “It’s about a group behavior pattern around a particular class of object. What I do is pattern recognition. I try to recognize a pattern before anyone else does.” Cayce Pollard’s particular talent is recognizing what will generate talk on the streets, cultural and consumer excitement, and she operates so instinctively that she refuses to provide any explanation of her judgments; she’s paid to say yes or no. Her current task is the rebranding of one of the world’s largest manufacturers of athletic shoes. She’s been asked to pass judgment on a new logo, a symbol intended to speak wordlessly, internationally. At the same time, she’s caught up in an online community devoted to something they call “the footage”—bits of film released via the Internet by an unknown person for unknown reasons. Some speculate that the bits of footage are from a complete work; others believe they’re from a work in progress; others debate whether the pieces are part of a single whole. “The footage” is a puzzle Cayce and others would like to solve. Also early in the novel, Cayce realizes that someone has broken into the apartment that she’s borrowing—and that a woman who works for another company knows far more about her than she can explain.
On the level of plot, then, Gibson establishes a number of puzzles that are eventually solved. But the theme of pattern recognition is conveyed in the prose as well. Gibso
n makes use of sentence fragments, or partial sentences, assuming the reader will recognize common syntactical patterns. He also mixes real and fictitious place names and product names, and familiar and newly coined slang and acronyms. Cayce refers to England, where she’s working, as a “mirror-world” of the United States, where she lives, with some things identical, some familiar but not quite the same (coins, the heft of a phone). Gibson reminds us that every work of fiction is a mirror-world (the term draws us, inevitably, to Alice’s Adventures in Wonderland, written by the mathematician and puzzle composer Lewis Carroll). As we read, we compare the world of the fiction to the world we live in. We look for similarities, note differences. This is true not only when we read realistic fiction, where we expect a more direct correspondence to “reality,” but when we read science fiction, fantasy, historical novels, and post-realistic fiction. How does what we read look like other things we’ve read? If we recognize Pattern Recognition’s allusions to Alice in Wonderland, what parallels do we draw? How do they inform our reading? If we’re familiar with other William Gibson novels, we might feel a similarity in voice and tone. If we’re not, we consciously or subconsciously draw connections of our own, quite possibly even to books and stories William Gibson has never read. As another character tells Cayce,
Musicians today, if they’re clever, put new compositions out on the web, like pies set to cool on a window ledge, and wait for other people to anonymously rework them. Ten will be all wrong, but the eleventh may be genius. And free. It’s as though the creative process is no longer contained within an individual skull, if indeed it ever was. Everything, today, is to some extent the reflection of something else.
Musical sampling, mash-ups, remixes of songs, and fan fiction may have us more aware than ever that every creative work is completed, or interpreted, by its audience, but the human tendency to see the self reflected in the world goes back at least as far as Narcissus—and of course the myth of Narcissus, which was familiar when Ovid retold it, is a story that means to reflect a recognizable human trait. We read fiction, in part, to see our world reflected. Richard Adams’s Watership Down might be about rabbits, but we care about those rabbits only because they have very human concerns. On the other hand, we might refer to a situation as a Catch-22 because we recognize the phenomenon Joseph Heller labeled in his best-known novel when we see it in our daily lives. As readers we’re able to understand—to decode—a new book or story or poem thanks in part to our life experience, and in part to all of the other books and stories we’ve read.
As writers, we assume our readers will be familiar with certain patterns, or conventions, though those might be very general. In Gibson’s novel, when we find out that someone has broken in to the apartment Cayce is using, we anticipate that the break-in will be connected to her job and/or to her interest in “the footage.” Why? Because our experience with fiction has conditioned us to expect that significant but apparently disparate events will ultimately be connected. This sort of pattern recognition occurs in the most conventional fiction—consciously or not, we all respond to the cues in a Hollywood film that tell us a certain character isn’t to be trusted—as well as in the most innovative or challenging fiction. “Difficult” fiction often seems difficult because of the way it delays or refuses to provide the kinds of connection—the patterns—we’re used to. The puzzle is unfamiliar, and its rules may not be immediately apparent.
Carole Maso’s collage novel The Art Lover is written in many short sections—some less than a page. The book has three distinct sets of characters, the text is often accompanied by unexplained images, and the captions to some of the images are often obscured or fragmentary, such as clippings torn from a newspaper. It takes even the most attentive reader a while to understand that the first character we’re introduced to, Allison, and her family, are characters in a novel being written by Caroline, another character in the book, whose father has recently died; and it isn’t until late in the book that Maso introduces the true story of the death of her friend, the artist Gary Falk. Carole Maso is reflecting her real-life loss in the story of the writer Caroline, who is in turn mirroring her loss of her father in the story of Allison. At times it might feel that, like Alice, we’re falling through the looking glass. But the book is arranged in six chronological sections, and very early our attention is drawn to significant images, including a starburst and fiddlehead ferns. Because we don’t have the traditional continuity of plot and character to guide us, we read Maso’s novel alert for repetitions of those images and indirect references to them. In this way, a writer can rely on something like insight thinking on the part of the reader. As readers, we’re encouraged to focus on information—details, images—that might merely be part of the setting in another novel but which will serve another role here; we’re forced to compare characters and to consider a variety of potential metaphors; and we’re asked to combine what we’re told to understand something larger. The repetition of images, the formal arrangement of material, and the relationships among the three sets of characters are pieces of a puzzle, and they serve to organize the book. While The Art Lover doesn’t look quite like most novels we read, and might initially seem frustrating, it offers distinct patterns the reader is led to recognize.
Benjamin Franklin was wrong (and no doubt knew it): mathematical novelties aren’t useless. Latin Squares were not invented, or created, to give us something to do during plane rides. They were famously explored by a contemporary of Franklin’s, the Swiss mathematician Leonhard Euler, and they have been particularly useful in controlling variables in experiments. Among other achievements, in 1736 Euler solved a problem known as the Seven Bridges of Königsberg. The city that was once Königsberg, Prussia, is beside the Pregel River and at that time included two large islands, which were connected to each other and the mainland by seven bridges. One day, some thoughtful person—probably a writer, procrastinating—wondered whether it was possible to walk a route that crossed each bridge exactly once and return to the starting point. (You can try it for yourself by using a pencil to draw a continuous line on the illustration, crossing each bridge just once and returning to where you begin.) Trial and error seemed to indicate that it wasn’t possible; but Euler abstracted the problem to one of nodes (the bits of land) and links (the bridges). This allowed him to determine under what circumstances it is possible to make a single complete circuit among any given number of nodes and links and under what circumstances it is not. His solution is the first theorem of graph theory and eventually led to the establishment of topology, a branch of mathematics concerned with the property of networks.
Königsberg, remembered for its bridges
In other words: a mathematician took a situation in the real world, turned it into a puzzle, solved it, looked for a larger pattern, or recurrent circumstance, and then applied his understanding of that circumstance to other real-world situations. This is how the kinds of puzzles contemplated not only by mathematicians but by biologists, physicists, astronomers, ecologists, and economists are not merely amusing, or trifling, but useful. They serve as models of experience. In the same way, a poem or novel or story reflects a real-world situation, character, problem, or idea in a way that allows us to consider it, and perhaps even understand it, differently. When Chekhov wrote that the artist’s job is to pose the question correctly, he was essentially saying that the artist, like Euler, must stand back and see the essence of the problem or the issue at hand; then he must find a way to frame it that focuses the reader’s attention on that essence.
All writers are puzzle makers. As models of our experience, stories and novels aim not to reduce that experience, or to simplify it, but to reflect its pleasures and sorrows, and to bring its mysteries into sharp focus.
8 These terms are unsatisfactorily vague and, in certain company, the cause of passionate debate. For this discussion, I’ll suggest that genre fiction is written by an author aware of certain conventions, for readers aware of those conventions, and largely
aims to satisfy both those readers and the conventions. That said, there are books we might call westerns or science fiction or detective novels or even romance novels that mean to challenge us, to lead us to consider some aspect of the world in a new way. We sometimes say books like these transcend their genre. Similarly, there are stories and novels that look like literary fiction but which intend only to please the reader and to satisfy the conventions of, say, the coming-of-age story; they are, like other genre fiction, intent primarily on entertainment. So many books blur the line that there is no clear line. Is Toni Morrison’s Beloved a ghost story? Is Wuthering Heights a romance novel? Is Cormac McCarthy’s All the Pretty Horses a western? Is Larry McMurtry’s Lonesome Dove? More important: outside of publishers’ sales meetings, when is it necessary or useful to attach labels to books?
9 And again: each of us is more than one reader. Or, we are each many kinds of readers. The fact that we enjoy T. S. Eliot’s Four Quartets doesn’t mean we can’t also enjoy Arthur Conan Doyle’s The Sign of the Four, though the reasons for our pleasure might be quite different.
10 The title of this section is a cryptogram, a simple substitution cipher in which each letter of the alphabet is consistently replaced by a different letter of the alphabet.
11 As almost anyone might have guessed, a human was behind the Turk’s genuinely impressive chess playing—a particularly nimble chess master who sat hidden in the ingeniously designed cabinet on a silently rolling seat, so that doors on both sides could be opened to reveal the automaton’s machinery and allow viewers to see completely through the cabinet, albeit one section at a time. In addition to being confined for long periods, the chess master had to regard the board from beneath, moving the pieces using magnets, demonstrating impressive dedication to a hoax. As Teller, of the magician duo Penn and Teller, has said, “You will be fooled by a trick if it involves more time, money, and practice than you (or any other sane onlooker) would be willing to invest.”