Pi (film)
Encyclopedia
Pi, also titled ,WorldCat gives the title as [Pi] and provides a note which states, "Title is the mathematical symbol for Pi." ("[Pi ]", WorldCat). Amazon gives the title as Pi with no notation concerning the math symbol ("Pi", Amazon). is a 1998 American psychological thriller
Psychological thriller
Psychological thriller is a specific sub-genre of the broad ranged thriller with heavy focus on characters. However, it often incorporates elements from the mystery and drama genre, along with the typical traits of the thriller genre...

 film written and directed by Darren Aronofsky
Darren Aronofsky
Darren Aronofsky is an American film director, screenwriter and film producer. He attended Harvard University to study film theory and the American Film Institute to study both live-action and animation filmmaking...

. It is Aronofsky's directorial debut, and earned him the Directing Award at the 1998 Sundance Film Festival
Sundance Film Festival
The Sundance Film Festival is a film festival that takes place annually in Utah, in the United States. It is the largest independent cinema festival in the United States. Held in January in Park City, Salt Lake City, and Ogden, as well as at the Sundance Resort, the festival is a showcase for new...

, the Independent Spirit Award for Best First Screenplay
Independent Spirit Award for Best First Screenplay
The Independent Spirit Award for Best First Screenplay is one of the annual awards given by Film Independent, a non-profit organization dedicated to independent film and independent filmmakers.-1990s:1994*David O...

 and the Gotham Open Palm Award. The title refers to the mathematical constant pi
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...

.The film's title sequence shows the Greek letter , followed by hundreds of lines of numbers representing the numerical value of the constant. However, the numbers are not accurate past the first eight decimal places. Like most of Aronofsky's films, [Pi] centers on a protagonist whose obsessive pursuit of ideal leads to severely self-destructive behavior. However, the strong psychosexual elements of the director's later work are not present.

Plot

Maximillian "Max" Cohen (Sean Gullette
Sean Gullette
Sean Gullette is a writer, actor, and filmmaker.-Biography:He was born in Boston and attended public schools and Harvard, where he acted in theater and films and directed plays....

), the story's protagonist
Protagonist
A protagonist is the main character of a literary, theatrical, cinematic, or musical narrative, around whom the events of the narrative's plot revolve and with whom the audience is intended to most identify...

 and unreliable narrator
Unreliable narrator
An unreliable narrator is a narrator, whether in literature, film, or theatre, whose credibility has been seriously compromised. The term was coined in 1961 by Wayne C. Booth in The Rhetoric of Fiction. This narrative mode is one that can be developed by an author for a number of reasons, usually...

, is a number theorist
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

 who believes that everything in nature can be understood through numbers. He is capable of doing simple arithmetic calculations involving large numbers in his head. Max also suffers from cluster headache
Cluster headache
Cluster headache, nicknamed "suicide headache", is a neurological disease that involves, as its most prominent feature, an immense degree of pain in the head. Cluster headaches occur periodically: spontaneous remissions interrupt active periods of pain. The cause of the disease is currently unknown...

s, as well as extreme paranoia
Paranoia
Paranoia [] is a thought process believed to be heavily influenced by anxiety or fear, often to the point of irrationality and delusion. Paranoid thinking typically includes persecutory beliefs, or beliefs of conspiracy concerning a perceived threat towards oneself...

, hallucination
Hallucination
A hallucination, in the broadest sense of the word, is a perception in the absence of a stimulus. In a stricter sense, hallucinations are defined as perceptions in a conscious and awake state in the absence of external stimuli which have qualities of real perception, in that they are vivid,...

s, and social anxiety disorder
Social anxiety disorder
Social anxiety disorder , also known as social phobia, is an anxiety disorder characterized by intense fear in social situations causing considerable distress and impaired ability to function in at least some parts of daily life...

. Other than a woman living next door who sometimes speaks to him, Max's only social interaction is with Sol Robeson (Mark Margolis
Mark Margolis
Mark Margolis is an American actor who has been making films since 1976.Margolis went to Temple University briefly before moving to New York City, where he studied drama with Stella Adler and at the Actors Studio...

), his old mathematics mentor.

Max begins making stock predictions based on the calculations of his computer, Euclid. In the middle of printing out his picks, Euclid suddenly crashes after spitting out a seemingly random 216
216 (number)
216 is the natural number following 215 and preceding 217.Since 216 = 3^3 + 4^3 + 5^3 = 6^3, it is the smallest cube that's also the sum of three cubes . It is also the sum of a twin prime...

-digit number, as well as a single pick at one-tenth its current value. Disgusted, Max tosses out the printout of the number. The next morning, he checks the financial pages and sees that the pick Euclid made was accurate. He searches desperately for the printout but cannot find it. Sol becomes unnerved when Max mentions the string of numbers, asking if the string was 216 digits long. When Max questions him about the string, Sol indicates that he came across such a number many years ago. He urges Max to slow down and try taking a break.

At a coffee shop, Max meets Lenny Meyer (Ben Shenkman
Ben Shenkman
Benjamin Shenkman is an American television, film and stage actor.-Life and career:Shenkman was born in New York City and raised in what he described as "the secular Eastern European Jewish tradition". He graduated from Brown University, and obtained a Masters of Fine Arts in 1993 from New York...

), a Hasidic Jew
Hasidic Judaism
Hasidic Judaism or Hasidism, from the Hebrew —Ḥasidut in Sephardi, Chasidus in Ashkenazi, meaning "piety" , is a branch of Orthodox Judaism that promotes spirituality and joy through the popularisation and internalisation of Jewish mysticism as the fundamental aspects of the Jewish faith...

 who coincidentally does mathematical research on the Torah
Torah
Torah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five books of the bible—Genesis , Exodus , Leviticus , Numbers and Deuteronomy Torah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five...

. Lenny demonstrates some simple Gematria
Gematria
Gematria or gimatria is a system of assigning numerical value to a word or phrase, in the belief that words or phrases with identical numerical values bear some relation to each other, or bear some relation to the number itself as it may apply to a person's age, the calendar year, or the like...

, the correspondence of the Hebrew alphabet
Hebrew alphabet
The Hebrew alphabet , known variously by scholars as the Jewish script, square script, block script, or more historically, the Assyrian script, is used in the writing of the Hebrew language, as well as other Jewish languages, most notably Yiddish, Ladino, and Judeo-Arabic. There have been two...

 to numbers, and explains how some people believe that the Torah is a string of numbers that form a code sent by God
God
God is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....

. Max takes an interest when he realizes that some of the number concepts Lenny discusses are similar to other mathematical concepts, such as the Fibonacci sequence
Fibonacci number
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; ....

. Max is also met by agents of a Wall Street
Wall Street
Wall Street refers to the financial district of New York City, named after and centered on the eight-block-long street running from Broadway to South Street on the East River in Lower Manhattan. Over time, the term has become a metonym for the financial markets of the United States as a whole, or...

 firm that are interested in his work. One of the agents, Marcy Dawson, offers Max a powerful classified computer chip called "Ming Mecca" in exchange for the results of his work, which Max eventually accepts.

Using the chip, Max has Euclid analyze mathematical patterns in the Torah. Euclid spits out the 216-digit number before crashing again. When his computer refuses to print out the number, Max begins to write it down. Midway through the writing, Max realizes that he knows the pattern, undergoes a sudden epiphany
Epiphany (feeling)
An epiphany is the sudden realization or comprehension of the essence or meaning of something...

, and passes out. Thereafter, Max appears to become clairvoyant and is able to visualize the stock market patterns he had been searching for. But his headaches also increase in intensity, and he discovers a strange vein-like bulge protruding from his right temple. Max has a falling out with Sol after the latter urges him to quit his work.

Dawson and her agents grab Max on the street, and try to force him to explain the 216-digit number. They had found the original printout and had been trying to use it to manipulate the stock market in their favor, but as a result, caused it to crash. Although Max is held at gunpoint, Lenny drives by and rescues him. However, Lenny and his companions make similar demands on Max to give them the number. They finally reveal their intentions: they believe the number was meant for them to bring about the messianic age
Messianic Age
Messianic Age is a theological term referring to a future time of universal peace and brotherhood on the earth, without crime, war and poverty. Many religions believe that there will be such an age; some refer to it as the "Kingdom of God" or the "World to Come".- Terminology: "messianic" and...

, as the number represents the unspeakable name of God. Max refuses, insisting that whatever the source of the number is, it has been revealed to him alone.

Max flees and tries to visit Sol, only to find that he has died. Max searches his house and finds mathematical scribblings similar to his own. On a Go board, with its pieces arranged in an Archimedean spiral
Archimedean spiral
The Archimedean spiral is a spiral named after the 3rd century BC Greek mathematician Archimedes. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity...

, Max finds a piece of paper with the 216-digit number. Driven to the brink of madness, Max experiences another headache and resists the urge to take his painkillers. Believing that the number and the headaches are linked, Max tries to concentrate on the number through the pain. After passing out, Max has a vision of himself standing in a white void and repeating the digits of the number. The vision ends with Max hugging his neighbor, who turns out to be an illusion. Max stands alone in his trashed apartment. Giving up, Max burns the paper with the number, and trepans
Trepanation
Trepanning, also known as trephination, trephining or making a burr hole, is a surgical intervention in which a hole is drilled or scraped into the human skull, exposing the dura mater in order to treat health problems related to intracranial diseases. It may also refer to any "burr" hole created...

 himself in the right temple with a power drill.

Later, a little girl with a calculator approaches Max in a park asking math problems. Max smiles and reveals that he can no longer perform complex mental calculations. He observes the trees blowing in the breeze, at peace.

Cast

  • Sean Gullette
    Sean Gullette
    Sean Gullette is a writer, actor, and filmmaker.-Biography:He was born in Boston and attended public schools and Harvard, where he acted in theater and films and directed plays....

     as Maximillian "Max" Cohen
  • Mark Margolis
    Mark Margolis
    Mark Margolis is an American actor who has been making films since 1976.Margolis went to Temple University briefly before moving to New York City, where he studied drama with Stella Adler and at the Actors Studio...

     as Sol Robeson
  • Ben Shenkman
    Ben Shenkman
    Benjamin Shenkman is an American television, film and stage actor.-Life and career:Shenkman was born in New York City and raised in what he described as "the secular Eastern European Jewish tradition". He graduated from Brown University, and obtained a Masters of Fine Arts in 1993 from New York...

     as Lenny Meyer
  • Samia Shoaib
    Samia Shoaib
    Samia Shoaib is an actress, filmmaker, and writer. She was born in Pakistan and raised in England. She moved to the United States where she studied English and Theater at the University of California and George Washington University. She studied acting at the Royal Academy of Dramatic Arts in London...

     as Devi
  • Pamela Hart as Marcy Dawson
  • Stephen Perlman as Rabbi Cohen
  • Ajay Naidu
    Ajay Naidu
    Ajay Kalahastri Naidu is an American actor.Naidu was born in Evanston, Illinois He attended Evanston Township High School. As an actor, he trained with the American Repertory Theater's Institute for Advanced Theatre Training at Harvard University.His first professional acting job was the film ...

     as Farrouhk
  • Kristyn Mae-Anne Lao as Jenna
  • Lauren Fox as Jenny Robeson
  • Clint Mansell
    Clint Mansell
    Clinton Darryl "Clint" Mansell, is an English musician, composer, and former lead singer and guitarist of the band Pop Will Eat Itself....

     as Photographer

Production

Pi was written and directed by Darren Aronofsky
Darren Aronofsky
Darren Aronofsky is an American film director, screenwriter and film producer. He attended Harvard University to study film theory and the American Film Institute to study both live-action and animation filmmaking...

, and filmed on high-contrast black-and-white
Black-and-white
Black-and-white, often abbreviated B/W or B&W, is a term referring to a number of monochrome forms in visual arts.Black-and-white as a description is also something of a misnomer, for in addition to black and white, most of these media included varying shades of gray...

 reversal film. It was produced on a sufficiently low budget of $60,000, but proved a financial success at the box office ($3,221,152 gross in the U.S.) despite only a limited release to theaters. It has sold steadily on DVD
DVD
A DVD is an optical disc storage media format, invented and developed by Philips, Sony, Toshiba, and Panasonic in 1995. DVDs offer higher storage capacity than Compact Discs while having the same dimensions....

.

Reception

The film was well received upon its release; on Rotten Tomatoes
Rotten Tomatoes
Rotten Tomatoes is a website devoted to reviews, information, and news of films—widely known as a film review aggregator. Its name derives from the cliché of audiences throwing tomatoes and other vegetables at a poor stage performance...

, the film has an 87 percent 'Fresh' rating based on 46 reviews. On Metacritic, the film has a rating of 72 (generally favorable reviews) out of 100 based on 23 reviews. Roger Ebert
Roger Ebert
Roger Joseph Ebert is an American film critic and screenwriter. He is the first film critic to win a Pulitzer Prize for Criticism.Ebert is known for his film review column and for the television programs Sneak Previews, At the Movies with Gene Siskel and Roger Ebert, and Siskel and Ebert and The...

 gave the film three and a half stars out of four, writing: "Pi is a thriller. I am not very thrilled these days by whether the bad guys will get shot or the chase scene will end one way instead of another. You have to make a movie like that pretty skillfully before I care. But I am thrilled when a man risks his mind in the pursuit of a dangerous obsession." James Berardinelli
James Berardinelli
James Berardinelli is an American online film critic.-Personal life:Berardinelli was born in New Brunswick, New Jersey and spent his early childhood in Morristown, New Jersey. At the age of nine years, he relocated to the township of Cherry Hill, New Jersey...

 gave the film three stars, writing: "[Pi] transports us to a world that is like yet unlike our own, and, in its mysterious familiarity, is eerie, intense, and compelling. Reality is a fragile commodity, but, because the script is well-written and the central character is strongly developed, it's not hard to suspend disbelief....It probably deserves 3.1416 stars, but since my scale doesn't support that, I'll round it off to three."

Mathematics

Pi features several references to mathematics and mathematical theories. For instance, Max finds the golden spiral
Golden spiral
In geometry, a golden spiral is a logarithmic spiral whose growth factor is , the golden ratio. That is, a golden spiral gets wider by a factor of for every quarter turn it makes.-Formula:...

 occurring everywhere, including the stock market. Max's belief that diverse systems embodying highly nonlinear dynamics
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...

 share a unifying pattern bears much similarity to results in chaos theory
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

, which provides machinery for describing certain phenomena of nonlinear systems, which might be thought of as patterns.

The film's duration is 1:23:45

The actual number Max discovers is not displayed in its entirety until 54:22. The number displayed on his monitor is:

94143243431512659321054872390486828512913474876027

67195923460238582958304725016523252592969257276553

64363462727184012012643147546329450127847264841075

62234789626728592858295347502772262646456217613984

829519475412398501

Arranged into 50 columns, this is in fact 218 digits, not the 216 digits as described in the film. All the partially displayed digits presented earlier on his monitor and the printout appear to be consistent with this number, with the exception that Sol's number transposes the digits at 62 and 63, exchanging the "23" for "32", and does not contain the regular count of digits per row found in Max's number. Also, in the short clips where Max is seen transcribing digits by hand, some of the sequences shown do not correlate to pieces of the number already shown on his computer screen.

Kabbalah

The 216-letter name of God sought by the characters of the film is known as the Shem ha-Meforash
Shemhamphorasch
The Shemhamphorasch is a corruption of the Hebrew term , which was used in tannaitic times to refer to the Tetragrammaton. In early Kabbalah the term was used to designate sometimes a seventy-two Letter name for God, and sometimes a forty two Letter name...

 or the Explicit Name. It comes from . Each of these three verses is composed of seventy-two letters in the original Hebrew
Hebrew language
Hebrew is a Semitic language of the Afroasiatic language family. Culturally, is it considered by Jews and other religious groups as the language of the Jewish people, though other Jewish languages had originated among diaspora Jews, and the Hebrew language is also used by non-Jewish groups, such...

. If one writes the three verses in boustrophedon
Boustrophedon
Boustrophedon , is a type of bi-directional text, mostly seen in ancient manuscripts and other inscriptions. Every other line of writing is flipped or reversed, with reversed letters. Rather than going left-to-right as in modern English, or right-to-left as in Arabic and Hebrew, alternate lines in...

 form — one above the other, the first from right to left, the second from left to right, and the third from right to left — one gets seventy-two columns of three-letter names of God.

The game of Go

In the film, Max periodically plays Go with his mentor, Sol. This game has historically stimulated the study of mathematics and features a simple set of rules that results in a complex game strategy. The two characters each use the game as a model for their view of the universe; Sol says that the game is a microcosm of an extremely complex and chaotic world, while Max asserts that patterns can be found in the complexity of its variations.SOL: Listen to me. The Ancient Japanese considered the Go board to be a microcosm of the universe. Although when it is empty it appears to be simple and ordered, in fact, the possibilities of game play are endless. They say that no two Go games have ever been alike. Just like snowflakes. So, the Go board actually represents an extremely complex and chaotic universe. That is the truth of our world, Max. It can't be easily summed up with math. There is no simple pattern.
MAX: But as a Go game progresses, the possibilities become smaller and smaller. The board does take on order. Soon, all moves are predictable.
SOL: So?
MAX: So, maybe, even though we're not sophisticated enough to be aware of it, there is an underlying order... a pattern, beneath every Go game. Maybe that pattern is like the pattern in the market, in the Torah. The two sixteen number.


Actors Sean Gullette
Sean Gullette
Sean Gullette is a writer, actor, and filmmaker.-Biography:He was born in Boston and attended public schools and Harvard, where he acted in theater and films and directed plays....

 and Mark Margolis
Mark Margolis
Mark Margolis is an American actor who has been making films since 1976.Margolis went to Temple University briefly before moving to New York City, where he studied drama with Stella Adler and at the Actors Studio...

 both spent many hours learning the game at the Brooklyn
Brooklyn
Brooklyn is the most populous of New York City's five boroughs, with nearly 2.6 million residents, and the second-largest in area. Since 1896, Brooklyn has had the same boundaries as Kings County, which is now the most populous county in New York State and the second-most densely populated...

 Go Club, and had the help of a Go consultant for the film.

Soundtrack

Pi launched the film scoring
Film score
A film score is original music written specifically to accompany a film, forming part of the film's soundtrack, which also usually includes dialogue and sound effects...

 career of Clint Mansell
Clint Mansell
Clinton Darryl "Clint" Mansell, is an English musician, composer, and former lead singer and guitarist of the band Pop Will Eat Itself....

.
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