The phrase "two plus two makes five" (or "2 + 2 = 5") is sometimes used as a succinct and vivid representation of an illogical statement, especially one made and maintained to suit an ideological agenda. Its common use originates from its inclusion in the novel Nineteen Eighty-Four by George Orwell, where it is contrasted with the true, mathematical phrase "two plus two make four". Orwell's protagonist, Winston Smith, uses it to consider the possibility that the State might declare "two plus two makes five" as a fact; he ponders that if everybody believes in it, does that make it true?
The novel 1984 wasn't the first time Orwell mentioned the concept. During his employment at the BBC he became familiar with the methods of Nazi propaganda. In his essay Looking Back on the Spanish War, published 4 years before 1984 was written:
Nazi theory indeed specifically denies that such a thing as "the truth" exists. […] The implied objective of this line of thought is a nightmare world in which the Leader, or some ruling clique, controls not only the future but THE PAST. If the Leader says of such and such an event, "It never happened"—well, it never happened. If he says that two and two are five—well, two and two are five. This prospect frightens me much more than bombs […]
It is probable that Orwell derived this notion from Nazi Reichsmarschall Hermann Göring, who once, in a debatably hyperbolic display of loyalty to Adolf Hitler, declared, "If the Fuhrer wants it, two and two make five!"
In Fyodor Dostoevsky's novel Notes from Underground, the protagonist implicitly supports the idea of two plus two making five, spending several paragraphs considering the implications of rejecting the statement "two plus two makes four."
His purpose is not ideological, however. Instead, he proposes that it is the free will to choose or reject the illogical as well as the logical that makes mankind human. He adds: "I admit that two times two makes four is an excellent thing, but if we are to give everything its due, two times two makes five is sometimes a very charming thing too."
Appearances in popular culture
"2 + 2 = 5" is a song on Radiohead's 6th album, Hail to the Thief.
The concept was featured in an episode of Star Trek: The Next Generation, "Chain of Command," in which Picard is tortured by a Cardassian, drawing heavily on the torture scenes from 1984. In this appearance, however, there are four lights shown—the Cardassian officer is attempting to make Picard admit there are five lights. At the last minute, Picard is rescued by his crew, proudly declaring once again that "there are four lights!". However, in a counseling session with Deanna Troi, Picard admits that he almost could see five lights at the end.
In the song "George Orwell Must Be Laughing His Ass Off" by Mea Culpa, the second verse begins with "If 2 plus 2 don't equal 5 I guess I'm just no fun."
Singer/songwriter Jonatha Brooke published a song called "When Two and Two are Five" with Jennifer Kimball (as The Story).
The Pet Shop Boys have a song called "one and one make five" on their 1993 album Very.
The song "The Panama Deception" by Anti-Flag begins with the text "Their two plus two does not equal four. Their two plus two equals whatever they want us to die for."
The Slashdot icon for its education section depicts a chalkboard with "2 + 2 = 5" written on it.
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