Pemulis and Hal: The Nonnegotiable Currency

A friendship denominated in favors

The closest thing Hal Incandenza has to a best friend is a drug dealer, and the novel prices the friendship in its very first full portrait of him: "Mario and his brother Hal both consider Pemulis a good friend, though friendship at E.T.A. is nonnegotiable currency" (p. 155, scene 048). That one sentence carries the whole friendship. Michael Pemulis — seventeen, Allston scholarship boy, E.T.A.'s pharmacologist, bookmaker, and quarterly urine vendor ("Clean urine is ten adjusted dollars a cc." p. 151; "Urine trouble? Urine luck!" p. 152, scene 048) — runs everything he touches as a business, complete with an anti-entrapment protocol ("Please commit a crime" / "Gracious me and mine, a crime you say?" p. 156). And yet the friendship itself is the one ledger the book shows balancing without cash. Hal is Pemulis's verbal tutor — "Hal Incandenza's most valiant efforts barely get Pemulis through" Avril's required Grammars (p. 154) — and Pemulis is Hal's math tutor for the Boards; Hal, who could easily pay, "gets his sterile urine gratis": "Pemulis depends on him for verbal-academic support, and dislikes owing favors, even to friends" (p. 155, scene 048). Each boy runs the half of the curriculum the other can't. The locker room knows them as a unit — "Peemster and Hal." "Halation and Pemurama." (p. 105, scene 034) — and the intimacy has a fact under it no other E.T.A. relationship can claim: "Hal has actually gotten actively high only with Pemulis" (p. 50, scene 013), which is exactly why Avril dreads her son "absorbing God alone knows what sort of esoteric designer compounds with reptilian Michael Pemulis" (p. 50). Hal buys his secret marijuana at retail from his best friend — "the Hope I bought retail from you not three days ago" (p. 1018, scene n110) — and the mercantile edge never once, on the page, cancels the devotion. That is the dyad's standing paradox, and the November plot is built to test it.

The friendship also spans the novel's widest class gap, and the book makes Hal carry the discomfort. Pemulis's whole self-presentation is the Allston chip worn as costume — "Mrs. Pemulis raised no dewy-eyed fools" (p. 156, scene 048), the yachting cap, the ALLSTON HS WOLF SPIDERS shirts — and at the Eschaton fence, watching Pemulis rage, Hal "wonders, not for the first time, whether he might deep down be a secret snob about collar-color issues and Pemulis, then whether the fact that he's capable of wondering whether he's a snob attenuates the possibility that he's really a snob" (p. 335, scene 073) — a perfect Hal-shaped thought, marijuana-recursive, about the one friend the family's world would never have supplied him. Even Pemulis's body reads to Hal as a figure for the difference: "everything about him seems to Hal to taper and come to a point, like a bad El Greco" (p. 334). The diction flows the other way too. Pemulis's Big Buddy sessions turn ten-year-olds into "kids that speak the lingo like veteran Jersey-shore croupiers" (p. 117, scene 036), and Hal's droll answering-machine games are borrowed straight from the master's recursive outgoing message ("This is Mike Pemulis's answering machine's answering machine" p. 854): on his last narrated morning Hal notes of his own machine-message joke that "This observation owed a debt to Pemulis" (p. 854, scene 165). By then the debts are all Hal has left of him.

Eschaton: the impresario and his amanuensis

The partnership's public monument is Eschaton. Pemulis is "far and away the greatest Eschaton player in E.T.A. history" (p. 322, scene 073), the game's mathematical architect — and its scripture is a joint work: "The vademecumish rulebook that Pemulis in Y.P.W. got Hal Incandenza to write" (p. 322). The collaboration survives in the novel's apparatus as its funniest artifact, the Mean-Value endnote: "Pemulis here, dictating to Inc" (p. 1023, scene n123), with Hal inscribing from memory and sniping in brackets — Pemulis's "occasional verbal flourishes Hal's—HJI" (p. 1023) — Pemulis naming his diagrams PEEMSTER and HALSADICK, setting the constant with "let d be the size of Hal's Unit" (p. 1024) and taking "Hal Incandenza's Addendum: In meters." (p. 1024) in stride, before the pure math-joy of the verdict: "This is wicked. This is fucking elegant." (p. 1024), signed "P.S. Allston Rules." (p. 1024). Two registers of genius ribbing each other inside one proof: the dyad at its height fits on a single endnote page.

On Interdependence Day the monument comes down, and the essay on the debacle as the novel's master image of representation-gone-wrong is maps-territory; what belongs here is the two friends' blocking. Pemulis presides as "sort of eminence grise" (p. 333, scene 073), and when real snow starts falling on the game's map he delivers the dyad's most famous line over the fence — "It's snowing on the goddamn map, not the territory, you dick!" (p. 333) — and the axiom behind it: "Players aren't inside the goddamn game. Players are part of the apparatus of the game." (p. 337). Hal, meanwhile, stands apart in the paralysis that will define his endgame, unable to tell whether he is wincing when Pemulis winces; as Otis Lord goes headfirst through the monitor, Pemulis is "telling Hal he hates to say he told them so" (p. 341). One friend screaming the rules, the other unable to locate his own face: the debacle is the dyad's late configuration rehearsed in miniature, and it is also the proximate cause of everything that follows — the summons, the urologist, the leverage, the expulsion.

There is a suspect shadow over the partnership's mathematics itself. The Mean-Value apparatus Pemulis dictates is genuinely wrong — a math-checker's catalogue of the novel's errors ("only four mistakes, two of which might well be typographical") finds two of them in the Eschaton endnote, and another in the derivative rule Pemulis teaches Hal for the Boards (Mike Strong's check) — and a community reading takes the errors as characterization: the tutor's math is deliberately bad, marking Pemulis as the counselor who "isn't as smart as he thinks" ([hn-threads-2026-07-10]), or even as a dependency-farmer keeping his verbal-support supplier hooked on tutorials. The archive holds that reading as a minority position, open and unsettled — the errors are real, the intent is not established, and the possibility of plain typography is preserved in the checker's own hedge; the full record lives in language-grammar. It acquired a specialist's outside leg in 2004, when the mathematician Michael Harris, reviewing Wallace's infinity book for the AMS Notices, found it "laced through and through with blunders of every magnitude" and extended the doubt to the novel's whole footnoted omniscience — Wallace's "familiarity with optics, Quebecois dialect, and psychotropic drugs is not as extensive as the numerous footnotes to IJ suggest" — while singling out, as the novel's math-voice, the "(admittedly ambiguous)" Pemulis (harris-ams-review). Ambiguous is right: the same record that impeaches the tutor's equations documents Wallace's own real fluency (bfn-math-melodrama), which is exactly what keeps the seeded-error reading alive without settling it.

Supplier, fixer, coach

Pemulis's chemistry runs both directions through Hal, and the novel is scrupulous about the double role. He is the supplier — the retail Bob Hope, the quarterly urine machinery, the "small-time drugs of distinguished potency" — and he is also, when Hal quits, the nearest thing the book gives Hal to a detox coach. The cleanout protocol is Pemulis's: "Mike says no more than thirty days to get it all out for sure. Cranberry juice, Calli tea, vinegar in water." (pp. 783–84, scene 157). The Kodiak plugs Hal chews through the late chapters are the substitute ritual of a boy following a switch-not-quit doctrine — on the drive to his Natick meeting "the Kodiak's almost like a cover or excuse" (p. 798, scene 160) — and the doctrine itself gets a full sermon in the calculus tutorial of 12 November (scene n321). Hal floats quitting everything — "Forever" — and Pemulis answers with the novel's hardest counter-catechism this side of Boston AA: "If you're addicted you need it, Hallie, and if you need it what do you imagine happens if you just hoist the white flag and try to go on without it, without anything?" (p. 1065); "You lose your mind, Inc. You die inside." (p. 1065); the Allston guys who quit cold and became machines — "You looked into their maps and something was gone. The walking dead." (p. 1066). His alternative is lateral: "The trick is the right switch for a man's wiring." (p. 1065). It is diagnosis and sales pitch fused so tightly they cannot be told apart — the switch he is recommending is the DMZ he has already bought — and the same endnote carries the friendship's plainest declaration: "Hal, you are my friend, and I've been friends to you in ways you don't even have a clue. So brace yourself for a growth-spurt." (p. 1064), and, at the end, "Incpuddle, all I know's I'm your friend. I am." (p. 1066). When Hal finally reaches for the clinical word, Pemulis closes the session with the gentlest thing the book's one materialist ever says: "That's just a word." (p. 1066). Ten days into abstinence Hal is asked, by the person who sold him the substance, "How you feeling in there already, brother?" (p. 1066) — the dealer and the sponsor sharing one voice, which is the dyad's deepest and least resolvable fact. (Where this sits in the novel's larger map of dependence and recovery is addiction-and-recovery.)

The urinalysis crisis shows the fixer at full stretch, and the novel runs three accounts of it side by side, none reconciled. In Hal's admiring version, delivered to Mario in the dark: "Pemulis—the alleged weak-stomached clutch-artist" (p. 772, scene 155) — the boy who before real matches is "a whole different person" (p. 264, scene 065), vomiting into a ball-bucket, whom "Schacht suspects Pemulis is physically 'drine-dependent, Preludin or Tenuate or something" (p. 267) — "Pemulis showed some serious brass under pressure, standing there over that urinal. He played the O.N.A.N.T.A. man like a fine instrument." "I found myself feeling almost proud for him." (p. 772); "He projected a kind of weary pragmatism the urologist found impossible to discount" (p. 774). In the narration's version, the reprieve was bought with leverage: "he and Inc'd escaped on-spot urinalysis only because Pemulis implied to Mrs. Incandenza that he'd tell the Incster about Avril having some sort of major-sport interlude with John Wayne" (p. 1068, scene n324). And in Pemulis's own version, muttered at the end: "Blarney wasn't why we got it, Inc, is the thing." (p. 908, scene 172). The archive carries all three as written — a genuine open dispute (the leverage's Avril-side story is wayne-afr-avril). What no account disputes is whom the thirty days were for. Pemulis "could pass a urine test hanging upside down in a high wind" (p. 783, scene 157); the fat-soluble problem is Hal's. "Booboo, the thirty days was actually for me, and Mike let me stand there with my Unit out and not say anything while he sold the urologist land and magazine subscriptions and Ginsu knives. He did it for me, and I'm not even the one they want." (p. 783, scene 157). Whatever card Pemulis played over that urinal, he played it — and spent it — for Hal.

The DMZ shadow, exactly as far as the ledger goes

The dyad's dark question is the DMZ, and this essay presents the question's shape rather than re-arguing it: the archive's full weighing is the hal-dmz adjudication, and the essay that walks the rival theories of Hal's collapse is hal-collapse. The facts of custody are a Pemulis story end to end. On 4 November he "finally landed 650 mg. of the vaunted and elusive compound DMZ or 'Madame Psychosis' from a small-arms-draped duo of reputed former Canadian insurgents" (p. 215, scene 057) and stashed it "wrapped tight in Saran and stashed deep in the toe of an old sneaker that sits atop the aluminum strut between two panels in subdorm B's drop ceiling, Pemulis's time-tested entrepôt" (p. 216). The plan is a three-man "experiment" the boys frame as their "right—duty, almost, to the spirits of inquiry and good trade practice" (p. 216), window fixed for 20–21 November. Two details deserve emphasis because the dosing debate tends to flatten them. First, Hal is no reluctant party: eyeing the tablets he asks "Two or even three tablets, maybe?", "knowing he sounds greedy but unable to help himself" (p. 213), and arranges the stash into a map of E.T.A. with a precision the narration calls "almost Zen" (p. 215). Second, Pemulis's DMZ diligence is aimed at protecting the window, not spiking it: Hal's one condition is med-library verification, and "Pemulis's only concern is is this DMZ he got for the WhataBurger detectable. He goes to the library and pores." (p. 785, scene 157), coming back with "Have I mentioned DMZ doesn't show up on a G.C./M.S.?" (p. 1064, scene n321). The cautionary tale is also his: the Leavenworth convict who on a massive dose "literally lost his mind, like the massive dose picked his mind up and carried it off somewhere and put it down someplace and forgot where" (p. 214, scene 057) — the story that returns as Hal's nightmare, Hal as the soldier everyone hears singing Ethel Merman: "It's me! It's me, screaming for help!" (p. 1064, scene n321), with its "quality of loneliness to it, though. Unlike anything" (p. 1064). Pemulis shrugs the dream off as "A standard nobody-understands-me dream" (p. 1064). Read a year forward, it is the most exact description of the Year of Glad the novel ever produces, planted in the friend's tutorial.

Then the custody story breaks. On 20 November Pemulis goes to the entrepôt and finds "at least eight panels of the drop-ceiling have somehow fallen out of their aluminum struts" — "No old sneaker is in evidence on the floor as he clears the panels to plant the stool" (p. 916, scene 174) — and the scene cuts off before he confirms anything. Who took the DMZ, where it went, and whether any of it ever reached Hal is resolved nowhere; the adjudication holds the crux undecidable by design, on positive exhibits of engineering that are mostly Pemulis-shaped — the cut-off search, the DMZ apparatus consigned almost wholly to endnotes, and Pemulis repeatedly starting to tell Hal something urgent and being interrupted every time. As for the readings that make this dyad a betrayal story: Pemulis dosed him is graded strained — a pure inference chain, kept alive as a possibility in the reconstruction literature (fiction-advocate-what-happened-pt1 carries the toothbrush-"out of anger" variant) but argued by no committed advocate, and the adjudication counts the friendship itself as evidence: the raid dispossesses him, and his documented loyalty to Hal runs the other way. The no-drug withdrawal reading is the crux's favored answer; the famous wraith-toothbrush is strained; Hal's self-dose stays open (and the motive triangle it needs — the appetite, the screen-beating pharmacology — is visible in the scenes above). A sideways community reading, Pemulis test-dosed marginal players to calibrate the stuff (with Troeltsch's pointedly recurring illnesses as the offered evidence: ijbc-ep03, seconded in ijbc-ep25, both paraphrased from audio), is held open as a minority claim about custody inside the academy, not about the route into Hal. The one documented pilferer of Pemulis's stashes, for what it is worth, is Troeltsch — the Tenuates that fell John Wayne were Pemulis's own, found after the broadcast as "his pilfered Tenuates in the little pecker's Sel-dane bottle" (p. 1073, scene n332) — a suspect the text supplies and no camp nominates. The honest dyad-reading of the whole DMZ shadow is therefore not did Pemulis poison his friend — the record runs against it — but something sadder: the chemistry that made the friendship's intimacy possible is also what makes Pemulis, in every reconstruction, the question's first suspect.

Seventeen November: the quietest disappearance in the book

Pemulis's destruction is the novel's most severe demonstration of its endnote architecture: a major character's expulsion happens entirely in the apparatus. The main text of 17 November carries only the public cover story — John Wayne "had had a violent allergic reaction to a decongestant" (p. 899, scene 170) — while the two endnotes hung off that day (scenes n324 and n332) hold the whole catastrophe. And the catastrophe is engineered as the cruelest irony available: "the Wayne-dosing had been a total accident and in no way Pemulis's deal, if anybody's Troeltsch's" (p. 1074, scene n332). The one time the school's standing culprit is actually innocent, he cannot say so — that afternoon, calculating that "a win or even three-setter w/ Freer would mean a place on the WhataBurger plane" (p. 1068, scene n324), he was "willing to violate a kind of personal honor-code and take pre-match Tenuate" (p. 1068), so clearing himself "would be tantamount to Clippertonizing himself" (p. 1074). Avril — whose exposure he had cashed a week before — counter-checkmates through deLint's mouth without appearing: the doorknobs "rubberized and grounded" (p. 1076), the files recryptographilated, and her blessing shaped like a curse, "may the road rise up to meet you whitherever your future travels lie." (p. 1075). "Pemulis got very cool and brass-mask-faced." (p. 1075) — the same brass Hal had eulogized at the urinal — and his interior register is one image: "The little deck-of-cards riffle of the wings of the Shit Fairy, which he privately envisions as a kind of violet incubus with the Da's saggy frown." (p. 1076). Expulsion means Allston, and Allston means the Da. His exit line is the WhataBurger to the last: "And this affects the WhataBurger, my chances?" (p. 1076). A community reading of the hearing — ijbc-ep34 (paraphrased from audio), with supports — takes the whole disposal as Avril's calculated counterstrike: expel the witness and his credibility dies with his enrollment, since nobody believes a busted dealer. The archive holds that as a minority reading, open; what the page itself gives is her conspicuous absence from the room and the prepared, coded answers.

What makes the endnote unbearable rather than merely ironic is what Pemulis is doing when the axe falls. He has come down early for the Freer match and found his thirteen-year-old Big Buddy Todd Possalthwaite weeping on a bench — "Nothing's true" — and the last free act of his E.T.A. career is a Big-Buddy intervention: the trust-math sermon. "Todder, you can trust math." "Whose truth is deductive truth. Independent of sense or emotionality." (p. 1071, scene n324) — math as "The nightlight on life's dark wall, late at night." (p. 1071). (That line reached print criticism: Harris quotes it as the novel's sincere math-credo, in the mouth of its ambiguous math-authority — harris-ams-review.) And then, called away to the catastrophe that will end him, he leaves the boy with the sentence that is his own biography compressed: "Never trust the father you can see" (p. 1071, scene n324). The counselor whose own visible father wore "a white Hanes T-shirt gone permanent yellow under the arms" is handing a weeping child the only father that never failed him — first-order predicate logic — minutes before the institution that replaced Allston throws him back to it. The book gives Pemulis no exit scene beyond this. He is never formally seen leaving; there is no farewell with Hal; his last attested position is a rumor relayed secondhand on the exhibition morning: "Michael Pemulis was nowhere to be seen since early this A.M., at which time Anton Doucette said he'd seen Pemulis quote 'lurking' out by the West House dumpsters looking quote 'anxiously depressed.'" (p. 965, scene 183). A principal character, architect of half the plot's machinery, exits the novel as an anxious shape by the dumpsters in someone else's sentence.

The asymmetry, and the erasure

Here is the finding this essay exists to state: the friendship's final movement is mutual, asymmetrical abandonment, and Hal's half comes first. On the night of 11 November — six days before the expulsion — Hal tells Mario, flatly: "It's Pemulis they want. I'm almost positive they're going to give Pemulis the Shoe by the end of the term. I don't know whether Pemulis knows this or not." (p. 783, scene 157) — and he itemizes the file on his friend coolly: the too-public dosing of an opponent at Port Washington, the traceable Visine-bottle urine sales. Hal knows. Hal says nothing to him. The boy who "let me stand there with my Unit out" and took the fall's whole risk onto his own urine is never warned by the friend who foresaw his sentence — and the novel never marks the omission, which is what makes it so cold to notice. The reciprocal service continues right up to the cliff: "Pemulis had poured a terrific volume of practical pre-Boards math into my head for two weeks, taking his own time and not asking for anything in return, being almost suspiciously generous about it" (p. 852, scene 165) — "suspiciously" is Hal's word, the friendship's mercantile grammar persisting even in gratitude, and readers who suspect the generosity was DMZ-adjacent lobbying have the scenes above to argue over. Then the debacle, and the mutual flinch: "Pemulis had been avoiding me ever since I returned from Natick on Tuesday—as if he sensed something." (p. 898, scene 170).

The last conversation (scene 172, 20 November) is the dyad's terminal X-ray. Pemulis appears in the Viewing Room doorway unshaven, twitchy-eyed, his color bad, to a Hal supine on the floor: "We've got some really important interfacing to do, brother." (p. 907). He opens the matter of "the tu-savez-quoi" (p. 908) and is deflected; corrects Hal's blarney version of the reprieve — "Blarney wasn't why we got it, Inc, is the thing." (p. 908) — and is deflected; pleads the thing's urgency — "When have I ever urgently asked you to dialogue before, Inc?" (p. 909) — and is deflected again, the warning cut off mid-sentence by Freer in the doorway. Whatever Pemulis needed his friend to know about the DMZ on the very weekend fixed for it dies undelivered, three starts, three interruptions — the adjudication counts the scene among the book's engineered silences. Hal's interior track, meanwhile, registers two things about his friend. One is a likeness nobody else would think to draw: "It is not Pemulis's way to apologize or explain or worry that you might think ill of him. In this he reminded me of Mario." (p. 906) — for one sentence the operator and the saint stand in the same light, both free of the self-monitoring that is eating Hal alive (the honest channel itself is hal-mario). The other is the friendship's death certificate, in Hal's own anhedonic murmur: "I was bored. I couldn't remember a time when Pemulis had bored me." (p. 908). And the scene's last service is almost too painful to gloss: Hal sends the friend with the urgent warning off to fetch a cartridge instead, and Pemulis — muttering "And me using the poor guy's lab" (p. 909) at the shelf of Himself's films — loads Good-Looking Men in Small Clever Rooms and cues it to the weeping film-teacher. The dealer's last act in the friendship is projectionist for the dead father's art.

After that, subtraction. Pemulis tries the door once more on the blizzard morning — "Mike Pemulis came by and asked if you were up and about" (p. 941, scene 179), relayed by Mario, unanswered — while Hal, on the floor, dates his own unmooring to the friendship's end: "I was trying to align myself along some sort of grain in the world I could barely feel, since Pemulis and I stopped." (p. 950, scene 179). Since Pemulis and I stopped: the quit and the friend share one clause, as they shared one economy all along. Even Hal's snow that morning is denominated in his friend: "Yachting-cap white." (p. 851, scene 165). Then the dumpster sighting, and nothing. In the Year of Glad chapter — Hal's chronologically last pages, where John Wayne, Gately, the Moms, Himself, and even the WhataBurger all surface in his stream — Pemulis is never named: not one sentence of scenes 001–003 carries him. That is a checkable absence, and unlike some of the book's designed holes it asks for no theory, only notice. Orin gets "little but hints"; Pemulis gets less — no fate, no forwarding address, no place in the survivor's memory. The novel spends six hundred pages building its funniest, sharpest, most competent character, the one boy who ran every system the academy had, and then demonstrates what E.T.A.'s currency was worth by letting him vanish between an endnote and a dumpster without his best friend ever once, on any page, fighting for him — or mentioning him again. Todder, you can trust math. The friendship was the one thing he couldn't compute, and the book's quietest cruelty is that it never gives him — or us — the final term.

Sources

This essay is anchored in the novel's own pages (scenes cited inline); the secondary record it draws on:

• The hal-dmz adjudication — the governing ledger for the DMZ question: withdrawal favored, Pemulis-as-doser strained, the undecidable-by-design flag and its Pemulis-shaped exhibits.
• harris-ams-review — a research mathematician's 2004 verdict on Wallace's displayed math, the extension of the doubt to IJ's footnoted expertise, and the "nightlight" credo quoted with Pemulis named its "(admittedly ambiguous)" carrier.
• hf-strong-dubious-math-in-ij — the worked catalogue of the novel's four math errors, two in the Eschaton endnote and one in the derivative Pemulis teaches Hal.
• bfn-math-melodrama — Wallace's demonstrated higher-math fluency, the counterweight that keeps the seeded-error reading live.
• [hn-threads-2026-07-10] — the intent-side community argument (the Polonius-keyed "isn't as smart as he thinks" reading), with its own hedge preserved.
• ijbc-ep34 — the endnote-332 close-reading: Pemulis innocent for once, Troeltsch's deal-cutting, and the Avril-counterstrike reading of the expulsion (paraphrased from audio).
• ijbc-ep03, ijbc-ep25 — the Pemulis-test-dosing reading (DMZ calibrated on marginal players; Troeltsch's illnesses as candidate evidence; paraphrased from audio).
• fiction-advocate-what-happened-pt1 — the reconstruction survey that keeps "Pemulis dosed the toothbrush out of anger" alive as a listed possibility.

The essay above quotes only the print-paginated record; the fuller theory-weighing it deliberately defers lives in hal-collapse and the hal-dmz adjudication.