I was thinking a lot in the last days about mathematical structures in IJ and I found the post by barone.brian very interesting. However I agree with Chris Hager about the possible nature of the four projects. The main concern in IJ was about feelings and emotions and themes, and not on the formal structure. Look for instance at the celebrated (and really beautiful) interview with Michael Silverblatt (

Silverblatt's interview) where we read:

"I did not sit down with, you know, "I'm going to do a fractal structure," or something" and also

"I think writing is a big blend of -- there's a lot of sophistication and there's a lot of kind of idiocy about it. And so much of it is gut and "this feels true / this doesn't feel true; this tastes right / this doesn't," and it's only when you get about halfway through that I think you start to see any sort of structure emerging at all".

However, during my two readings (+partial re-readings) of IJ, I was looking all the time to references to mathematics. So, if we forget the four projects, it is still worth investigating for more mathematical structures in IJ. Maybe it is not the main point in reading a book like IJ, but that's all I can do.

Clearly I'd like to try to avoid to fall in the intentional fallacy. We can use DFW interviews and essays to try to understand his projects, but, most of the time, it is better, and maybe more respectful of Wallace's will, to try to use his text only. Our role should be to give our point of view, actually the true and active reader's role, on the actual text, not trying to mimic Wallace's intentions. Maybe we could find something which IS in the book (at least in our minds reading the book), but not in the Wallace's plans...

Looking at the mathematical structures considered by barone.brian, I don't think that linear structures are relevant in the context of the book. Linearity is just evoked at p. 82 about Extra-Linear dynamics, and I found the arguments about their inclusion a bit pointless. On the other hand, there is a clear occurrence of quadratic structures: it is easy to find parabolas, circles, ellipses, as some people did. Here, however, I would like only (since more should be say about unbounded functions, as Greg Carlisle did) to point out a conic section which is missing in the previous list (conic sections are obtained by cutting a cone by a plane, and all the previous curves belong to this family), namely the hyperbola. Strictly connected to the rhetoric figure of hyperbole (in which statements are exaggerated), it is implicitly contained in the term "hype" (etymology: shortening of hyperbole), one of the main concern for the young players. However, in its main meaning we find only one mention of this term, which occurs at p. 96:

*************************

"'Beat. Worn the heck out.’

'Worn the fuck-all out is more like.’

'Wrung dry. Whacked. Tuckered out. More dead than alive.’

'None even come close, the words.’

'Word-inflation,' Stice says, rubbing at his crewcut so his forehead wrinkles and clears. 'Bigger and better. Good greater greatest totally great. Hyperbolic and hyperbolicker. Like grade-inflation.’"and after some few lines

"Hal raises his eyebrows at Stice and smiles. 'Hyperbolicker?’

'My daddy as a boy, he'd have said "tuckered out'"ll do just fine.’

'Whereas here we are sitting here needing whole new words and terms.’

'Phrases and clauses and models and structures,' Troeltsch says, referring again to a prescriptive exam everyone but Hal wishes now to forget. 'We need an inflation-generative grammar.’"*********************************

Again Wallace is addressing the problem of communication and also his investigation in new directions for the novels, the difficulty to find a new way to express old feelings: "

we are sitting here needing whole new words and terms". And I add, to do that we need to make hyperboles, which is actually what Wallace did a lot of times. However, it seems to me that there is a more interesting and hidden connection between hyperbola (with an "a") and the structure of IJ.

First look at the hyperbola graph:

Plot of hyperbola on WikipediaWe have two branches which are completely separate and go towards the infinity. They are closed near the origin and there is a clear double central symmetry (in both directions). For these reasons, I'd argue that the hyperbola is a more appropriate form (with respect for instance to the parabola) to represent the structure of the book. As usual, to explain a metaphor is a bit like explaining a joke, but anyway I would like to try.

The branches are separate mostly as the lives of Hal and Gately. They are closed near the origin as ETA and Ennet House are, but still they do not touch. The double symmetry is both in the structure of the book (the symmetry between the first and the second half) and in the lives of Hal and Gately (if you look at the hyperbola in the other direction you see two sort of "parabolas", so you have the rise and fall of Hal and the fall and rise of Gately).

However, the main point about the two branches of the hyperbola is in the fact that they intersect at infinity, so outside of our horizon, as the intersection of Hal and Gately in the book. When I say "intersect at infinity" I mean a real thing, which is however a bit difficult to view.

Luckily, as usual in mathematics, we can find a way to see the unseen. Actually, by a change of variables (IYI, this is called inversion

Inversion from Wikipedia), we can move the infinity point in 0 (and the 0 at infinity) and our hyperbola is transformed in a ...Lemniscate! (a.k.a. the symbol of infinity)

Lemniscate on Wikipedia. [Notice that in Everything&more, DFW shown a very good knowledge of this curve and its different equations...]

To see better what I mean, take a basket ball and glue on the surface an infinity sign (quite large, that the border of the rings are on the other side of the ball). Then, if you look the center of the infinity sign, you will see a big X, but if you turn the ball on the other side, you will see two branches of an hyperbola.

So, if the hyperbola is what we see, the infinity sign contains what is unseen in the book, but implicitly evoked.

This infinity symbol is mostly implicit in the text (not only in the title!), and we find it only in two places. The first time here (masked):

p. 42

"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."and the second (explicitly) here:

n.307

"... this is one of only two total times Orin has perceived himself as the approachee, the other being the 'Swiss hand-model' on whose nude flank he's been furiously tracing infinity signs all during the Moment Subject's absence."I don't know (and in some sense, I don't care, as far as the text is supporting my arguments) if Wallace was really concerned with these complex mathematical structures, but in "Everything&More" he played a bit on a similar construction, namely he put in a one-to-one correspondence the points of the [0,1] interval with the points of the Real line, through a sort of stereographic projection (E&M, p. 123-124), which is similar to the inversion procedure.

Finally, I would like to connect this analysis to another thread in this forum, namely

The meaning of "X"Somebody (Roxanne) pointed out the strange occurrence of a lot of Xs, which I also examined in the wallace-| forum:

The complete X-theory. In later posts Roxanne and nickymendoo connected this X stuff to the Chiasma.

From Merriam-Webster online:

* Etymology: New Latin, X-shaped configuration, from Greek, crosspiece, from chiazein to mark with a chi, from chi (x)

1 : an anatomical intersection or decussation — compare optic chiasma

2 : a cross-shaped configuration of paired chromatids visible in the diplotene stage of meiotic prophase and considered the cytological equivalent of genetic crossing-overand so to the intersection figure.

It is also connected with Chiasmus: In rhetoric, chiasmus (from the Greek: χιάζω, chiázō, "to shape like the letter Χ") is the figure of speech in which two or more clauses are related to each other through a reversal of structures in order to make a larger point; that is, the clauses display inverted parallelism.

I found that this was a very interesting remark, since for longtime I was convinced that IJ was built as a Moebius strip (a flat version of the infinity sign), but still I was unable to find the intersection point.

Now, if we accept that the intersection of the two main characters happens at infinity, we have a perfect chiasmic structure. which is also indicated by the presence of Xs along all the book. I think this choice (to move a part of the plot out of the text) was not just a whimsy by Wallace. He wanted to create a strong tension and active role in the reader, with a strongly connected, but unresolved plot. So, maybe, the Wallace's

jest was to move to the

infinity the missing part of the plot.