In 2016 members of the University of Vermont’s Computational Story Lab quantified the “complex emotional trajectories” of 1,327 classic works by tracking the frequency of words classified as happy (including joy, love, and peace) or unhappy (including hate, shame, and death). The results from the researchers’ so-called hedonometer show the relative rise and fall of positive and negative emotions in books available on Project Gutenberg.

The team at the Computational Story Lab—which also has quantified happiness on Twitter, in the news, and elsewhere—found inspiration in Kurt Vonnegut’s theory of the shape of stories, an idea he originally developed while working on a master’s in anthropology. Vonnegut argued that stories have simple shapes that trace the arc of the relative good or ill fortune of their protagonists, a theory he shared in lectures and in writing.

Vonnegut was not the first person to consider the shape of a story. In Laurence Sterne’s novel Tristram Shandy, Corporal Trim, uncharacteristically at a loss for words, sums up the experience of life as a single, celibate man with a flourish of his cane. Sterne wordlessly illustrates the flourish with a squiggle printed right on the page that wends its way upward in a diagonal slalom and culminates in a loop with a long tail. (Sterne reportedly paid for the woodcut himself.)

Sterne’s squiggle has grown in significance beyond its original narrative; it has come to serve as a synecdoche for the novel as a whole, a fictional autobiography that undertakes so many digressions and asides that the narrator’s birth does not take place until halfway through. In her book Meander, Spiral, Explode: Design and Pattern in Narrative, Jane Alison points out that while we think of narrative as temporal, it is also visual: we experience a story in linear progression, but when we understand it, and are able to grasp an author’s meaning, we see the whole. In reading, she writes, “we travel not just through places conjured in the story, but through the narrative itself.” If Tristram Shandy is a snaking path topped with a curlicue, what shapes do other stories take?

Freytag’s Pyramid, developed by the German novelist and playwright Gustav Freytag in his 1863 book Technique of the Drama, is perhaps the most recognizable graph of narrative form. Freytag describes the rising action of a play as an upward slope, culminating in the apex of the plot’s climax before descending to its conclusion. Alison calls for authors to move beyond Freytag. She writes:

For centuries there’s been one path through fiction we’re most likely to travel—one we’re actually told to follow—and that’s the dramatic arc: a situation arises, grows tense, reaches a peak, subsides. Teachers bid young writers to follow the arc (or triangle or pyramid). If you ask Google how to structure a story, your face will be hammered with pictures of arcs. And it is an elegant shape, especially when I translate arc to its natural form, a wave. Its rise and fall traces a motion we know in heartbeats, breaking surf, the sun passing overhead. There’s power in a wave, its sense of beginning, midpoint, and end; no wonder we fall into it in stories. But something that swells and tautens until climax, then collapses? Bit masculo-sexual, no? So many other patterns run through nature, tracing other deep motions in life. Why not draw on them, too?

Writing narratives with different shapes, as Alison suggests, may require us to think about narrative differently.

If narrative cannot be reduced to just the relative tension in a scene and instead comprises the form a story takes, the emotion being conveyed, the fate of the characters, their joy and their sadness, then narratives might move beyond simple arcs. Martín Solares argues in How to Draw a Novel that a novel’s shape must represent the nonlinear nature of its narrative—its side plots and digressions, its repeated motifs and scenes, its changes of perspective and the relative dominance of those perspectives. Solares might agree with Corporal Trim that the life he could not articulate with words was:

The mythologist Joseph Campbell, concerned primarily with the forward momentum of protagonists, thought stories were not arcs or squiggles but circles. In his 1949 book The Hero with a Thousand Faces, he claimed that “all the religions of all time, the social forms of prehistoric and historic man, the arts, the philosophies, the prime discoveries in science and technology, the very dreams that blister sleep” were underpinned by the “simple basic, magic ring of myth.” The cornerstone of this “monomyth”—a term borrowed from James Joyce’s Finnegans Wake—was what Campbell called “the hero’s journey,” a cyclical progression in which the protagonist heeds a call to action, passes trials, meets and loses mentors, and ultimately returns home fundamentally transformed.

Campbell included two diagrams of the hero’s journey, each consisting of a circle transected by a horizontal “threshold of adventure.” Though they are not prominent features of the book—together they take up less than one of the book’s nearly four hundred pages—their simplicity greatly facilitated the spread of his theory that all stories are fundamentally the same. Instructors of literature and film have been especially avid consumers, annotating versions of the diagram to show similarities in the plots of stories ranging from the Odyssey to Star Wars—the first draft of which, George Lucas admits, was rewritten to more closely fit Campbell’s theory—and Harry Potter. The diagram has also seeped into other areas of American culture. As the author’s protégé Phil Cousineau recalled in his preface to the 2003 edition of Campbell’s collected works,

A Silicon Valley consultant sent me a diagram he had made, adapting the hero’s journey for people in the business world, saying it helped them see a beginning, a middle, and an end in every business deal.

Similarly, a 2016 marketing guide explained how physicians can harness Campbell’s work for the purposes of improving patient feedback, illustrated with adaptations of the diagram demonstrating how the hero’s journey can apply to the experiences of undergoing cancer treatment, bariatric surgery, and rhinoplasty.

Both Freytag and Campbell created a story shape they intended to be applied universally, for all stories—perhaps even nonfictional ones about daily business deals or medical procedures. Allowing for a larger variety of shapes, Vonnegut and the scholars at the Computational Story Lab both saw their charts as representing a number of stock story types. Vonnegut talked about at least eight story shapes, including man in the hole (something bad happens to the main character, who works through it to end up better than at the outset) and boy meets girl (the main character finds something wonderful, loses it, and gets it back). The Computational Story Lab team identified six basic arcs—rags to riches, tragedy, man in the hole, Icarus, Cinderella, and Oedipus—but each book’s arc is distinct, deviating in some way from the ideal shape it most closely resembles. Solares allows that some shapes might describe more than one novel but seems most interested in the uniqueness of each shape: how each novel moves in its precise way, drawing the meander pattern best suited to the story it tells.

The hedonometer uses computational analysis to draw each text’s emotional arc. It takes Vonnegut’s assertion that the shapes of stories are something that could be fed into a computer one step further, by using a computer to determine the shapes in the first place. Team members assign numeric values indicating relative happiness to over ten thousand words. Laughter scores an 8.5, the highest, while beauty is a 7.6. On the other end of the scale, suicide is a 1.3, and in the middle, questions scores a 5. They then divide a text into two hundred sections of equal length, count the frequency of these words in each section, and use those values to assign a happiness number to that section. By plotting those numbers in sequence, we can see the ups and downs of each book’s emotional trajectory.

Below we consider the trajectories of famous books that vary wildly, zigging where their compatriots zag, reaching joyful heights where others sag. Grouping books together, we see how strictures of genre can send works of the same type down similar emotional slides or squiggles. Significant plot points in each book are annotated in the graphs, making it easy to see and interrogate the relationship between the shape of a story and the emotions of the characters trapped inside of it.

Shakespeare’s Comedies

The division of Shakespeare’s plays into tragedies, comedies, and histories comes to us from the First Folio, a collection of thirty-six plays published by two of the playwright’s colleagues after his death. The comedies frequently tell stories of disguise or mistaken identity—in both As You Like It (1599) and Merchant of Venice (c. 1596) women disguise themselves as men—and are nearly always love stories; Love’s Labour’s Lost (c. 1595) and A Midsummer’s Night’s Dream (c. 1595) see couples overcome obstacles, both political and supernatural. More emotionally constant than the tragedies, Shakespeare’s comedies show only slight variations in their relative happiness. Merchant, sometimes considered a “problem play”—not quite a tragedy, not quite a comedy—has the most dramatic ups and downs.

Shakespeare’s Tragedies

While each tragedy is “individual through and through,” the critic A.C. Bradley wrote in 1904, “they have, in a sense, one and the same substance.” What differs from play to play is exactly when the inexorable march toward catastrophe and death begins. Romeo and Juliet (1597) and Hamlet (c. 1600) provide their heroes some happiness before a steep decline, while King Lear (c. 1603) is almost all denouement. Graphed, Othello (c. 1603) reveals itself to be more of a slow burn: the plot is “merely incubating” for the first half of the play, Bradley explains, until “it bursts into life, and goes storming, without intermission or change of direction, to its close.”

Enslaved People’s Narratives

Emerging as a genre in the mid-eighteenth century, the autobiographical “slave narrative” quickly became one of the abolitionist movement’s most powerful tools in winning white Americans’ hearts and minds. Of the roughly seventy examples published before the end of the Civil War, Frederick Douglass’ A Narrative of the Life of Frederick Douglass (1845) was by far the most commercially successful, selling more than thirty thousand copies in its first five years. It also produces the most straightforward plot happiness graph of the four considered here, highlighting key differences in the other three narratives: the higher starting points of Olaudah Equiano’s The Interesting Narrative of the Life of Olaudah Equiano (1789) and Solomon Northup’s Twelve Years a Slave (1853) reflect their authors’ early lives as free people, and Harriet Jacobs’ long, frustrating time as a fugitive results in periods of stagnation interrupting the upward trajectory of Incidents in the Life of a Slave Girl (1861).

Epics

Although long narrative poems focusing on the deeds of heroes have a much longer history, preserving the orally transmitted Iliad and Odyssey in writing around 700 bc marked the beginning of the epic tradition in Western literature. Closely modeled on the Homeric epics both structurally and thematically, the Aeneid was unfinished at the time of Virgil’s 19 bc death, leaving scholars to wonder whether the Roman poet intended a happier ending. The smoother emotional trajectory of Beowulf (c. 725) would not surprise J.R.R. Tolkien, who argued that the Old English work is not an epic at all but should be considered a “heroic-elegaic poem” instead. “In a sense,” he wrote in 1936, “all its first 3,136 lines are the prelude to a dirge.”

Gothic Novels

Gothic fiction, known for having dark, dramatic, and often supernatural themes, first appeared in England in the late eighteenth century, but the genre continuously reinvented itself throughout the nineteenth century. In an era of cross-pollination between the gothic and the romantic, Mary Shelley wrote Frankenstein (1818), which asks fundamental questions about the nature of life and humanity in a story of hubris, murder, and revenge. Emily Brontë’s Wuthering Heights (1847) and Nathaniel Hawthorne’s The Scarlet Letter (1850) bring the gothic into the Victorian era, with stories of people haunted (sometimes literally) by former lovers and past decisions. Oscar Wilde wrote The Picture of Dorian Gray (1891), his story about a man whose corruption by decadence affects only his portrait, during a late nineteenth-century gothic revival. Usually thrilling and suspenseful, gothic novels tend toward emotional turbulence.

Utopias

From a Greek word meaning “no-place,” the term utopia was first coined by Thomas More in his 1516 book of the same name, describing an ideal society on a fictional island. Although not the first to describe such a place, More’s work has inspired numerous other attempts to fictionalize an ideal world. In most of these stories utopia cannot be achieved or has some flaw. Sutton E. Griggs’ Imperium in Imperio (1899) imagines a shadow U.S. government run by African Americans, but ends with the rise of a violent and unstable leader. In 1915, Charlotte Perkins Gilman published Herland, where three men travel to a land inhabited only by women and learn that they cannot adapt to a world without gender norms. A notable exception is Edward Bellamy’s Looking Backward (1888), which imagined the perfection of the year 2000 and ends quite happily with the protagonist married to the woman he loves.