To judge from comments in the #infsum twitter stream, the long Eschaton chapter seems to divide readers' opinions. Speaking as someone who loves this long passage, I think much of it throws light on the novel as whole in the way it wonderfully dramatizes the breakdown of a painstakingly constructed logical system. Eschaton offers a sort of analogue for IJ itself. Greg Carlise's study of IJ, for instance (which I haven't looked at yet), takes its title, Elegant Complexity, from the description of Eschaton offered here (322).
But it isn't simply, or even primarily, the complexity of Eschaton which makes it an interesting analogue for the novel. The breakdown of Eschaton calls into question the relationship between a fiction and the world it represents, between what Pemulis calls the "map" (the representation) and the "territory" (the reality) it stands for. Like Infinite Jest, Eschaton "takes place" in a "noncontemporary," but not too distant, historical moment (the recent, Cold War past in the case of Eschaton; the immediate future in the case of IJ). Yet this sense of historical distance is itself as permeable as the game's governing fiction proves to be; as footnote 126 reminds us, it is "well-nigh impossible to keep the present from infecting even a playful and childlike Historical Consciousness" (1025).
How does the text relate to the world? The representation to reality? The "map" to the "territory"? What the Eschaton episode demonstrates is the difficulty of maintaining any hard and fast distinction between the world and the way we imagine it. For Pemulis, of course, such "delimiting boundaries . . . are Eschaton's very life-blood" (335). But the things we use to represent the world are also part of the world; and it is sometimes hard to keep them apart. Such is the case of Ingersoll's "launching" a "5-megaton thermonuclear weapon" at Ann Kittenplan (336). For Pemulis this is a ridiculous misconstrual of the game, of the "one ground-rule boundary that keep Eschaton from degenerating into chaos" (338)--of a rule so basic to the game that it is unwritten, a sort of preaxiom. But the joke here is on Pemulis and his fanatical, but ultimately doomed attempt, to keep the map and the territory separate. (Really Otis Lord is the hero here, no?)
All of which is great fun, but the Eschaton chapter also provides one of the most fascinating opportunities to ask a basic question about IJ: who is the narrator of this novel? The novel opens in the first person, with Hal himself narrating (Remember back there?). The Wardine and Yrstruly sections of the novel (remember back there?) are also written in a (dialect-inflected) first person.
But most of the novel is offered in the third-person, making liberal use of what English professors (and would-be English professors) might call "free indirect discourse." Consider a passage from a little later in the novel. We might be taken aback first reading this description of Gately: "He'd switched to menthols at four months clean because he couldn't stand them and the only people he knew that smoked them were Niggers..." (478). The reason, I think, that most readers will concede that this is not sheer racism on Wallace's part, is that it is not Wallace who uses the N-word here, but Gately (how we feel about Gately, mind you is complicated; but really, he isn't a bad guy, this comment aside). The third person narrator here adopts the vocabulary/style of a character, performing a sort of ventriloquism. Such free indirect discourse (of which Joyce's Portrait of the Artist as a Young Man is perhaps the most canonical English language example) is one Wallace's key tools.
So, who is the speaker of the Eschaton chapter? The narrative is offered in the jaunty conversational voice of someone who is clearly familiar with ETA. Hal is not the speaker (as he is the opening pages of the novel), but the narrative is closely allied with his consciousness: "But if Hal had a luger pointed at him and were under compulsion to try, he'd probably start by explaining..." (322). And the chapter offers editorial interpolations that come not from some disembodied omniscient third person, but from a participant in the life of ETA, even if an anonymous, unnamed participant. When the narrator notes, "You should have seen Michael Pemulis just about eat the whole world alive during pre-Eschaton summits..." (325), he speaks as someone who has been there, seeing Pemulis just about eat the whole world alive. But the narrator is also flexible enough to move around a bit, and has knowledge that none of the Eschaton players seem to have (re: "the mint-green advertorial Ford sedan" ). This is the strength of free indirect discourse.
And then, in footnote 123, we get something else entirely. We get the characters self-consciously narrating; or, more precisely, we get one character narrating and another transcribing his words. This is not the first time in the novel that the narrator seems self-consciously aware of his own narration. But the wonderful humor of this footnote is a product of the competing voices of Pemulis and Hal.
"Pemulis here, dictating to Inc" the footnote begins. This scene of dictation, in which Pemulis attempts to explain the Mean Value Theorem to the reader (wikipedia offers a clearer summary than Pemulis, for those interested), seems to be occurring as the two sit in the Gatorade Pavilion watching the game with Struck, Axford, and Troelstch, smoking "what looks like a hand-rolled psychochemical cigarette" and drinking "suspiciously bracing Gatorade" (329, note the faux-naive, ironic tone the third-person narrator here adopts). Pemulis even asks Hal, in the course of the footnote, "Why don't you just pass that certain item back over here, Inculator" (1023 n.123). Pemulis's reluctance to name the joint directly is presumably because using he is being recorded by Hal. (And for the reader who reads this endnote in the order in which it occurs in the text, on p.323, what Pemulis means by "that certain item" may be unclear; it is only later, p. 329, that the narrator elaborates).
So part of the humor of endnote 123 comes from Pemulis, better than half in the bag, struggling, to explain some nugget of Calculus, as Hal jots down his explanation. But Hal he doesn't let Pemulis's words pass without editorial comment. Hal both improves, and mocks, Pemulis's explanation. Using the Mean Value Theorem, Pemulis explains, "lets you multi-regress the results so Combatants get rewarded for past thermonuclear largesse [occasional verbal flourishes Hal's --HJI]" (1023 n.123). Hal marks Pemulis's solecisms and blunders as he goes with sic's. And, perhaps most humorously, Hal even notes his own uncertainty about what Pemulis really means with a [sic?]. Here is Pemulis's conclusion, complete with Hal's editorializing:
It's going to be interesting to see if [sic] Hal, who think's he's just too sly trying to outline Eschaton in the 3rd-person tense [sic] like some jowly old Eschatologist with leather patches on his elbows [sic], if Inc can transpose [sic?] the math here without help from his Mumster. (1024 - 25)
Sic itself is Latin, meaning literally "thus," and is usually used to indicate to a reader that something that looks like an error in a quotation was indeed... "thus" in the original. The first [sic] above is because Pemulis is using "if" when, I think, he should be using "whether." The second is because the 3rd-person is not a "tense." The final, after transpose, is there because Hal is unsure whether Pemulis is using transpose in a technical, mathematical sense (Hal's grammar is a lot better than his math)--I don't think he is. I don't know what that third [sic] is doing though.
P.S. Allston Rules.