Two plus two make five
Encyclopedia
The phrase "two plus two equals five" ("2 + 2 = 5") is a slogan used in George Orwell
's Nineteen Eighty-Four
as an example of an obviously false dogma
one must believe, similar to other obviously false slogans by the Party in the novel. It is contrasted with the phrase "two plus two makes four", the obvious—but politically inexpedient—truth.
Orwell's protagonist
, Winston Smith
, uses the phrase to wonder if the State
might declare "two plus two equals five" as a fact; he ponders whether, 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.
Eventually, while undergoing electric torture, Winston declared that he saw five fingers when in fact he only saw four ("Four, five, six — in all honesty I don't know"). The Inner Party
interrogator of thought-criminals
, O'Brien
, says of the mathematically false statement that control over physical reality is unimportant; so long as one controls their own perceptions to what the Party wills, then any corporeal act is possible, in accordance with the principles of doublethink ("Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once").
. During his career at the BBC
, he became familiar with the methods of Nazi
propaganda
. In his essay "Looking Back on the Spanish War
", published in 1943 (six years before the publication of Nineteen Eighty-Four
,) Orwell wrote:
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 "Two Plus Two Equals Five", 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
.
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 makes five!" In Nineteen Eighty-Four, Orwell writes:
, the protagonist implicitly supports the idea of two times two making five, spending several paragraphs considering the implications of rejecting the statement "two times two makes four."
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."
Dostoyevsky 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 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 Hugo here is echoing earlier French thought — Sieyes, in his "What is the Third Estate?
" uses the phrase, "Consequently if it be claimed that under the French constitution, 200,000 individuals out of 26 million citizens constitute two-thirds of the common will, only one comment is possible: it is a claim that two and two make five."
It is very plausible that Dostoyevsky 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 changed his opinions to something that fit no 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 back 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.
However, by redefining what we mean by "2" and "5", we can make the answer anything we like. For instance, if by "2" we mean "any real number which rounds to 2" and by "5" we mean "any real number which rounds to 5", then from 2.4+2.4=4.8 we conclude that "2+2=5". A difficulty with this approach, of course, is that it runs afoul of Lincoln's dictum that calling a tail a leg doesn't make it one. The question at this point gets bogged down in the philosophy of language, and in any event has nothing to do with mathematics.
In his play Dom Juan
, Moliere
's title character is asked what he believes. He answers that he believes that two plus two equals four. Belief
is the psychological state in which an individual holds a proposition or premise to be true. A belief is separate from knowledge
. Were certain absolute knowledge to exist, belief in an existential claim would be unnecessary. Moliere seeks the freedom to believe that two plus two equals four. Orwell seeks the freedom to say that two plus two equals four, as an objective fact which the Party cannot touch.
Rene Descartes
' realm of pure ideas considers that self-evident ideas such as two plus two equals four may in fact have no reality outside the mind. According to the first meditation, the standard of truth is self-evidence of clear and distinct ideas. However, Descartes questions the correspondence of these ideas to reality.
George Orwell
Eric Arthur Blair , better known by his pen name George Orwell, was an English author and journalist...
's Nineteen Eighty-Four
Nineteen Eighty-Four
Nineteen Eighty-Four by George Orwell is a dystopian novel about Oceania, a society ruled by the oligarchical dictatorship of the Party...
as an example of an obviously false dogma
Dogma
Dogma is the established belief or doctrine held by a religion, or a particular group or organization. It is authoritative and not to be disputed, doubted, or diverged from, by the practitioners or believers...
one must believe, similar to other obviously false slogans by the Party in the novel. It is contrasted with the phrase "two plus two makes four", the obvious—but politically inexpedient—truth.
Orwell'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...
, Winston Smith
Winston Smith
Winston Smith is a fictional character and the protagonist of George Orwell's 1949 novel Nineteen Eighty-Four. The character was employed by Orwell as an everyman in the setting of the novel, a "central eye ... [the reader] can readily identify with"...
, uses the phrase to wonder if the State
Inner Party
The Inner Party represents the oligarchical political class in Oceania, and has its membership restricted to 6 million individuals . Inner Party members enjoy a quality of life that is much better than that of the Outer Party members and the proles...
might declare "two plus two equals five" as a fact; he ponders whether, if everybody believes in it, does that make it true?
Consensus reality
Consensus reality is an approach to answering the philosophical question "What is real?" It gives a practical answer: reality is either what exists, or what we can agree seems to exist....
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
Doublethink
Doublethink, a word coined by George Orwell in the novel 1984, describes the act of simultaneously accepting two mutually contradictory beliefs as correct, often in distinct social contexts. It is related to, but distinct from, hypocrisy and neutrality. Its opposite is cognitive dissonance, where...
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.
Eventually, while undergoing electric torture, Winston declared that he saw five fingers when in fact he only saw four ("Four, five, six — in all honesty I don't know"). The Inner Party
Inner Party
The Inner Party represents the oligarchical political class in Oceania, and has its membership restricted to 6 million individuals . Inner Party members enjoy a quality of life that is much better than that of the Outer Party members and the proles...
interrogator of thought-criminals
Thoughtcrime
In the dystopian novel Nineteen Eighty-Four by George Orwell, a thoughtcrime is an illegal type of thought.In the book, the government attempts to control not only the speech and actions, but also the thoughts of its subjects, labelling disapproved thought as thoughtcrime or, in Newspeak,...
, O'Brien
O'Brien (1984)
O'Brien is a fictional character and the main antagonist in George Orwell's novel Nineteen Eighty-Four. The protagonist Winston Smith, living in a dystopian society governed by the Party, feels strangely attracted to Inner Party member O'Brien. Orwell never reveals O'Brien's first name.Winston...
, says of the mathematically false statement that control over physical reality is unimportant; so long as one controls their own perceptions to what the Party wills, then any corporeal act is possible, in accordance with the principles of doublethink ("Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once").
George Orwell
George Orwell had used the concept before publishing Nineteen Eighty-FourNineteen Eighty-Four
Nineteen Eighty-Four by George Orwell is a dystopian novel about Oceania, a society ruled by the oligarchical dictatorship of the Party...
. During his career at the BBC
BBC
The British Broadcasting Corporation is a British public service broadcaster. Its headquarters is at Broadcasting House in the City of Westminster, London. It is the largest broadcaster in the world, with about 23,000 staff...
, he became familiar with the methods of Nazi
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
propaganda
Propaganda
Propaganda is a form of communication that is aimed at influencing the attitude of a community toward some cause or position so as to benefit oneself or one's group....
. In his essay "Looking Back on the Spanish War
Spanish Civil War
The Spanish Civil WarAlso known as The Crusade among Nationalists, the Fourth Carlist War among Carlists, and The Rebellion or Uprising among Republicans. was a major conflict fought in Spain from 17 July 1936 to 1 April 1939...
", published in 1943 (six years before the publication of Nineteen Eighty-Four
Nineteen Eighty-Four
Nineteen Eighty-Four by George Orwell is a dystopian novel about Oceania, a society ruled by the oligarchical dictatorship of the Party...
,) Orwell wrote:
In the view of most of Orwell's biographers, the main source for this was Assignment in Utopia by Eugene Lyons
Eugene Lyons
Eugene Lyons was an American journalist and writer. A fellow traveler of the Communist Party in his younger years, Lyons became highly critical of the Soviet Union after having lived there for several years as a correspondent of United Press International...
, an account of his time in the Soviet Union. This contains a chapter "Two Plus Two Equals Five", 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
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
.
However, Orwell may also have been influenced by Nazi
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
Reichsmarschall
Reichsmarschall
Reichsmarschall literally in ; was the highest rank in the armed forces of Nazi Germany during World War II after the position of Supreme Commander held by Adolf Hitler....
Hermann Göring
Hermann Göring
Hermann Wilhelm Göring, was a German politician, military leader, and a leading member of the Nazi Party. He was a veteran of World War I as an ace fighter pilot, and a recipient of the coveted Pour le Mérite, also known as "The Blue Max"...
, who once, in a debatably hyperbolic display of loyalty to Adolf Hitler
Adolf Hitler
Adolf Hitler was an Austrian-born German politician and the leader of the National Socialist German Workers Party , commonly referred to as the Nazi Party). He was Chancellor of Germany from 1933 to 1945, and head of state from 1934 to 1945...
, declared, "If the Führer wants it, two and two makes five!" In Nineteen Eighty-Four, Orwell writes:
Dostoyevsky and Victor Hugo
In Fyodor Dostoyevsky's Notes from UndergroundNotes from Underground
Notes from Underground is an 1864 short novel by Fyodor Dostoyevsky. Notes is considered by many to be the first existentialist novel...
, the protagonist implicitly supports the idea of two times two making five, spending several paragraphs considering the implications of rejecting the statement "two times two makes four."
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."
Dostoyevsky was writing in 1864. However, according to Roderick T. Long, Victor Hugo
Victor Hugo
Victor-Marie Hugo was a Frenchpoet, playwright, novelist, essayist, visual artist, statesman, human rights activist and exponent of the Romantic movement in France....
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 Hugo
Victor Hugo
Victor-Marie Hugo was a Frenchpoet, playwright, novelist, essayist, visual artist, statesman, human rights activist and exponent of the Romantic movement in France....
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 Hugo here is echoing earlier French thought — Sieyes, in his "What is the Third Estate?
What is the Third Estate?
What Is the Third Estate? is a pamphlet written by French thinker and clergyman Abbé Emmanuel Joseph Sieyès in January 1789, shortly before the outbreak of the French Revolution...
" uses the phrase, "Consequently if it be claimed that under the French constitution, 200,000 individuals out of 26 million citizens constitute two-thirds of the common will, only one comment is possible: it is a claim that two and two make five."
It is very plausible that Dostoyevsky 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 changed his opinions to something that fit no conventional labels.
The idea seems to have been significant to Russian literature
Russian literature
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...
and culture. Ivan Turgenev
Ivan Turgenev
Ivan Sergeyevich Turgenev was a Russian novelist, short story writer, and playwright. His first major publication, a short story collection entitled A Sportsman's Sketches, is a milestone of Russian Realism, and his novel Fathers and Sons is regarded as one of the major works of 19th-century...
wrote in prayer, one of his Poems in Prose
Poems in Prose
Poems in Prose is an illustrated collection of prose poems by Clark Ashton Smith. It was released in 1965 and was published by Arkham House in an edition of 1,016 copies. The book is a nearly complete collection of Smith's prose poetry.-Contents:...
"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
Leo Tolstoy
Lev Nikolayevich Tolstoy was a Russian writer who primarily wrote novels and short stories. Later in life, he also wrote plays and essays. His two most famous works, the novels War and Peace and Anna Karenina, are acknowledged as two of the greatest novels of all time and a pinnacle of realist...
's last words when urged to convert back to the Russian Orthodox Church
Russian Orthodox Church
The Russian Orthodox Church or, alternatively, the Moscow Patriarchate The ROC is often said to be the largest of the Eastern Orthodox churches in the world; including all the autocephalous churches under its umbrella, its adherents number over 150 million worldwide—about half of the 300 million...
: "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.
Self-evident truth
If "two plus two equals five" is used as a propositional statement about integers, it must be either true or false.However, by redefining what we mean by "2" and "5", we can make the answer anything we like. For instance, if by "2" we mean "any real number which rounds to 2" and by "5" we mean "any real number which rounds to 5", then from 2.4+2.4=4.8 we conclude that "2+2=5". A difficulty with this approach, of course, is that it runs afoul of Lincoln's dictum that calling a tail a leg doesn't make it one. The question at this point gets bogged down in the philosophy of language, and in any event has nothing to do with mathematics.
In his play Dom Juan
Dom Juan
Dom Juan or The Feast with the Statue is a French play by Molière, based on the legend of Don Juan. Molière's characters Dom Juan and Sganarelle are the French counterparts to the Spanish Don Juan and Catalinón, characters who would later become familiar to opera goers as Don Giovanni and Leporello...
, Moliere
Molière
Jean-Baptiste Poquelin, known by his stage name Molière, was a French playwright and actor who is considered to be one of the greatest masters of comedy in Western literature...
's title character is asked what he believes. He answers that he believes that two plus two equals four. Belief
Belief
Belief is the psychological state in which an individual holds a proposition or premise to be true.-Belief, knowledge and epistemology:The terms belief and knowledge are used differently in philosophy....
is the psychological state in which an individual holds a proposition or premise to be true. A belief is separate from knowledge
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...
. Were certain absolute knowledge to exist, belief in an existential claim would be unnecessary. Moliere seeks the freedom to believe that two plus two equals four. Orwell seeks the freedom to say that two plus two equals four, as an objective fact which the Party cannot touch.
Rene Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...
' realm of pure ideas considers that self-evident ideas such as two plus two equals four may in fact have no reality outside the mind. According to the first meditation, the standard of truth is self-evidence of clear and distinct ideas. However, Descartes questions the correspondence of these ideas to reality.
In popular culture
- In the Star Trek: The Next GenerationStar Trek: The Next GenerationStar Trek: The Next Generation is an American science fiction television series created by Gene Roddenberry as part of the Star Trek franchise. Roddenberry, Rick Berman, and Michael Piller served as executive producers at different times throughout the production...
episode "Chain of Command, Part II", PicardJean-Luc PicardCaptain Jean-Luc Picard is a Star Trek character portrayed by Patrick Stewart. He appears in the television series Star Trek: The Next Generation and the feature films Star Trek Generations, Star Trek: First Contact, Star Trek: Insurrection, and Star Trek Nemesis...
is tortured by a CardassianCardassianThe Cardassians are an extraterrestrial species in the Star Trek science fiction franchise. First introduced in the 1991 Star Trek: The Next Generation episode "The Wounded", the species originating on the fictional Alpha Quadrant planet Cardassia Prime...
in a manner similar to a torture scene from Nineteen Eighty-Four. 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 about to be brought back to his crew, he defiantly declares, once again, "There are four lights!". However, later in a counseling session with TroiDeanna TroiCommander Deanna Troi is a main character in the science-fiction television series Star Trek: The Next Generation and related TV series and films, portrayed by actress Marina Sirtis. Troi is half-human, half-Betazoid and has the psionic ability to sense emotions. She serves as the ship's counselor...
, Picard admits that he believed he did see five lights at the end. - In Ayn RandAyn RandAyn Rand was a Russian-American novelist, philosopher, playwright, and screenwriter. She is known for her two best-selling novels The Fountainhead and Atlas Shrugged and for developing a philosophical system she called Objectivism....
's Atlas ShruggedAtlas ShruggedAtlas Shrugged is a novel by Ayn Rand, first published in 1957 in the United States. Rand's fourth and last novel, it was also her longest, and the one she considered to be her magnum opus in the realm of fiction writing...
, the hero John GaltJohn GaltJohn Galt was a Scottish novelist, entrepreneur, and political and social commenter. Because he was the first novelist to deal with issues of the industrial revolution, he has been called the first political novelist in the English language.-Life:Born in Irvine, North Ayrshire, Scotland, Galt was...
posits that "the noblest act you have ever performed is the act of your mind in the process of grasping that two and two make four". Responding to this claim, psychologist Albert Ellis wrote "Here Rand falsely notes that two and two make four: and that you are noble for grasping this 'fact.' She fails to note that two and two, definitionally make four; and that her own mind, apparently, isn’t sufficiently noble to acknowledge this definition." - The opening track of RadioheadRadioheadRadiohead are an English rock band from Abingdon, Oxfordshire, formed in 1985. The band consists of Thom Yorke , Jonny Greenwood , Ed O'Brien , Colin Greenwood and Phil Selway .Radiohead released their debut single "Creep" in 1992...
's album Hail to the ThiefHail to the ThiefHail to the Thief is the sixth studio album by the English rock band Radiohead, released in June 2003 through Parlophone Records. After two Radiohead albums that featured heavily processed vocals, less guitar, and strong influence from experimental electronica and jazz, Hail to the Thief was seen...
is "2 + 2 = 5 (The Lukewarm.)2 + 2 = 5 (song)"2 + 2 = 5" is a song by the English rock band Radiohead, released as the third and final single from their sixth album Hail to the Thief in 2003. The song reached number 15 on the United Kingdom singles chart.-Lyrics and background:...
". - A bonus track on Star OneStar OneStar One is a Dutch progressive metal supergroup/side-project of Arjen Anthony Lucassen of Ayreon fame. Unlike Ayreon, the band did not follow one storyline; instead, each song was a different story with a sci-fi concept, most of the tracks based on existing movies and series.-Origins and first...
's album Victims of the Modern Age, inspired by the movie "1984", is called "2 + 2 = 5" - In The Fairly Odd Parents on NickelodeonNickelodeon (TV channel)Nickelodeon, often simply called Nick and originally named Pinwheel, is an American children's channel owned by MTV Networks, a subsidiary of Viacom International. The channel is primarily aimed at children ages 7–17, with the exception of their weekday morning program block aimed at preschoolers...
, Mr. Crocker gives Timmy the math question, what is 2+2? Timmy answers 5. Crocker tells him that he's wrong before Stephen HawkingStephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
enters the classroom, completing a long mathematical equation on the board, proving that 2+2 is 5. At the end of the episode, Crocker storms out and says Hawking is wrong, and says 2+2 is actually 6. - In MonkMonk (TV series)Monk is an American comedy-drama detective mystery television series created by Andy Breckman and starring Tony Shalhoub as the titular character, Adrian Monk. It originally ran from 2002 to 2009 and is primarily a mystery series, although it has dark and comic touches.The series debuted on July...
, after solving a murder inside of a mental hospital at which he was wrongly imprisoned, title character Monk states, "I just want 2 and 2 to make 4 again."
See also
- Asch conformity experimentsAsch conformity experimentsThe Asch conformity experiments were a series of studies published in the 1950s that demonstrated the power of conformity in groups. These are also known as the Asch Paradigm.-Introduction:...
– for more on how the influence of a majority can affect how a single person thinks. - Mathematical fallacy
- 4x4=124x4=124×4=12 is the fifth album by Canadian electronic artist deadmau5 . It was released worldwide on December 6, 2010 through Virgin Records. The album was released in the United States on December 7, 2010 through Ultra Records...
External links
- Two Plus Two Equals Red, Time Magazine, Monday, Jun. 30, 1947