A Supposedly Fun Blog

July 15, 2009

The Garden of Looping Paths

Filed under: Uncategorized — Julian Sanchez @ 4:18 pm

“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?EpitrochoidOn1

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.


  1. […] a show of extreme foolhardiness, I’ve got a long, rambling post over on A Supposedly Fun Blog about the narrative structure of Infinite Jest. The foolhardy part is that I’m basing my […]

    Pingback by Literary Lemniscates — July 15, 2009 @ 4:26 pm | Reply

  2. What a neat analysis. I don’t know whether or not it’ll hold up throughout the book, but I’ll be eager to read your updates as you get deeper in.

    Comment by Daryl Houston — July 15, 2009 @ 5:33 pm | Reply

  3. DFW claimed in an interview that the book was structured like a Sierpinski Gasket. Which I can sort of see, in spots, but mostly it just makes me a little dizzy. Good catches w/ the infinity stuff, though — I don’t think it really holds up as a basis for the book’s structure, but it’s definitely relevant and there’ll be more to build on as you continue.

    Comment by the teeth — July 15, 2009 @ 6:04 pm | Reply

  4. I wrote just a tiny little thing about the Sierpinski gasket stuff (turns out there’s something Cantorian about its structure) here. Didn’t want to mention it before b/c it’s such a trifling thing next to this analysis, but since you brought up Sierpinski, I figured I’d point it out.

    Comment by Daryl Houston — July 15, 2009 @ 6:16 pm | Reply

  5. Click on the link to “forewarned” in the body of the post for the interview where DFW talks about the Sierpinsky gasket business, though he doesn’t go into any great detail. If we take it seriously, though, we should expect a structure of nested triangles rather than loops, which means we ought to be looking for triplets. So far, though, it looks like five is the more salient number. A repeating pattern of five narrative voices. Five sections to Hal’s opening. Five Incandenzas (Hal, Mario, Orin, Himself, Moms). Five main areas of the tennis academy (four buildings and the central pavilion with the courts). So maybe he’s speaking loosely and we should be looking for a pentagonal fractal structure? Again, probably a mistake to theorize this early, but keeping my eyes open.

    Comment by Julian Sanchez — July 15, 2009 @ 6:33 pm | Reply

  6. […] — I’ll believe there are green shoots when Julian Sanchez doesn’t have time to put stuff like this together. […]

    Pingback by Matthew Yglesias » Endgame — July 15, 2009 @ 10:14 pm | Reply

  7. Just a little additional convergence. Once I got to page 223 and saw the breakdown of subsidized time, I resolved to go through and put numbers next to all of the chapter headings. I wrote the years down in numberical order and started flipping through the book, writing a number, 1-9, next to the headings. Of course, most of the book takes place in YDAU, the 8th year of subsidized time, so I ended up writing a few dozen 8s in the margins of my book, because of which my book now has even more references to the infinity symbol. Sure, simple numerology, the 8th year of standardized time, but it made me chuckle through this post, in between getting my mind thoroughly blown.

    Comment by Zach — July 15, 2009 @ 11:28 pm | Reply

  8. Just a follow to follow up on the S. Gasket thing: in the interview DFW admits that a large sections of his original manuscript got left on the cutting room floor so that the book’s structure as published is a little lopsided.

    Zach, if I’m recalling correctly, YDAU corresponds to our calendar year 2008 so maybe that too is an example of the recurring lemniscate and not a coincidence.

    Comment by Rice — July 16, 2009 @ 12:36 am | Reply

  9. The title of the Beatles song is actually “I Want to Tell You.”

    Comment by Brodysattva — July 16, 2009 @ 12:54 am | Reply

  10. Not sure whether it’s relevant but an S.G. has an infinite perimeter but zero area in 2D and an infinite surface area but zero volume in 3D.

    Comment by Rice — July 16, 2009 @ 1:17 am | Reply

  11. This is a nitpick, but I’m thinking that properly respecting the use/mention distinction would keep Borges’ riddle from being self-violating.

    Comment by Neil the Ethical Werewolf — July 16, 2009 @ 1:18 am | Reply

  12. Re: 11

    As written, the Borges sentence is

    [. . .] the answer is chess .


    [. . .] the answer is ‘chess.’

    so ‘chess’ is being used in the sentence (i.e., the answer is the game of chess itself, not the word ‘chess’). Since ‘chess’ is being used, I think it is right to think it is self-violating.

    Comment by Criminally Bulgur — July 16, 2009 @ 2:16 am | Reply

  13. That’s right, Bulgur, Borges doesn’t put the quotes around chess in the way that a philosopher should when mentioning a term. But there’s a question of whether he’s still really mentioning the term and using philosophically inappropriate punctuation, or whether he’s really using it and the punctuation is correct.

    I think the fruitful question to ask here is: What is the answer to a riddle? Is always it a series of words, or the thing the words describe? As I see it, answers are linguistic entities, so I’d think it was a series of words. Answers probably shouldn’t differ in ontological status from questions, which really should be linguistic entities. (After all, questions don’t describe anything, so it’d be hard to point to the nonlinguistic thing the question was.) But maybe there’s some further argument to be given.

    Comment by Neil the Ethical Werewolf — July 17, 2009 @ 2:05 am | Reply

  14. Er, put the quotes around “chess” — but in some kind way I think my mistake helps my point.

    Comment by Neil the Ethical Werewolf — July 17, 2009 @ 2:07 am | Reply

  15. “In a riddle whose answer is chess, what is the one word you must under no circumstances use?”

    Is “chess,” as used in that sentence, the sign or the signified?

    Is there any plausible riddle whose answer is chess itself rather than the word? If I ask you a question, can you properly answer it by sitting down and playing a board game?

    Rarely have such momentous questions been pondered unstoned.

    Comment by southpaw — July 17, 2009 @ 6:09 am | Reply

  16. I agree with both of you that the natural thing to do would have been to mention ‘chess,’ and that plenty of people fail to mark off their mentioning of words orthographically. This is, however, Borges, so it leaves the possibility open that he is doing something intentionally weird.

    Comment by Criminally Bulgur — July 17, 2009 @ 12:08 pm | Reply

  17. “Rarely have such momentous questions been pondered unstoned.”

    Dude, this is what I do for a living. Now if you’ll excuse me, I have to get back to editing the part of my paper on whether it’s wrong to commit child abuse against adults, torture a bicyclist who’s not a bicyclist, or murder the dead.

    Comment by Neil the Ethical Werewolf — July 17, 2009 @ 9:36 pm | Reply

  18. […] passivity. I’m talking about an active surrender here. The actively-surrendered reader will sift through reams of mathematical arcana in order to tease out the implications of an oblique reference, or follow an obscure narrative […]

    Pingback by Infinite Summer » Blog Archive » infinitedetox: Waving the White Flag: Reading as Rehabilitation — July 22, 2009 @ 7:20 pm | Reply

  19. […] with passivity. I’m talking about an active surrender here. The actively-surrendered reader will sift through reams of mathematical arcana in order to tease out the implications of an oblique reference, or follow an obscure narrative […]

    Pingback by That Was the Week That Formerly Was : Journeyman — August 3, 2009 @ 9:21 pm | Reply

  20. I think there is a bigger reference to the lemniscate and cardioid. I discussed about that in two posts in the Infinite Summer forum. Maybe you are interested. http://infinitesummer.org/forums/viewtopic.php?f=12&t=410&start=10

    Comment by robbi60 — August 25, 2009 @ 7:05 am | Reply

  21. Does anyone know if Bobby Fischer and David Foster Wallace met.

    Comment by Linda Fraley — January 22, 2010 @ 5:54 am | Reply

  22. Good analysis, keep it up.

    Comment by GardenTubLover — September 10, 2010 @ 2:28 pm | Reply

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