Infinite Jest can be read as a loose allegory of Shakespeare's Hamlet, sometimes veering into parody. Hamlet, like Infinite Jest, is a high-stakes family tragedy. The play revolves around Prince Hamlet of Denmark, who begins seeing his father's ghost. Hamlet's uncle Claudius, who has married Hamlet's newly-widowed mother, Gertrude, callously insists that Hamlet needs to get over his father's death. Hamlet becomes convinced that Claudius murdered his father. He spends the play trying to prove Claudius guilty and get revenge. Along the way, many people are hurt or killed. Among the dead is Hamlet's beloved Ophelia, who dies by suicide after Hamlet kills her own father.
Some of the characters in Infinite Jest are easy to map onto the characters in Hamlet. For instance, after James Incandenza dies, his brother-in-law Charles Tavis slips easily into his place as the headmaster of E.T.A. Charles Tavis also seems to have a longstanding sexual relationship with his own adoptive sister, Avril, that has been going on for years (he is almost certainly Mario's biological father). In this tangle of relationships and power dynamics, James is clearly Hamlet's dead father. He even appears to some characters in the novel as a "wraith," or ghost. Meanwhile, it is easy to see Gertrude in Avril and Claudius in Charles Tavis. Plenty of other characters and relationships seem to be inspired by Hamlet in more complicated ways. For example, Hal, Orin, Mario, and Gately all have moments when they act like Prince Hamlet himself. Joelle resembles Ophelia, but so do other characters who die by suicide and leave their loved ones behind, blaming themselves.
The Incandenzas are powerful within the world of elite youth tennis and even (largely by accident) in the political world. Still, they are a bit pathetic to be serious royals in the way Hamlet represents the royal family of Denmark. Whereas Hamlet famously frets over "something rotten in the state of Denmark," Hal spends most of the novel fretting over the rotten tooth in his mouth. While many people at Ennet House are struggling to stay alive in the face of major systemic injustice, the Incandenzas treat their obsessions—grammar, youth tennis, bad experimental film—as though the stakes are just as high. In a sense, the stakes really are that high. James tries increasingly absurd kinds of performance art to connect with his son. When it all fails, he microwaves his own head. Absurdity notwithstanding, Wallace makes clear that Hal's relationship with his father and his death holds all the love, trauma, and confusion of a more "serious" father-son relationship.
The title of the novel is a clue to what Wallace is doing with allegory and parody. In Shakespeare's play, Hamlet remembers a long-dead court jester, Yorick, as a "fellow of infinite jest." This scene is famous for the way it depicts death as the thing that finally saves everyone, poor and rich alike, from the injustices of life. Now that he is dead, Yorick's social rank doesn't matter; he can be remembered simply as the man who always made people laugh. James Incandenza is a parody of Yorick in that his legacy is a dark practical joke—he literally entertains people to death. Wallace uses this and other parodies of Hamlet to suggest that humans are all the same in life as well as in death. No matter how "well-off" any of the characters are, and no matter how trivial their concerns seem, they are all doomed to spend their lives finding ways to numb themselves or otherwise deal with the pain of being alive.
Chapter 10 tells the story of how Don Gately ends up at Ennet House after he is linked to the death of Guillaume DuPlessis, an operative from Québec. This backstory foreshadows a major revenge plot that never fully comes to fruition, ultimately parodying revenge tragedies like Shakespeare's Hamlet:
Don Gately... had, of course, a special place in the heart of a remorseless Revere A.D.A. with judicial clout throughout Boston’s three counties and beyond, an of course particularly remorseless A.D.A., as of late, whose wife now needed Valium even just to floss, and was patiently awaiting his chance, the A.D.A. was, coldly biding his time, being a patient Get-Even and Cold-Dish man just like Don Gately, who was, through no will to energy-consuming violence on his part, in the sort of a hell of a deep-shit mess that can turn a man’s life right around.
Revenge comedies like Hamlet are usually very serious, depicting their protagonists' descent into madness and unethical behavior in the service of righting a great wrong. While the characters may appear foolish for losing sight of anything but their vendetta, the vendetta itself usually comes from a truly devastating betrayal—the murder of a loved one, perhaps, or manipulation that causes the protagonist to betray their own values.
In this case, Gately and the A.D.A. become enemies through a series of pranks and blunders that are far too silly to kick off a real revenge tragedy. Gately stages a break-in at the A.D.A.'s house just to mess with him. This demonstration that their home can be breached sets off over-the-top anxiety in the A.D.A.'s wife, who might not be suited to live in a house with a man who regularly deals with crime. Gately and his partner in crime later kill DuPlessis by accident; they don't realize he is home when they are breaking into the house, and they try to deal with the situation by tying him up and gagging him. Unfortunately, he has such a bad head cold that he cannot breathe through his nose. The only reason Gately is caught is because this A.D.A. is already obsessively angry with the burglar for exacerbating his wife's anxiety, and he recognizes Gately's method of breaking and entering. Sending Gately to get sober is this A.D.A.'s great revenge, at least in this round of their feud. This passage suggests that the score is yet to be fully settled between the two men. Gately might still get back at the A.D.A.
Comically, the feud with the A.D.A. turns out to be for Gately "the sort of hell of a deep-shit mess that can turn a man's life right around." Going to AA is, surprisingly, the best thing Gately has ever done for himself. He remains scared throughout his time there that he might trip up and land back before the A.D.A. The A.D.A. does show up again at the end of the novel, but he is on his own sobriety journey and is simply trying to forgive Gately. The feud ultimately fizzles out instead of building to catharsis.
In Chapter 18, Hal and a group of other students discuss the competitive, grueling nature of their tennis training at E.T.A. When Hal emphasizes all of their "aloneness," Ingersoll responds with a parody of an idiom:
‘We’re all on each other’s food chain. All of us. It’s an individual sport. Welcome to the meaning of individual. We’re each deeply alone here. It’s what we all have in common, this aloneness.’
‘E Unibus Pluram,’ Ingersoll muses.
Ingersoll is playing on the United States motto, "E Pluribus Unum." A rough translation of this Latin phrase, "united we stand," has slipped into American idiom. However, the phrase really translates to "out of many, one." Ingersoll reverses it, essentially saying, "out of one, many." He means that all the E.T.A. students make up a unified team at matches, but behind this united front is a collection of individuals all competing with each other for the highest rank and the best chance of a professional tennis career.
This parody of the United States motto also functions as a snide remark about the U.S. and O.N.A.N. Mario's Interdependence Day film suggests that the official seal of the United States has been updated. Where it once depicted an eagle holding a banner with "E Pluribus Unum" printed on it, it now depicts an eagle with a maple leaf in its mouth. The "one nation out of many" that once existed has devolved into one nation that is eating another. What's more, all the characters in the book seem to have their own personal interests that they prioritize over any collective interests. Patriotism and teamwork, Ingersoll suggests, are things of the past.
In Chapter 42, an allusion to a 17th-century Christian allegory helps emphasize that the game of Eschaton is a parody of Christian doctrine about the end of the world:
Eschaton takes eight to twelve people to play, w/ 400 tennis balls so dead and bald they can’t even be used for service drills anymore...The vademecumish rulebook that Pemulis in Y.P.W. got Hal Incandenza to write...is about as long and interesting as J. Bunyan’s stupefying Pilgrim’s Progress from This World to That Which Is to Come, and a pretty tough nut to compress into anything lively (although every year a dozen more E.T.A. kids memorize the thing at such a fanatical depth that they sometimes report reciting mumbled passages under light dental or cosmetic anesthesia, years later).
The game of Eschaton is named after a religious concept. Several religions, including but not limited to Christianity, predict an apocalypse that will culminate in an "eschaton." People believe that during the eschaton, God's existence will become undeniable (for instance, through Christ's return in person to earth). Many believe that at this point, God will select certain worthy people to save from Armageddon. Eschatology treats life on earth as an allegory for the apocalypse: when people die, if they have been faithful, their spirit ascends to heaven just as they would during the "end times." Pilgrim's Progress was a wildly popular book based on eschatology. Depicting the struggle of a man named Christian to travel from "The City of Destruction" to "The Celestial City," it portrays the spiritual journey to heaven as an actual journey on earth. Christian literally struggles with concrete representations of concepts like "vanity" and "despond," eventually overcoming them and finding his way to the "Celestial City" (i.e. heaven). The book makes the point that every event in a person's life is a stop on the road to heaven or hell.
In Infinite Jest, the game of Eschaton parodies this entire concept. Whereas Christian's whole life is a path toward an end, the young tennis players play Eschaton over and over, in an endless loop. By the end of the chapter, the reader has the sense that the game is convoluted and essentially pointless other than as an exercise in following pedantic rules that players learn to recite like a religious catechism. The narrator compares the rule book Hal has written to Pilgrim's Progress mostly because it is long and boring to read, but also because it technically lays out the path to victory. The comparison suggests that eschatology, too, is an infinite exercise in rule-following that people keep playing without end even after they ought to have won already.
This parody is connected to a broader parody in the novel, playing on the similarity between the words "eschatology" and "scatology." While "eschatology" is preoccupied with the way the spirit can transcend the physical world, "scatology" is the study of feces. The novel is full of scatological humor (toilet humor) and vivid depictions of bodily functions, even as it considers deep questions about the human spirit and the point of life. Wallace parodies the concept of eschatology not just to skewer it, but furthermore to suggest that bodily functions, sunburns, heartbreak, trauma, and anxiety are all part of the meaning of life. Rather than transcend or "win" anything by following the rules, the characters' main challenge in the novel is to live in the visceral here and now, as disturbing, upsetting, or even boring as it may be.
In Chapter 56, Pemulis overhears part of a therapy session between Stice and Dr. Rusk. Rusk's extended explanation of her diagnosis, "counterphobia," is a parody of Freudian psychoanalysis that is steeped in dramatic irony:
‘GI Joe typically being cathected as an image of the potent but antagonistic father, the “military” man, with “GI” representing at once the “General Issue” of a “weapon” the Oedipal child both covets and fears and a well-known medical acronym for the gastro-intestinal tract, with all the attendant anal anxieties that require repression in the Oedipal phase’s desire to control the bowels in order to impress or quote “win” the mother, of whom the Barbie might be seen as the most obviously reductive and phallocentric reduction of the mother to an archetype of sexual function and availability, ..."
Stice has come into Dr. Rusk's office because he has been seeing inanimate objects move around him, seemingly of their own accord. Rusk explains that the intense pressure of elite athletics must be making Stice anxious to control the objects around him. Ignoring Stice's protestations that he does not care about action figures, Rusk goes on at length about how children become obsessed with G.I. Joe and Barbie because they see the toys as symbols of their parents. She makes far-fetched connections between the acronym "G.I." and boy children's desire to impress their mothers by controlling their bowel movements. She then explains that boys might become obsessed with Barbies because of a repressed sexual attraction to their mothers.
Most of what Rusk says here falls in line with Freudian psychoanalysis (which has been heavily reworked or outright abandoned by modern psychologists). What makes her speech a parody is her almost free-association between G.I. Joe and gastrointestinal issues, along with her over-the-top insistence that the Oedipus complex must explain Stice's issues. She believes so deeply in sex, incest, and bathroom habits as driving forces of psychology that she doesn't notice that Stice isn't following her at all—nor is she following him. He can't keep up with her jargon, mistakenly assuming at first that "counterphobia" is fear of linoleum. Meanwhile, Rusk mistakenly assumes that Stice is complaining about a paranoid obsession with the objects in his room. On the contrary, he is disturbed that he is actually seeing the objects move. The implication in the book is that the wraith of Hal's father is haunting Stice, which is an entirely different issue from the one Rusk is trying to address. Stice doesn't even know what is real and what is in his head, and Rusk jumps to conclusions before Stice can fully describe his problem.
With this scene, Wallace shows that Freudian psychoanalysis (and sometimes talk therapy more generally) can be an inflexible script that gets in the way of real, helpful connection between a therapist and a patient: simply putting a person in a room with a therapist can make them feel even more alienated from the rest of the world. Many more modalities of talk therapy have become widely available since the time when Wallace wrote Infinite Jest. However, getting the right kind of help can still be a challenging process even for those with no barriers to access. Rusk's reaction to Stice's wraith problem is a comical and exaggerated way for Wallace to criticize the mental healthcare system for failing to listen to patients or consider when it may be the real world, and not the patient's mind, that is broken.