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Fun with Triangles

August 8, 2009

I’m just gonna throw this right out there. No idea, really, what the significance is.

  1. On p. 502 a young James Incandenza describes how he knocked over a lamp in his bedroom, which in turn sheared off his bedroom door’s knob, which “began then to roll around in a remarkable way, the sheared end of the hex bolt stationary and the round knob, rolling on its circumference, circling it in a spherical orbit, describing two perfectly spherical motions on two distinct axes.” In other words, “a circle was rolling around what was itself the circumference of a circle” (cf. the fitviavi mold used to synthesize DMZ, which itself only grows on other molds).It’s kind of hard to imagine this (and what’s with that totally useless diagram in the book? All I can say is WTF), so take a look at the photo below, which, if I’m reading correctly, shows a physical model of what Wallace is talking about. The wire arcs denote the path of a single point on the handle of Wallace’s doorknob as it rolls around the stationary end of the hex bolt. This totally cool image, btw, came from Cornell University.cycloid
    The important thing to note here is that if you were to look straight down on the image from above, the wire arcs would look like a triangle. In other words, you’d be looking at a triangle within a circle.
  2. Triangle within a circle, eh? Where have we seen that before? Check p. 445, where Gately is describing biker Bob Death of water-joke fame: “the guy’s got a jailhouse tatt of AA’s weird little insignia of a triangle within a circle.” Hmmm.Blue Logo
  3. Finally, recall that Wallace said the book was loosely structured like a Sierpinski gasket, which is a fractal built out of an infinite number of triangles.180px-Sierpinski_Triangle.svg
  • UPDATE — Thanks, Matthew Morse! P. 476-477: “The giant distant CITGO sign’s like a triangular star to steer by… everyone says [it’s] hollow and you can get up inside there and stick your head out in a pulsing neon sea but nobody’s ever personally been up there.”Photo by Flickr user katherine of chicago, used under a Creative Commons license.

In all three four instances, you’ve got a big ol’ triangle smack in the center of these visual constructions. Like I said, I’m at a loss as to the significance, if any, of the connection. I’m particularly baffled re: what the rolling doorknob has to do with the development of JOI’s interest in “the possibilities of annulation,” other than the obvious fact of a circle rolling around on the circumference of another circle. There is a certain michevious irony in the fact that JOI, who eventually drinks himself to suicide, is launched on his career path by a geometric shape that’s an analog of the AA logo.

7 Comments leave one →
  1. Matthew Morse permalink
    August 9, 2009 12:30 am

    Another giant triangle, this time in a giant square: the Citgo sign Gately passes as he is driving to Inman Square.

  2. August 9, 2009 8:33 am

    I found myself thinking also of the method by which a cardioid is made (which I think somebody over at A Supposedly Fun Blog described). I’m having trouble visualizing this exactly right, but this looks like it would generate sort of a disjointed 3D cardioid. Neat observation re the triangle in the circle.

  3. August 9, 2009 11:02 pm

    Re: Significance? Not that I know this from any even remote kind of experience, but within many psycho-babblish sort of family therapy crowds, you will hear talk of dysfunctional family relationships which rely heavily on Triangulation. For lack of a better link:

    This pretty much describes what’s going on here in this amazing mattress scene, what it always seemed to be about from my perspective. And then after this scene we have another weird Avril/Tavis/Hal scene, with all sorts of tense mother-son complication. It gets all Gertrude/Hamlet on us–another family rife with Triangulation issues.

  4. August 9, 2009 11:02 pm

    P.S. Your stuff is really great and informative.

  5. Mike Niemeyer permalink
    April 5, 2011 1:12 pm

    “(and what’s with that totally useless diagram in the book? All I can say is WTF.)”

    I was very confused by this as well. Do you know of any Infinite Jest blogs or academic books studying Infinite Jest that shed light on the diagram and what exactly it means? I was never very clever when it came to math, but I appreciate David Foster-Wallace’s work enough to want to understand this aspect more. Any help would be fine.

  6. Sebastian permalink
    January 4, 2013 3:50 pm

    The diagram has two figures in it. One of them is to show the three dimensions with designated x, y and z. The outer circular motion only moves in the x and y dimensions, therefore, a two dimensional motion. The inner circular motion would have to move in all three dimensions, (i.e. z and x when the stick of the door knob aligns horizontally – z and y when the sick aligns vertically, or the other way round depending on perspective) Only the important dimension, namely z (the only one that the outer motion does not move in), is noted in the figure.
    This figure reminds tremendously of the most important part of ‘E .A. Abbot’s inescapable-at-E.T.A. book Flatland’ (page 281-282). In the part of the book that I am speaking of, a square who lives and perceives only two dimensions is visited by a being, the sphere(!) who can move in the z dimension as well. The sphere, however, can only be perceived by the square in two of its dimensions. (e.g. when the sphere is at the same level as the square, he looks like a big circle in 2D. When the Sphere rises a little bit he looks like a smaller circle in 2D as it is most wide in the middle)
    As I understand it, the purpose of Flatland is to show the reader that even though we can only perceive a reality confined to our standard 3D, there may be more. The book was most certainly made ‘inescapable-at-E.T.A’ by the former Headmaster JOI. Coincidence?
    Next step: Can this book or its views also be paralleled to ‘annulation’? I’ll try and ask my friend who studies chemistry what ‘annulation’ is as i have no idea.

  7. reachandpull permalink
    November 26, 2014 10:41 am

    “JOI, who eventually drinks himself to suicide”

    Well, actually, no. If you recall, he sobered up in order to finish the titular Infinite Jest. And, while still completely sober, he killed himself most horrifically with the specific aim of turning into a wraith. There is no other explanation. It was no mere alcoholic’s suicide. I guess he must have learned about the transcendant communicative power of wraithhood from his BFF Lyle, who is a wraith throughout the entire novel, except for the one subtle scene near the end where his grisly death in the locked sauna is recounted. As a wraith, JOI would get to roam the circumscribed 2D world of non-wraiths like a 3D sphere from another dimension (great comment, Sebastian) alternatingly inhabiting and inspiring all the dots whose worldviews are tragically limited. It’s the standpoint of a God, the standpoint of a ghost, and also happens to be the standpoint of an omniscient 3rd person narrator. We living dots would only get to relate to that standpoint when the cyclical motion is frozen still at the right moment, when we are bedridden, or sitting in an AA meeting listening to others, or motionlessly immersed in a novel, etc. Now, considering the gasket, there would be spherical/annular roaming within each of the triangles, perhaps only requiring a single wraith given the instantaneity of movement.

    There are 981 pages in every edition, so perhaps there are three 327-page triangles, and within each of those three 109-page triangles, or a Sierpinskian composite overlay of 327-page portions, etc. Triangles of what? Relationships between major characters and/or factions? Hal, Gately, Steeply the structural big three? Each having his own big three of relationships? I don’t know. I’ve only read it once, in 2008. And back then I didn’t skeletonize the book for scaffolding secrets. I absorbed the characters and the plots and gists, and by doing so I think I paid attention to the right things. I’ll be reading it again, though, soon, and I’ll be sure to pay attention to the structural gamesmanship more this time. Could be meaningful. Or at least fun.

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