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Film / π

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"When I was a little kid, my mother told me not to stare into the sun.
So once, when I was six, I did.
The doctors didn't know if my eyes would ever heal.
I was terrified. Alone in that darkness.
Slowly, daylight crept in through the bandages, and I could see.
But something else had changed inside me.
That day, I had my first headache."
— Opening monologue of Maximillian Cohen

9:13. Personal note: describe π here.

π (pronounced "pi") is a 1998 film that marked the directorial debut of Darren Aronofsky, who also wrote the film and co-created its story. Best described as a surrealist Psychological Thriller, the film was made for $135,000 and won a number of awards including the 1998 Sundance Film Festival's award for Best Director. In his first film score work, the movie's electronic soundtrack was assembled by Clint Mansell, a future long-time collaborator with Aronofsky, who contributed the frenetic drum-and-bass theme.

The film revolves around Maximillian "Max" Cohen, a reclusive, paranoid, migraine-afflicted math genius who, with his home-built supercomputer Euclid, has come to a series of unshakable truths:

1. Mathematics is the language of nature.
2. Everything around us can be represented and understood through numbers.
3. If you graph these numbers, patterns emerge.
Therefore: There are patterns everywhere in nature.

Through his investigating, Max stumbles upon a 216-digit number that seems to hold some universal secret. As he continues his research, his headaches worsen, he begins experiencing vivid hallucinations, and he becomes the target of Wall Street firm agents interested in profiting from his work as well as a sect of Hasidic Jews who want him to help find patterns in the Torah. Though he pushes on, determined to puzzle out the number's meaning, his mind might not be ready to comprehend it.

Shot in minimalist, high-contrast black and white, the film is very atmospheric with relatively little dialogue, and also quite confusing, to an overall effect that is often compared to Eraserhead.note 

This film provides examples of:

  • Affably Evil: The kabbalistic Jews, who explain to Max the reason for their obsession, being genuinely sorry when one of their own punches Max in the face, and letting Max go when he refuses to give them the number (although Max explains it by saying that the group must have already tried all possible 216-digit combinations and haven't gotten the answer they seek, which they acknowledge).
  • Animal Motifs: Max finds ants as well as goo infesting his apartment after he loads it into his computer Euclid. A possible interpretation is that the number, which is the blueprint for all creation, causes Euclid to begin creating simple organic matter. The goo and ants also fit into the themes of madness and decay that increasingly plague Max.
  • Applied Phlebotinum: The "Ming Mecca" computer chip that Dawson uses to bait Max, and provides Euclid the processing power to fully realize the number. Max is disbelieving that the firm can even provide it (because they're classified technology), but Dawson simply says that the firm has plenty of connections.
  • Arc Number: Rather than just being a motif, it's the driver of the plot — a 216-digit number that can do anything from predict the stock market to revealing the true name of God.
  • Big "NO!": Max yells out one when he comes back from his apparent Near-Death Experience.
  • Bittersweet Ending: We can only guess whether or not Max's self-trepanation was done for real, but the closing scene definitely shows him having become a happier man.
  • Blank White Void: In one of his visions, Max finds himself in exactly that setting. It's implied that he's standing on the border of life and death as he calmly starts to recite the universal number, which has previously been noted to possibly be God's true name. He wakes up from this state, only to realize that he was probably hallucinating.
  • Blasphemous Boast: The slogan of stock brokerage firm Lancet-Percy is "only God is perfect", boasting about the firm's eighty percent reliability with its predictions. They spend the film trying to obtain a number that they believe will allow them to manipulate the stock market at will and turn their prediction rates an even hundred.
  • Blinded by the Sun: As narrated by Max, he stared into the sun for too long when he was six and injured his eyes in the process. The incident had some lasting effect on his mental world, giving him the ability to perform complex calculations on the spot but also leaving him with paranoia and schizoid personality disorder.
  • Body Horror: Subtly. A small, Hebrew-letter shaped lump appears in Max's head. This, his headaches getting worse, and Sol's two strokes all imply that the number can literally mess with your head.
  • Bookends: Max says the same line towards the beginning and end of the film.
    "When I was a little kid, my mother told me not to stare into the sun. So once when I was six, I did."
  • Brown Note: The film is about a number sequence that helps define the universe. However, the process of determining this number is fatally destructive to a computer, be it machine or human.
  • I Call It "Vera": "Euclid", Max's home-made supercomputer — most probably after the Greek mathematician.
  • Child Hater: Downplayed, then subverted. Max is annoyed when the young neighbor girl tries to constantly test him on his math skills. He warms up to her by the end, it seems.
  • Creator Cameo: Composer Clint Mansell plays the photographer whom Max thinks is stalking him.
  • Creator Thumbprint: The first of various Aronofsky films with an underlying theme of "obsession leading to destruction." It also says a lot about Aronofsky's films that this one, in which the protagonist willfully (although ambiguously) drills a chunk of his brain off, is the one with the most unambiguously happy ending so far.
  • Combat Pragmatist: Max prefers to run from Marcy Dawson's thugs, but at one point, they chase him into a grocery store where he grabs a can of soup and uses it to brutal effect.
  • Cool Old Guy: Sol, Max's former teacher, mentor, and friend. He gives Max sage advice on getting on with life, not becoming obsessed with his work, and coaches him in Go. It's all but stated outright that Sol discovered the number long before Max did.
  • Cyberpunk: Max's apartment is taken up by a supercomputer, so every scene at home has a ton of wires and machinery everywhere. The evil stock firm further tips the story into cyberpunk territory.
  • Cyberpunk Is Techno: By Clint Mansell (such as the film's theme/Leitmotif for Max) with contributions from other groups like Massive Attack. Their song "Angel" from Mezzanine is used on the soundtrack.
  • Deliberately Monochrome: Filmed in ultra-high-contrast black and white to show Max's distorted world.
  • Driven to Suicide: Not "kill" suicide, but the effects of the number on Max's life and body drive him to destroy the part of him that matters to him the most — a symbolic suicide. Before that, there is a lot of "computer melting down" and "self-destruct" symbology, such as Euclid's literal self-destruction because of the number, and Max putting his injector gun up to his head (to deliver an injection directly to the lump) while screaming obscenities (to his neighbours having sex next door, which he can hear and is driving him nuts, on top of his migraine's pain).
  • Earn Your Happy Ending: The ending leaves you with more questions than answers, but at least Max is happy, one way or another.
  • "Eureka!" Moment: Played with. Max consults with Sol about the numerical sequence he's trying to solve. Sol tells him the trope-naming story about Archimedes, which leads to this exchange:
    Sol: So what's the lesson?
    Max: That an answer will come.
    Sol: No, it's the wife! You have to relax!
  • Facecam: One of the more famous uses of the SnorriCam, an Aronofsky trademark. The DVD contains some footage of a test run with Max in a convenience store.
  • Fade to White: Most notable in the climax.
  • Foreshadowing: If asked why he stopped searching for patterns within the digits of pi, Sol (in most instances) reacts dismissively. After mentioning Euclid's "crash", Max begins to suspect that this nonchalance has been deliberately misleading:
    Max: Just a long string of digits—
    Sol: How many?
    Max: [shrugs] I don't know...
    Sol: [intensely] What is it? A hundred and fifty, a thousand? Uh, two hundred and sixteen?! How many?
  • Faux Affably Evil: Marcy Dawson (the Lancet-Percy representative) first tries to swindle Max to help her stock prediction firm with cookie-cutter sweet-talking and false smiling, which she completely ditches in her last scene, where she's putting a gun to Max's head to force him to comply.
  • Formulaic Magic: Max's dogmatic treatment of math as "the language of nature" seems to push past "math is capable of explaining everything in existence" into "math determines our existence." The effects of the number point to the latter, as it seems to have a catastrophic effect on anything it contacts: the stock market, Sol's health, and eventually Max's (already tenuous) sanity.
  • Freeze-Frame Bonus: The number does appear in-screen in one scene.
  • Gainax Ending: Max is shown to trepan himself at the end of the movie, voiding himself of his mathematical genius. Whether this is literal or symbolic is left up to the viewer.
  • God: The Jewish group believes that the universal number is the true name of God, and that they will come closer to the Messianic Age by invoking it. Max is ambivalent about this notion, but feels that only he is worthy because it was given to him.
  • Go Mad from the Revelation: The entire point of the movie is that this happens when you try to find the ratio that rationalizes pi, predicts the stock market, and is also the true name of God.
  • Hacker Cave: Euclid is an extravagantly cheap, lovingly customized mainframe that threatens to overrun every square centimeter of Max's tiny fortress of an apartment. His landlady doesn't much like it.
  • Hates Being Touched: Max winces every time someone touches him or even looks like they are about to touch him.
  • Haunted Technology: Max uses his supercomputer Euclid to decode the 216-digit number somehow related to God and the structure of the universe, which seems to make it leak some sort of goo (presumably the idea is that it is creating primordial life). Basically, his computer is possessed by God.
  • Hell Is That Noise: The high-pitched beep that sounds every time Max has a migraine attack.
  • Hikikomori: Max is a shut-in.
  • Inner Monologue: Done by Max; train-of-thought stuff such as telling at what time he's doing an action, his Madness Mantra, and remembering factoids that reinforce it.
  • Important Haircut: Max shaves his head as things start going downhill. Of course, there's a reason why he does it.
  • Instant A.I.: Just Add Water!: What happens after Max connects the mysterious Ming-Mecca chip to Euclid. That is, if one can believe Sol — outwardly rationalistic, yet painfully aware of forbidden mysticism — when the former professor explains how the 216-digit number makes machines "aware of their silicon nature".
  • Intelligence Equals Isolation: Max's quest for the universal number has left him utterly disconnected from the rest of humanity, to the extent that he even fears leaving his apartment if he could run into someone.
  • Kubrick Stare: Max gives one right at the end of the film just before he trepans himself.
  • Lobotomy: In the end, Max lobotomizes himself with a power drill.
  • Logic Bomb: The universal number for both computers and people.
  • Lucky Charms Title: The title is usually just depicted as the symbol for pi.
  • Mad Mathematician: Max lives like a hermit, plagued by migraines and social anxiety as he dives into the mathematical heart of the universe. The closer he gets to the ultimate answer, the more insane he becomes. The only way he can achieve peace is to physically burrow out his mathematical ability by trepanning himself with a power drill.
  • Madness Mantra: Max "restates his assumptions" several times throughout the film, which includes his various theories as well as the story of how he started getting migraines after looking into the sun too long.
  • Madness Montage: The "hip-hop montages" of surreal imagery illustrating Max's degenerating mental state.
  • Maybe Magic, Maybe Mundane: Either the number really is connected to God and Max's insanity is due to some supernatural force, or the number is just a really complex equation that Max obsesses over to the point of insanity (and he's just lucky/unlucky enough to meet other people with a similar obsession). The climax counts as well, since it could be literal or symbolic.
  • Messy Hair: Max, as befitting a reclusive math genius. His neighbor tries to adjust it, but he squirms away.
  • Mind Screw: The A.V. Club called it "like Eraserhead re-envisioned by cyberpunk author William Gibson." Mix a paranoid mathematical genius, Hebrew numerology, conspiracies, neurological headaches, the secret name of God, and the aforementioned paranoid mathematical genius taking a drill to his head to escape all this crap. To top it off, it's filmed in extremely high-contrast black and white and scored to techno music.
  • Minimalistic Cover Art: Some posters (and covers of a few DVD versions) show only the ratio's mathematical symbol.
  • Mouthful of Pi: Not strictly pi, but Max can do rather complicated arithmetic in his head, and in the climax, he recites the numbers while having a breakdown. Ironically, the actual number pi appears nowhere in the movie except the opening credits, which do show pi itself counted out to thousands of numbers, but only the first 8 digits after the decimal point are correct.
  • Near-Death Experience: In the climax, Max experiences his greatest migraine attack so far. As he goes mad from the pain, he suddenly finds himself in a white void and recites the numerical designation of God's name which he was never supposed to discover. His neighbor begs him to come back and comforts him in her arms when he is resuscitated. Then it turns out that he was hallucinating all of it and is truly alone.
  • Non-Indicative Name: Neither the actual number π, nor what it represents (the ratio of the circumference of a circle to its diameter), is important to the plot of this film at all.
  • Number Obsession: Max is looking for a mathematical formula that will allow him to see the underlying pattern of the universe. He's shown by a man named Lenny Meyer how the original Hebrew alphabet, which has alphanumeric value, can represent certain concepts mathematically, a concept known as Gematria, and suggests that the Torah is a code sent by God. It also coincides with a 216-digit number Max uncovered trying to write a program to unlock his theory, which Sol urges him to abandon, lest he become a mere numerologist. In the end, Max seems to find the secret he was looking for, which causes him to Go Mad from the Revelation, and he performs trepanation for a form of Laser-Guided Amnesia.
  • Number of the Beast: The number that drives the plot is 216 digits long.
  • Prescience by Analysis: Max is trying to find the universal constant that will allow him to predict every pattern in nature. Specifically, the stock brokerage firm Lancet-Percy is funding his research to help them predict the stock market with perfect accuracy.
  • The Professor: Sol, Max's mentor and one of the few people Max actually talks to.
  • Rage Against the Reflection: Max smashes his bathroom mirror in pain during a severe migraine attack. The climax involves him drilling a hole through his head while looking into the mirror.
  • Religion is Magic: Zig-zagged. The Kabbalistic Jews know about the universal number, and it is related to the Torah, but they are unable to discover it themselves. In the end, they are no closer to it than a stockbroking firm.
  • Right Through the Wall: Max can hear his neighbor having sex with her boyfriend right through the wall of his apartment. Not played for laughs, however; at the same time, Max is obsessively working on his computer to pursue the universal number, emphasizing how detached he is from everyday life.
  • Rule of Symbolism: Ants (as in "buggy" computers and decay), the slime (Euclid's decay, same as Max), numbers (especially the Golden Ratio — duh), brains (hallucinations leading to insanity and self-trepanation), God (like the stock prediction firm's slogan of "Only God is Perfect" to reflect their 80% accuracy, the group of Jews looking for God's true name by working numerology on the Torah, some of Max's breakdowns looking like religious experiences).
  • Scary Black Man: Gender-inverted with Marcy Dawson, the stockbroker who hounds Max for the universal number.
  • Sci-Fi Writers Have No Sense of Scale: Examining all possible numbers with 216 decimal digits, one per second, would take a time that's unconceivably larger than the estimated age of the Universe.
  • Sharpshooter Fallacy: Sol warns Max against obsessing over the 216-digit number (and overworking in general) because if he does so he will stop being a mathematician and turn into a "numerologist", starting to look for any way to shove a meaning to the number, even thinking that regular events he performs add up to 216 (amount of steps he takes to get somewhere, amount of seconds in an elevator, etc.). Dawson and the Jews appear to showcase this devolving, thinking that Max's number is the key to manipulate the stock market (not "predict", manipulate) and that it's God's name, respectively.
  • Sinister Subway: Max, in the throes of a horrible migraine, experiences a nightmarish hallucination in the empty New York subway, in which he chases a bleeding man (who may be himself) and follows the trail of blood to a bloody brain lying at the foot of a staircase, which he probes with a pen, producing audio and visual hallucinations in his own brain.
  • Smart People Play Chess: Max and Sol play Go, which factors into several mathematical and visual motifs.
  • Sniff Sniff Nom: Max examines some primordial goo that has built up in Euclid's electronics by looking at it, smelling it and then tasting it.
  • Technology Porn: Averted for most of the film with Max's supercomputer "Euclid"; it's quite obviously home-made, and looks it. Played straight when Marcy Dawson offers him a "Ming Mecca" chip as payment and Max is utterly incredulous that she could get her hands on anything so powerful.
  • These Are Things Man Was Not Meant to Know: The 216-digit number overwhelms anyone or anything that tries to compute it, repeatedly crashing Euclid and threatening to drive Max insane. It's also implied that Sol's second stroke came about because he started researching the number again. Just a partial number brings along an epic stock market crash. It's repeatedly linked with the sun, which fried Max's optic nerves when he gazed at it and killed Icarus when he flew too close to it. Ultimately, Max abandons his quest and chooses to simply live life in ignorance, possibly drilling out his mathematical genius to escape the number's curse.
  • This Is a Drill: Max trepans himself with a carpenter's drill. Or does he?
  • Through the Eyes of Madness: There is one scene which is clearly a hallucination: Max finding a human brain in a subway bathroom. As for the rest... who knows?
  • Video Full of Film Clips: A music video for the soundtrack's "πr^2" is included on the DVD, with shots from the film interspersed with random color footage of ants (a major recurring motif).
  • Villainous Rescue: The Jews save Max from Dawson and her goons' strong-arming attempt, because they have need of Max's knowledge of the number.
  • The Vitruvian Pose: The drawing itself is featured when Max overlays it with a sketch of the Golden Ratio.
  • Weapons-Grade Vocabulary: The number, among other things, is a true name of God, so knowing it has bad effects on body and sanity. Heck, a computer calculating it created slime and ants as side-effect. Pretty large effect for a mere 216 digit number.
  • Writers Cannot Do Math: Ironically, for a film that's about a mathematician and even titled after a mathematical constant, you would think this trope would be averted. Alas, even this film isn't safe from that trope.
    • Several mathematical facts get mixed up (for example, the golden ratio is usually phi, not theta).
    • Max guesses that the Jews have already "intoned" every possible name of God, which the rabbi does not deny. This would be completely impossible if each name were a 216 digit number. However, earlier Lenny shows that words in Hebrew have numeric values based on the sum of the values of their letters, so the Jews might actually be looking for a word that adds up to 216. Barring some unmentioned grammatical limitations, it would probably still be impossible to intone every single possible permutation.