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Deus ex machina is Latin for "god from the machine" and is a calque from the Greek "από μηχανής θεός", (pronounced 'apo mekhanes theos'). It originated with Greek and Roman theater, when a mechane would lower a god or gods onstage to resolve a hopeless situation: thus god comes from the machine. The phrase deus ex machina has been extended to refer to any resolution to a story which does not pay due regard to the story's internal logic and is so unlikely it challenges suspension of disbelief, and presumably allows the author to end it in the way he or she wanted.
The pronunciation of the phrase is a problem in English. Traditional ways of saying Latin would have it something like DAY-us ex MAK-in-a, more modern ways of saying Latin would give perhaps DAY-oos ex MAH-kin-ah, but many people naturally bring in the modern English m'SHEEN, resulting in a mixed pronunciation.
The Greek tragedian Euripides was notorious for using this plot device.
Spoiler warning: Plot or ending details follow.
A few more recent examples, where it isn't literally a god-like being, but is a similar sudden, arbitrary resolution of plot, are in the films The Joyless Street and Pandora's Box by G.W. Pabst. In Pandora's Box, the movie is ended when for no apparent reason the main character is murdered by Jack the Ripper. Similarly, in Medium Cool, the final scene ends with the lead characters being killed in a car accident.
Stephen King's novel The Stand would arguably be another example: a minor character who has gone insane in the desert returns to Las Vegas with an atomic bomb, which is set off by an electrical charge taking the shape of a hand, destroying the city. The characters in Boulder believe the charge to have been the "Hand of God." Many of King's novels have a deus ex ending. In the Peter Straub/Stephen King novel The Talisman, one of the characters is said to be driving a Deus ex machina.
Monty Python and the Holy Grail is another example; however, the ending — in which the movie comes to a sudden halt when the entire cast is arrested — is intentionally preposterous in this case.
The Night's Dawn Trilogy by Peter F. Hamilton is also often said to be ended using this, although it is possible to be a deliberate usage. An alien artifact known as "the Sleeping God" is utilised to solve a problem which over 3000 pages have been working through in less than 5 minutes. (or an hour in the "Tinkerbell/Ketton" events).
Many comic book characters can be seen as walking dei ex machinis. Wolverine is viewed by many fans of the X-Men comics as such. His mutant powers include an incredibly fast healing factor (making him nearly invincible), enhanced senses, and a skeleton of adamantium, a fictional metal which is indestructible. Lifeguard, also from the X-Men, is widely considered by her detractors to be the ultimate deus ex. Her mutant ability is to manifest any necessary ability to save lives, which makes her a quick fix for the writers if any characters are stuck in a tight spot.
See also: plot
In Isaac Asimov's I, Robot it is used as a part of the description of the relationship between humans and robots.
In Bored of the Rings, Frito and Spam are rescued by Deus Ex Machina Airlines (parodying Frodo and Sam being rescued by eagles at Mount Doom).
Deus Ex Machina is also the name of the ship Joel Hodgson uses to escape from the Satellite of Love on the television show Mystery Science Theater 3000.
Further, in its abbreviated form it is the name of a Warren Spector computer game Deus Ex.
Nick Bostrom, who is a philosophy professor at Oxford and Yale, has a on this topic. Robert Freitas, whose perspective is quite insightful, also as some worth reviewing.
In The Matrix Revolutions, the third movie of the Matrix series, the Deus Ex Machina is the ultimate power in the machine world. With presumedly intentional irony, that godlike machine does provide a way out of a seemingly hopeless situation.
In the end of Donnie Darko, Donnie actually says this phrase, though it is very difficult to make out. This is obviously deliberate usage and a prime example of the technique.
In Adaptation, the main character, the screenwriter who is writing the screenplay of The Orchid Thief, takes a screenwriting class where he is told not to end his movie with a Deus Ex Machina. Because of this, he deliberately uses a Deus Ex Machina (in this case, an alligator) to kill the opposing character.
The Smashing Pumpkins penultimate album MACHINA/The Machines of God (followed by an internet-only release MACHINA II/The Friends & Enemies of Modern Music) took its title from an abbreviation of the phrase. Frontman Billy Corgan wrote the concept album based on the plot that he and the band were emissaries of God.
Deus ex Machinae is also the name of the first album released by the SID metal band Machinae Supremacy
At the end of Dodgeball: A True Underdog Story, the treasure chest containing the main character's gambling winnings has the phrase 'Deus ex Machina' written on it.
The character of Puck ends William Shakespeare's "A Midsummer Night's Dream" with a decidely Deus Ex Machina flair.
The Square Enix video game Final Fantasy I begins with a deus-ex-machina-like appearance of the Light Warriors.