The phrase "two plus two make 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. Logic, from Classical Greek λόγος logos (the word), is the study of patterns found in reasoning. ... An ideology is a collection of ideas. ...

Its common use originates from its inclusion in George Orwell's Nineteen Eighty-Four (Part Three, Chapter Two), where it is contrasted with the true, mathematical phrase "two plus two make four." Orwell's protagonist, Winston Smith, uses the phrase to wonder if 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? Smith writes, "Freedom is the freedom to say that two plus two make four. If that is granted, all else follows." Later in the novel, Smith attempts to use doublethink to teach himself that the statement "2 + 2 = 5" is true, or at least as true as any other answer one could come up with. Eric Arthur Blair (25 June 1903[1][2] – 21 January 1950), better known by the pen name George Orwell, was a British author and journalist. ... Nineteen Eighty-Four (commonly written as 1984) is a dystopian novel by the English writer George Orwell, published in 1949. ... The main character is the central figure of a story. ... Peter Cushing as Winston Smith in the 1954 BBC Television adaptation of Nineteen Eighty-Four, with Donald Pleasence as Syme. ... In the world of George Orwells Nineteen Eighty-Four, The Party which controls Oceania is split into two halves: the Inner Party and the Outer Party. ... This article or section does not cite its references or sources. ...

History

Lewis

C.S. Lewis uses this phrase in his Mere Christianity to refer to a devoid of common humanness and morality.^[1] Clive Staples Lewis (November 29, 1898 – November 22, 1963), commonly referred to as C. S. Lewis, was an author and scholar. ... Mere Christianity is a book by C. S. Lewis, adapted from a 1943 series of BBC radio chats broadcast while Lewis was an Oxford don during World War II and it is considered a classic work in Christian apologetics. ...

Orwell

Orwell had used the concept before publishing 1984. 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 four years before 1984, Orwell wrote: The British Broadcasting Corporation, usually known as the BBC (and also informally known as the Beeb or Auntie) is one of the largest broadcasting corporations in the world in terms of audience numbers, employing 26,000 staff in the UK alone and with a budget of more than £4 billion. ... National Socialism redirects here. ... An Australian anti-conscription propaganda poster from World War One U.S. propaganda poster, which warns against civilians sharing information on troop movements (National Archives) The much-imitated 1914 Lord Kitchener Wants You! poster Brochure of the Peoples Temple, portraying cult leader Jim Jones as the loving father of the...

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 […]

In the view of most of Orwell's biographers, the main source for this was Assignment in Utopia by Eugene Lyons, an account of his time in the Soviet Union. This contains a chapter "2+2=5", which was a slogan used by Stalin's government to predict that the Five year plan would be completed in four years, which for a time appeared widely in Moscow. This article does not cite its references or sources. ... Five-Year Plans or Piatiletkas (пятилетка) were a series of nation-wide centralized exercises in rapid economic development in the Soviet Union. ... Location Position of Moscow in Europe Government Country District Subdivision Russia Central Federal District Federal City Mayor Yuriy Luzhkov Geographical characteristics Area  - City 1,081 km² Population  - City (2007)    - Density 10,469,000   8537. ...

However, Orwell may also have been influenced by Nazi Reichsmarschall Hermann Göring, who once, in a debatably hyperbolic display of loyalty to Adolf Hitler, declared, "If the Führer wants it, two and two make five!" ^[2] In 1984, Orwell writes: National Socialism redirects here. ... The original uniform of the Reichsmarschall Hermann Göring shown in the Luftwaffe-Museum in Berlin. ... Hermann Wilhelm Göring (also Goering in English) (January 12, 1893 – October 15, 1946) was a German politician and military leader, a leading member of the Nazi Party, second in command of the Third Reich, and commander of the Luftwaffe. ... Hitler redirects here. ...

Zamyatin

Yevgeny Zamyatin's novel We, an acknowledged precursor to Nineteen Eighty-Four, has an advocate of the totalitarian state discussing the sum "two times two makes four" in an argument against freedom. The character argues that it would "be an absurdity if these two and two were to get notions about some sort of freedom - i.e., about that which is clearly an error". Yevgeny Zamyatin by Boris Kustodiev (1923) Yevgeny Ivanovich Zamyatin (Евге́ний Ива́нович Замя́тин sometimes translated into English as Eugene Zamyatin) (February 1, 1884 – March 10, 1937) was a Russian author, most famous for his novel We, a story of dystopian future which influenced George Orwells Nineteen Eighty-Four and Aldous Huxleys Brave... We (Russian: )[1] is a dystopian novel by Yevgeny Zamyatin completed in 1921. ...

Dostoevsky & Victor Hugo

In Fyodor Dostoevsky's 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." Fyodor Mikhailovich Dostoevsky (Russian: Фёдор Миха́йлович Достое́вский, IPA: , sometimes transliterated Dostoyevsky  ) (November 11 [O.S. October 30] 1821 – February 9 [O.S. January 28] 1881) is considered one of the greatest Russian writers. ... Notes from Underground (also translated in English as Notes from the Underground or Letters from the Underworld) (1864) is a short novel by Fyodor Dostoevsky. ...

His purpose is not ideological, however. Instead, he proposes that it is the free will to choose or reject the logical as well as the illogical 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."

Dostoevsky was writing in 1864. However, according to Roderick T. Long, Victor Hugo had used the phrase back in 1852. He objected to the way in which the vast majority of French voters had backed Napoleon III, endorsing the way liberal values had been ignored in Napoleon III's coup. Victor-Marie Hugo (pronounced in French) (26 February 1802 — May 1885) was a French poet, novelist, playwright, essayist, visual artist, statesman and human rights campaigner, perhaps the most influential exponent of the Romantic movement in France. ... Charles Louis Napoléon Bonaparte (April 20, 1808 - January 9, 1873) was the son of King Louis Bonaparte and Queen Hortense de Beauharnais; both monarchs of the French puppet state, the Kingdom of Holland. ...

Victor Hugo said "Now, get seven million five hundred thousand votes to declare that two and two make five, that the straight line is the longest road, that the whole is less than its part; get it declared by eight millions, by ten millions, by a hundred millions of votes, you will not have advanced a step." Victor-Marie Hugo (pronounced in French) (26 February 1802 — May 1885) was a French poet, novelist, playwright, essayist, visual artist, statesman and human rights campaigner, perhaps the most influential exponent of the Romantic movement in France. ...

It's very plausible that Dostoevsky had this in mind. He had been sentenced to death for his participation in a radical intellectual discussion group. The sentence was commuted to imprisonment in Siberia, and he then changed his opinions to something that doesn't fit any conventional labels.

The idea seems to have been significant to Russian literature and culture. Ivan Turgenev wrote in prayer, one of his Poems in Prose "Whatever a man prays for, he prays for a miracle. Every prayer reduces itself to this: Great God, grant that twice two be not four." Also similar sentiments are said to be among Leo Tolstoy's last words when urged to convert to the Russian Orthodox Church: "Even in the valley of the shadow of death, two and two do not make six." Even turn-of-the-century Russian newspaper columnists used the phrase to suggest the moral confusion of the age (e.g. Novoe vremia (New Times), 31 October 1900). Russian literature refers to the literature of Russia or its émigrés, and to the Russian-language literature of several independent nations once a part of what was historically Russia or the Soviet Union. ... Ivan Turgenev, photo by Félix Nadar (1820-1910) For other uses, see Turgenev (disambiguation). ... Poems in Prose is an illustrated collection of prose poems by Clark Ashton Smith. ... Count Lev Nikolayevich Tolstoy (Russian: , IPA:  ), commonly referred to in English as Leo Tolstoy (September 9 [O.S. August 28] 1828 – November 20 [O.S. November 7] 1910) was a Russian novelist, writer, essayist, philosopher, Christian anarchist, pacifist, educational reformer, vegetarian, moral thinker, and an influential member of the Tolstoy... The Russian Orthodox Church (Russian: ), also known as the Orthodox Christian Church of Russia, is that body of Christians who are united under the Patriarch of Moscow, who in turn is in communion with the other patriarchs and primates of the Eastern Orthodox Church. ...

Television

• In an episode of Star Trek: The Next Generation, "Chain of Command," Captain Picard of the Starship Enterprise is tortured by a Cardassian in a manner similar to a torture scene from 1984. During the episode the Cardassian officer tries to coerce Picard to admit seeing five lights when in fact there were only four. Picard valiantly sticks to reality. Near the end when Picard is rescued by his crew, he proudly declares, once again, that "there are [only] four lights!". However, later in a counseling session with Deanna Troi, Picard admits that he believed he could see five lights at the end. This admission is reminiscent of a scene in 1984 when the protagonist Winston Smith is electroshocked into declaring that he saw five fingers when in fact he only saw four ("Four! Five! Six! I don't know!").
• In the animated television series The Fairly Oddparents, crazed teacher Mr. Crocker declared that if he had magical fairy godparents he would "make 2 + 2 = fish". A later episode had Stephen Hawking saying to the same teacher that 2 + 2 = 5. At the end of the episode Mr. Crocker is shown saying that 2 + 2 = 6, not five.

The title as it appeared in most episodes opening credits. ... Chain of Command is an episode of Star Trek: The Next Generation that aired in two parts during the sixth season of the series. ... Captain Jean-Luc Picard (July 13, 2305-) is a fictional Starfleet officer in the Star Trek TV series and films. ... Cardassians are a spacefaring race in the fictional Star Trek universe. ... Commander Deanna Troi is a fictional character in the Star Trek universe, played by the actress Marina Sirtis in the series Star Trek: The Next Generation (TNG), Star Trek: Voyager, Star Trek: Enterprise (the latter two only in guest appearances), and in several Star Trek films. ... The Fairly OddParents is an American animated television series created by Butch Hartman. ... In fairy tales, a fairy godmother is a fairy or person with magical powers who acts as a mentor or parent to someone. ... Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ...

Websites

• ThinkGeek produces a popular t-shirt that says "2+2=5 for extremely large values of 2" as a parody on the concept of mathematical approximation.
• The Slashdot icon for its education section is a chalkboard with "2 + 2 = 5" written on it.

ThinkGeek is an electronic commerce company based in Fairfax, VA as part of the Open Source Technology Group. ... Slashdot, often abbreviated as /., is a technology-related news website which features user-submitted and editor-evaluated current affairs news with a nerdy slant. ...

Songs

• "2 + 2 = 5" is a song on Radiohead's 6th album, Hail to the Thief.
• 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 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."
• Thomas Dolby writes in his song "That's why people fall in love" (from the album Astronauts and Heretics) that "Two and Two make five and quarter, that's why people fall in love."
• On a less explicitly political note, in the eponymous theme song from the film School of Rock, Jack Black sings "Recess is in session/two and two make five."
• Five for Fighting has a bonus song on the second disc of their album Battle for Everything entitled "2 + 2 Makes Five".

2 + 2 = 5 is a song by Radiohead, released as the last single from their sixth album Hail to the Thief in 2003 (see 2003 in British music). ... Radiohead are an English rock band from Oxfordshire, initially formed by school friends in 1985. ... Hail to the Thief, or The Gloaming as it is subtitled, is the sixth studio album by English rock band Radiohead, released on June 9, 2003 in the United Kingdom and June 10 in the United States and Canada. ... Mea Culpa is a Latin phrase that translates into English as my fault, or my own fault. In order to emphasize the message, the adjective maxima may be inserted, resulting in mea maxima culpa, which would translate as my most [grievous] fault. ... Jonatha Brooke is an American folk-rock singer-songwriter. ... Jennifer Kimball is a vocalist, songwriter, and multi-instrumentalist who was part of The Story along with friend and Amherst College classmate Jonatha Brooke. ... Anti-Flag is a American political punk band from Glenshaw, Pennsylvania [1], a blue collar suburb of Pittsburgh. ... Thomas Dolby (born Thomas Morgan Robertson, on 14 October 1958) is an English musician best known for his 1982 synth pop hit She Blinded Me With Science. He is also a successful session musician, music producer, inventor and entrepreneur, whose company Beatnik, Inc. ... School of Rock is a 2003 comedy film starring Jack Black. ... Jack Black (born Thomas J. Black, Jr. ... Five for Fighting is the stage name of U.S. singer-songwriter John Ondrasik. ...

Relevance to estimated errors

• "2 + 2 = 5, for sufficiently large values of 2" is a reminder about the way estimation errors compound in numerical calculations. One example is when rounding is directly involved: 2.4 is rounded down to 2 ("a large value of 2"), while 2.4 + 2.4 (which is equal to 4.8) is rounded up to 5.

In mathematics, the phrase sufficiently large is used in contexts such as: is true for sufficiently large which is actually shorthand for: there exists an such that is true for all . ... Rounding is the process of reducing the number of significant digits in a number. ...

References

1. ^ Lewis, C.S. Mere Christianity, p. 5
2. ^ Hermann Göring. Museum of Tolerance Multimedia Learning Center. Retrieved on May 28, 2005.
3. ^ George Orwell. Nineteen Eighty-Four. Secker and Warburg (1949). ISBN 0-452-28423-6