2 + 2 = 5

The phrase "two plus two equals five" ("2 + 2 = 5") is a slogan used in many different forms of media, but more specifically in George Orwell's Nineteen Eighty-Four as an example of an obviously false dogma one may be required to 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 it, does that make it true? 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").

History

Victor Hugo and Fyodor Dostoyevsky

In Fyodor Dostoyevsky's Notes from Underground, 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 twice two makes four is an excellent thing, but if we are to give everything its due, twice 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." Here, Hugo is echoing earlier French thought—Sieyès, 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 some that they would 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.

George Orwell

George Orwell had used this concept before publishing Nineteen Eighty-Four. 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:

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 "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 spoke of the Nazis, so he may have been referencing the 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:

In the end the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four? Or that the force of gravity works? Or that the past is unchangeable? If both the past and the external world exist only in the mind, and if the mind itself is controllable—what then?

Self-evident truth

In his play Dom Juan, Molière'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. Molière 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.

René 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.

In popular culture

• In the Star Trek: The Next Generation episode "Chain of Command, Part II", Captain Picard is tortured by a Cardassian in a manner similar to the torture of Winston Smith by O'Brien 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 counselling session with Troi, Picard admits that he believed he did see five lights at the end.
• In Ayn Rand's Atlas Shrugged, the hero John Galt 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".
• "2 + 2 = 5" (a.k.a. "The Lukewarm.") is the opening track on English rock band Radiohead's sixth album, Hail to the Thief, released in 2003.
• In the Abra-Catastrophe! special of The Fairly OddParents, multiple characters state that the magic "Fairy-versary" muffin is so extremely powerful that it could "make two plus two equal fish!". In another episode of Fairly Oddparents, Remy Buxaplenty hires Stephen Hawking to prove that 2 + 2 = 5 to Mr. Crocker. At the end of the episode, Crocker chases after Hawking stating that 2 + 2 = 6.
• In presidential debates prior to 2009 Iranian presidential elections, reformist candidate Mir Hossein Mousavi accused his interlocutor, president Ahmadinejad, of being illogical and said: "If you ask (the president) what two by two makes he would answer five." In the following days, one of the slogans chanted by Mousavi's supporters was "two by two makes five!"
• In Mikhail Bakunin's God and the State, he classifies Deism as: "Imagine a philosophical vinegar sauce of the most opposed systems, a mixture of Fathers of the Church, scholastic philosophers, Descartes and Pascal, Kant and Scottish psychologists, all this a superstructure on the divine and innate ideas of Plato, and covered up with a layer of Hegelian immanence accompanied, of course, by an ignorance, as contemptuous as it is complete, of natural science, and proving just as two times two make five; the existence of a personal God."
• Some computers return the invalid argument error message "2 + 2 = 5 for very large values of 2 and very small values of 5"

See also

• Asch conformity experiments – for more on how the influence of a majority can affect how a single person thinks.
• Mathematical fallacy

Further reading

• Euler, Houston (1990), "The history of 2 + 2 = 5", Mathematics Magazine, 63 (5), Reviewed by Andy Olson: 338–339
• Krueger, L. E.; Hallford, E. W. (1984), "Why 2 + 2 = 5 looks so wrong: On the odd-even rule in sum verification", Memory & Cognition, 12 (2): 171–180, PMID 6727639 {{citation}}: Unknown parameter |lastauthoramp= ignored (|name-list-style= suggested) (help)

External links

• Two Plus Two Equals Red, Time Magazine, Monday, 30 Jun 1947