Fractals are everywhere. Look at a tree: from trunk to branch to branchlet to twig, you see about the same shape, same proportions. Consider a cloud or an island: impossible to say if you’re seeing something small or enormous, because the proportions of puff or curve stay the same. The mathematician Benoit Mandelbrot made up the word fractal in 1975 for irregular patterns like these all over nature, patterns that roughly replicate themselves at different scales and could go on forever. Geometry made no sense of these shapes, yet they seemed to follow a mathematical system that involved splitting and splitting again. Mandelbrot’s word comes from frangere: break in pieces, shatter. Lightning, coastlines, rivers splitting into ever smaller streams, cauliflower, capillaries, lungs. A core shape forms a blueprint for possibly endless growth. Spirals are actually fractal, too; they don’t branch, but do self-replicate at different scales, winding inward or outward.
Here’s a recent fractal discovery (noted by Florence Williams in The Nature Fix): Jackson Pollock’s paintings have fractal structuring. The zags and streaks follow that same-but-at-a-different-scale pattern. Fantastically, our eyes’ own scanning patterns are often fractal, too. So there’s a soothing connection, maybe, between how our eyes move across space and many of the largest forms in that space? I can gaze at trees and clouds an awfully long time, delighting in the intricacy of edges and the way tiny mimics enormous.
Another new fractal discovery: many major writers—Woolf, Joyce, James, Bolaño—create fractals with their sentences. A word-count analysis of their texts shows self-replicating ratios between sentence lengths. The researcher Stanislaw Drozdz explains that fractals “point to the hierarchical organization of phenomena and structures found in nature. So we can expect natural language, which represents a major evolutionary leap of the natural world, to show such correlations as well. Their existence in literary works, however, had not yet been convincingly documented.” The most fractal works—meaning fractals of fractals—were stream-of-consciousness narratives, although it’s not clear whether that style reveals depths of consciousness or the writer’s imagination. But fractals forming the shape of a whole narrative are what interest me: texts that start with a “seed” or blueprint that spawns several more. To be clear: where in cellular narratives, like “Lust” and “Captivity,” the segments are equal, in fractal narratives an initial segment is more likely to be compacted like a seed and generate the rest.
CLARICE LISPECTOR’S “THE FIFTH STORY”
This four-page story is as many stories in one and ends with a fifth story beginning. Here’s how it starts:
This story could be called “The Statues.” Another possible title would be “The Killing.” Or even “How to Kill Cockroaches.” So I shall tell at least three stories, all of them true, because none of the three will contradict the others. Although they constitute one story, they could become a thousand and one, were I to be granted a thousand and one nights.
The first story, “How to Kill Cockroaches,” begins like this: I was complaining about the cockroaches. A woman heard me complain. She gave me a recipe for killing them. I was to mix together equal quantities of sugar, flour and gypsum. The flour and sugar would attract the cockroaches, the gypsum would dry up their insides. I followed her advice. The cockroaches died.
The first incarnation of the story is a sketch of events minus detail or depth. Next comes the second story: same beginning and plot, but the loupe now magnifies the desire to kill cockroaches. The narrator “coldly wanted one thing only.” With desire comes a bit more texture than in the tale of pure incident, but this desire isn’t nuanced. Now the third story, “Statues”: same start and plot, but the loupe moves farther along the storyline, focusing upon the consequences of killing. The narrator looks down upon a scene of ruin, “dawn breaking over Pompeii,” tragic cockroach carcasses caught in final expressions of self-reproach, resignation. Nuance has arrived: tragedy! The fourth turns the lens inward: the narrator’s horror of murder twists away from her desire to kill. She’s slaughtered cockroaches once; can she kill again when “this same night an infestation will reappear, swarming slowly upwards”? Ah, psychological complexity.
And finally, preposterously:
The fifth story is called “Leibnitz [sic] and the Transcendence of Love in Polynesia.” It begins like this: I was complaining about the cockroaches.
Self-replication but with difference: from bare incidents to melodrama to tiny tragedy to psychological story of inner struggle. And then to a wild point a hundred miles away, a point that looks outlandish, but maybe with a telescope I can just make out the path there. A hint of Leibniz’s law that self-identical objects must be indiscernible from themselves? I don’t know. I do know that the story could un-end, could keep making new variations of itself forever. So how to end? Here with a mad leap, something so surprising we crash.
CARYL PHILLIPS’S CROSSING THE RIVER
I first read this right after Sebald’s Emigrants, and in my mind they still feel akin. Like Sebald, Phillips treats a horror of human history, here the Atlantic slave trade and tortured relations among black and white people ever since. Crossing the River is, like The Emigrants, also made of four discrete narratives, but with no one narrator binding them. Instead, the book is polyphonic, taking the points of view of four characters and delivering them in different styles: letters, diary entries, mixtures of third person and first. Yet the stories all grow from a single seed: an original form of “intercourse” between white and black.
We begin in 1752 with a lyrical prologue in the voice (mostly) of an African man who sells his children to an English slave-trader:
A desperate foolishness. The crops failed. I sold my children. I remember. I led them (two boys and a girl) along weary paths, until we reached the place where the mud flats are populated with crabs and gulls. Returned across the bar with the yawl, and prayed a while in the factory chapel. I watched as they huddled together and stared up at the fort, above which flew a foreign flag. Stood beneath the white-washed walls of the factory, waiting for the yawl to return and carry me back over the bar. In the distance stood the ship into whose keep I would soon condemn them. The man and his company were waiting to once again cross the bar. We watched a while. And then approached. Approached by a quiet fellow. Three children only. I jettisoned them at this point, where the tributary stumbles and swims out in all directions to meet the sea. Bought 2 strong man-boys and a proud girl. I soiled my hands with cold goods in exchange for their warm flesh. A shameful intercourse. . . . And soon after, the chorus of a common memory began to haunt me.
For two hundred and fifty years I have listened to the many-tongued chorus. And occasionally, among the sundry, restless voices, I have discovered those of my own children. My Nash. My Martha. My Travis. Their lives fractured. Sinking hopeful roots into difficult soil.
I’ll come back to those curious italicized lines after looking at how the book grows from this kernel. We move from the prologue to three stories about metaphorical versions of those children as they struggle over the next two hundred and fifty years; joining their stories is one about the white slave-trader Hamilton. Nash we “meet” again in 1840: no longer enslaved in America, he’s returned to Africa to build Liberia but is sexually pursued by the former slaveholder Edward. Next we see Martha in the 1870s when she, an old woman, struggles in the cold to reach her daughter out west, and a white woman tries to help her. Travis we meet in 1940s England, where he’s posted as a U.S. serviceman and falls in love with a white woman, Joyce. Between the stories about Martha and Travis is one about Hamilton, the man who bought the children in 1752. His story comes as a splicing together of ship-journal entries, documenting his ice-cold business, and love letters to his wife in England.
So we’ve begun with an original sin, the original exchange between white and black, as a “shameful intercourse,” and each narrative sprouting from that core explores an aspect of this “intercourse.” A white man sexually pursues a black man; a white woman tries to keep a black woman from freezing; a white woman and a black man begin a tender but dangerous love affair, one that produces a child. The overall narrative moves from shameful intercourse to loving intercourse between black and white, centuries later, and a new child is born from this love. This child, too, is initially forfeited—put up for adoption—but at the end, at least tentatively, he returns. We slowly journey from original sin to love (loved is the book’s final word), from giving up children to taking them back, from terrible disorder to something approaching decent human order. The book ends with an epilogue in which the original father “embraces” his far-flung children and his new white “daughter”:
I hear a drum beating on the far bank of the river. A breeze stirs and catches it. The resonant pounding is borne on the wind, carried high above the roof-tops, across the water, above the hinterland, high above the tree-tops, before its beat plunges down and into the interior. I wait. And then listen as the many-tongued chorus of the common memory begins again to swell . . .
And I hope that amongst these survivors’ voices I might occasionally hear those of my own children. My Nash. My Martha. My Travis. My daughter. Joyce. All. Hurt but determined. Only if they panic will they break their wrists and ankles against Captain Hamilton’s instruments. A guilty father. Always listening. There are no paths in water. No signposts. There is no return. A desperate foolishness. The crops failed. I sold my beloved children. Bought 2 strong man-boys, and a proud girl. But they arrived on the far bank of the river, loved.
As in Goodbye, Columbus and The Lover, the end mirrors the beginning yet with differences showing how much has changed. But Crossing the River has a more spatial structure than those novels: no single storyline leads from start to end; instead, the parts have juxtapositional relations, in concept rather than causality. The prologue spawns each of the narratives as a version of itself but a bit different—a tree-trunk putting out branches. And the prologue is a miniature plan for the whole on the line level, too. Look at it again: in the roman lines we hear the voice of the father; in the italicized lines, that of Hamilton. Such intimate intertwining of black and white! And at the end of the book, in the epilogue, the father even speaks to his lost children in the language of fractals: “You are beyond. Broken-off, like limbs from a tree. But not lost, for you carry within your bodies the seeds of new trees.” Even more fractals: he speaks of selling his children “where the tributary stumbles and swims out in all directions to meet the sea,” and of his children themselves as sinking “hopeful roots into the soil.”
In fact, the entire narrative feels fractal, if you remember the word’s deep sense as irregular or broken. Despite all the Is in the book, there is no authorial I, no single point of solidity, identity, or home. This fragmented way of telling, as well as breaking up time, reflects the profound shattering within the lives of the characters. Design here is as important as story. Form follows function? Design helps deliver sense.
ANNE CARSON’S NOX
Although not a fiction, Nox is so inventive that I willfully include it in this museum. It’s about the loss of Carson’s brother, Michael, and comes in a somber gray box whose lid you gingerly lift to find a paper accordion: a twenty-seven-yard strip of paper folded a hundred times. At the beginning is a smudged xerox of the Latin poet Catullus’ poem 101, an elegy to his own lost brother. Then you turn fold after fold to find the poem’s Latin words one by one, each with a (partly made-up) lexical entry. Each entry in turn triggers fragments of memoir, photos, envelopes, letters, stamps, drawings, paintings, blank pages, lines of poetry on slips like fortunes. All of these fragments stem from the core of Nox: lost Michael. He’d run away from home, traveled overseas, fallen silent, recently died. Nox is an elegy to him, a prowling after a loved brother whose life Carson barely knew, a prowling by way of Catullus’ elegy.
In a way, the narrative follows the line of a mystery, like one of Sebald’s recountings, starting with the end of a life and trying to understand it. But Carson can know so little. Instead, Nox’s power is in the exploration, the struggle to pass through the scrim of unknowing—that is, to translate, to carry the unknown over to the known. This passage is at the center of Nox, beside a lexical entry for indigne:
7.1 I want to explain about the Catullus poem (101). Catullus wrote poem 101 for his brother who died in the Troad. Nothing at all is known of the brother except his death. Catullus appears to have travelled from Verona to Asia Minor to stand at the grave. Perhaps he recited the elegy there. I have loved this poem since the first time I read it in high school Latin class and I have tried to translate it a number of times. . . . [O]ver the years of working at it, I came to think of translating as a room, not exactly an unknown room, where one gropes for the light switch. I guess it never ends. A brother never ends. I prowl him. He does not end.
The following fold gives us the Latin word frater, brother, with a fragmentary photo of a shadow, maybe Michael’s. And then—
Prowling the meanings of a word, prowling the history of a person, no use expecting a flood of light. Human words have no main switch. But all those little kidnaps in the dark. And then the luminous, big, shivering, discandied, unrepentant, barking web of them that hangs in your mind when you turn back to the page you were trying to translate.
At the heart of Nox: a lost brother and the brain ache of trying to know him and so much that’s unknowable: to pass through paining blur. As a reader (or viewer), I follow the search, as fractured as it is; I follow, above all, the sense of searching. In one way this book is highly spatial—a reader draws webs across folds, across media. Some words recur and bind the whole: night, light, ash, egg, dog, stairwell, festive, blush. And connections can be constellatory, with synaptic links forming among seemingly far-flung elements: lexical entries, bits of story, photos, stamps.
In 1.3, for instance (quoted material my italics): “In . . . Copenhagen, under a wide thin sorrowful sky, as swans drift down the water.” After this comes Latin aequora, whose lexical entry includes “surface of the sea,” “soaring over open sea.” Soon after comes vectus, whose entry includes “travel by sea, sail,” “be carried on wings, fly.” Facing this is a scene about a letter Michael had sent his mother from France, the single letter that she (on her deathbed) tells Carson she wants to keep. On the next fold comes advenio, a lexical note for which is “(of ships) to arrive, put in”; “come into the hands of.” Facing this, a photograph of Michael as a boy with his mother on a dock framed by water. Then we turn the fold to a gorgeous sequence of spreads with full-color copies of envelopes and foreign stamps (AEROGRAM, LUFTPOST, PAR AVION), and finally the single letter from Michael that his mother wants. So this series of nine spreads gives—subtly—a sweep of traveling over water, flying, airmail letters, arriving, until the letter from Michael to his mother gloriously appears and tells you that you hadn’t imagined it, no: those glimmers really were brightening, until at last you had a constellation, a map of meaning.
Nox is spatial, with no storyline leading a viewer through. Like Sebald’s Emigrants, it’s a web—a “barking web” that hangs in your mind? Yet it grows from a single seed, Catullus’ poem, the words in that poem so compacted with meanings and potential that they can keep branching to grow the whole, a fractal—fragmented? interrupted? unending?—elegy to a lost brother.