“In a riddle whose answer is chess, what is the one word you must under no circumstances use?” The question comes from Borges’ short story “The Garden of Forking Paths,” in which the narrator’s ancestor (we’re told) aspired to create an infinite labyrinth. He ultimately constructed his labyrinth not in space but through time and narrative, writing a great sprawling novel in which many possible—and contradictory—futures coexist, converge, and splay off into variegated chaos again. The forbidden word, of course, is “chess”—making that opening question a riddle in violation of its own rule.
I bring this up because—confession time—I’m a ways behind the group here, with hopes of catching up to my page quota presently. But having been forewarned—I hope a little Googling isn’t “cheating”—that the book’s structure is significant, and constitutes some sort of fractal pattern, I’ve been trying to pay attention to that in the early part of the book. (The convenient thing about a genuine fractal pattern is that it should be apparent at the microlevel fairly quickly.) And I’ve found that I keep thinking, as I go, of that old trickster Borges—not just because I think I may glimpse the outline of a maze being built, but also because I think I keep seeing little hints at its shape in the form of conspicuous omissions. In the Borges story, the ancestor’s novel is a meditation on time that scrupulously avoids using the word “time” or its derivatives. The present-but-unnamed pattern here seems to be the ∞ symbol.
The first one to jump out at me (on page 47 of my copy) came in the first section devoted centrally to Orin, when we’re told this about his latest “Subject” or one-night-stand:
Not real bright—she thought the figure he’d trace without thinking on her bare flank after sex was the numeral 8, to give you an idea
Well, now that’s certainly an odd thing to write, isn’t it? A figure that, traced on skin, might be mistaken for a numeral 8 sounds like it’s got to be the “∞” —the infinity symbol or lemniscate. But why allude to it in this oblique way? Why the implication that of course she must be some sort of dumb bunny if she thought of an 8 instead of recognizing the “∞”? Let’s assume DFW isn’t just being peculiar for no reason, and that this oblique reference to a lemniscate in a book called Infinite Jest is supposed to make us stop and scratch our heads a bit. (Don’t be a dumb bunny, reader! Spot the lemniscate!) DFW does seem to have a thing for that symbol—in his book Everything and More about the mathematics of infinity (actually the only DFW book I owned before picking up this novel) he rather quirkily insists on using the symbol in place of the word throughout. Might there be a few other lurking lemniscates?
In an early footnote, we’re told that the Enfield Tennis Academy itself is in the unusual shape of a cardioid. I had to look it up too. It’s a curve resembling a heart, constructed by taking two adjacent circles in contact at a single point—rather like a lemniscate—and rotating one around the other, as shown in the graph here. We’re told that the architect of this unorthodox structure, one A.Y. Rickey, is the only guy “on the whole East Coast” who could pull it off. This same architect used to “wow Hal and Mario in Weston by taking off his vest without removing his suit jacket.” This, we’re told, is later exposed as “a cheap parlor-trick-exploitation of certain basic features of continuous functions, which revelation Hal mourned in a Santa’s-not-real type of secret way, and which Mario simply ignored, preferring to see the vest thing as plain magic.” I don’t think it’s much of a stretch to see this as a winking acknowledgment that, as we begin to cotton to how the novel’s “architect” is putting it together, we can decide to regard it as a gimmick—no big deal once you see how the trick is done—or follow Mario’s example and just enjoy it. Also, note that the reason you can take a vest off without removing the coat—the “basic feature of continuous functions”—is that vest-inside and vest-outside are topologically equivalent, as all simple polygons are. Usually, the circle is considered the basic shape to which all these “genus one” shapes are equivalent. The basic shape for the next level of complexity, the “genus two” polygon, is—you guessed it—the figure-eight or lemniscate.
Flipping back still further, I found another hint of a lemniscate way back in the second section of Hal’s opening first-person narrative. Hal is recounting a second-hand anecdote, which he himself has forgotten despite playing a central role, and so relies on brother Orin’s recollection. A very young Hal has eaten some sort of weird mold—there’s a hint this may be somehow connected to his later condition—sending his mother into a panic. But Orin’s recollection “diverges at this point”:
In his first memory, the Mom’s path around the yard is a broad circle of hysteria:
‘God.’ she calls out.
‘Help! My son ate this!’ she yells in Orin’s second and more fleshed-out recollection, yelling it over and over, holding the speckled patch aloft in a pincer of fingers, running around and around the garden’s rectangle while O. gaped at his first real sight of adult hysteria. [...] Orin remembers noting how even in hysterical trauma her flight-lines were plumb, her footprints Native-American-straight, her turns, inside the ideogram of string, crisp and martial, crying ‘My son ate this! Help!’ and lapping me twice before the memory recedes.
Two loops joined at a point of divergence—here in time and memory rather than space—with extra care taken to draw our attention to the shape. Again, either this is a frivolous bit of embellishment dropped in for no good reason, or it’s there because it’s doing some kind of work. So let’s take as a working hypothesis that DFW wants us to have lemniscates on the brain for some reason.
Back to the structure of the narrative, then. We start with Hal’s first-person narration, which (so far—and skimming ahead a bit, it looks like this holds based on the date headings) is a classic in medias res framing device, taking place chronologically after the action that follows. At the very end of Hal’s section, we get cryptic flashes of events and characters yet to be introduced, and the inviting close “So yo then man what’s your story?” We begin at the end, which already suggests a kind of structural loop.
Of course, what immediately follows is not Hal’s story, but the introduction of a new character, Erdedy, in third-person narrative. Then we jump back in time and back to Hal and his father, with a scene that plays out exclusively through dialogue—no narrative but what the characters speak out loud to each other. Back to what appears to be the “present” of most of the book (Year of the Depend Adult Undergarment) for a very short scene framed in 3rd person, though with dialogue between Orin, Hal, and Mario. Tangent: As in the Borges story, there’s a conspicuous omission of “time” here. Orin calls and offers the first line of a Beatles song: “I want to tell you. My head is filled with things to say.” Hal’s reply is the start of line two: “I don’t mind. I could wait forever.” He leaves off the end of the line—
and title of the song: “I Got Time.” (Memory FAIL. The song is called “I Want to Tell You.”) But if the reader supplies it, Orin’s reply, “That’s what you think,” suddenly feels rather more ominous. Anyway, another scene gives us another new character, again in third person, the Saudi medical attache.
Again, just as a working hypothesis, call that cycle one. The next scene change is, I think, the first time we jump year-headings without the little circular symbol that had previously accompanied those transitions. So another hint that maybe we’re supposed to regard this scene change differently than the others. We’re suddenly back in first-person again, for the first time since Hal’s opening: DFW’s frankly cringe-inducing attempt to write Black English in the voice of young Clenette. New scene, back to third-person (like the Hal-Erdedy transition) to introduce Bruce Green, Mildred Bonk, and dope dealer Tommy Doocey. (A potential symmetry: We’re meeting a dope dealer in the scene opposite desperate prospective dope-buyer Erdedy’s.) Yet again, we have a transition from third-person to a scene with two of the Incandenzas (this time Hal and Mario) told entirely through the spoken dialogue between the characters. There’s a one-sentence coda reminding us of the medical attaché, which seems to displace the usual circle-symbol between year-changes here, but then we get two more third person scenes, for Orin and then finally back to Hal. This second “cycle,” if that’s what it is, then gives way to a pair of single-paragraph codas for the attaché and Mario, followed by another time-jump, this one also missing the usual circular symbol. The end of Mario’s coda is again a bit incongruous, possibly a hint to the reader: “The reason being it’s a lot easier to fix something if you can see it.” You can imagine a narrative built not on a perfect repeating pattern, but a “broken” one, where the “solution” to the story’s puzzle requires the reader to spot the basic pattern, find the spot where the pattern “breaks” and then mentally “repair” it. Is DFW slyly telling us that’s what we’ll have to do as we read? Too soon to tell, but I’ll keep an eye out.
Now, that symmetry in narrative voice—first person, third person, dialogue, third person, third person—seems too neat to be coincidental, so I’m going to go ahead and assume he’s deliberately setting up this kind of double loop that starts and ends with Hal. The pattern of the five sections of Hal’s opening passage is actually quite similar, though it doesn’t exactly match up. The opening is straight first person. The next section is formally first person, but actually Hal is describing Orin’s recollection of an event—”Orin says he can remember…”—so there’s a sense in which it’s sort of functionally third-person: He’s narrating a scene from Orin’s memory, even though he happens to be present in it. Third section is almost entirely dialogue. And then it sort of breaks down, because the fourth (also dialogue-heavy) and fifth sections are unambiguously first-person again, though in a sort of detached way where Hal is no longer really an agent in the scene.
Anyway, it’s easy enough to build a pretty theory that works for limited data points; I throw it out now so people can see my initial thoughts before the whole thing crashes on the shoals of reality if the rest of the book doesn’t fit the model. But if I’m at least part-right about the shape DFW is constructing, it also gives us another way of reading the title: The hidden lemniscate—infinity—as the author’s little joke or trick; an “infinite jest” meaning a farce shaped like a ∞. I hope this is correct, less because I like being proven right—though there’s that—but because it’s pretty cool if that is what he’s doing and he pulls it off.