2 + 2 = 5

This article is about the phrase. For the song by Radiohead, see 2 + 2 = 5 (song).

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 electroshock 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").

History

Orwell

Orwell had used the 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 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:

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?

Dostoevsky and Victor Hugo

In Fyodor Dostoevsky'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 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 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'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 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 (e.g. Novoe vremia (New Times), 31 October 1900.

Self-evident truth

- - In certain cases, two plus two can sometimes equal five. Two plus two can always equal four only when all numbers are integers and absolute in a ratio scale. Outside these conditions, two plus two does not always equal four. - - In an interval scale, zero is not an absolute value. When measuring temperature in a non-Kelvin scale, four degrees above zero is not twice as warm as two degrees above zero. Even in a ratio scale, two plus two will equal five for large values of 2 and small values of 5. For example, 2.4 still rounds down to 2, but when doubled, it becomes 4.8, which rounds to 5. This is possible because 2 actually represents a range of values which is rounded to 2 for daily practical purposes. Every measurement is always rounded off to the nearest measuring point. It can never be exact. In an integer-based counting system, the measuring point is the nearest integer. - - Yet since the most common daily use of numbers is as integers in a ratio scale used for counting units, most people assume that two plus two automatically equals four and that nothing else is possible. Two plus two is considered so self-evident a truth that no further discussion is admitted. A belief in this truth can have no connection with sense perception or experimentation, because either would prove that the statement is not an absolute truth. - - 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", Picard is tortured by a Cardassian 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 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". 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 Radiohead's album Hail to the Thief is "2 + 2 = 5 (The Lukewarm.)".
• A bonus track on Star One's album Victims of the Modern Age, inspired by the movie "1984", is called "2 + 2 = 5"
• In Portal, as GLaDOS is being damaged, she says "two plus two is [static] ten ... IN BASE FOUR - I'M FINE!".
• In The Fairly Odd Parents on Nickelodeon, Crocker gives Timmy the math question, what is 2+2? Timmy answers 5. Crocker tells him that he's wrong before Stephen Hawking enters the classroom, completing a long mathematical equation on the board, proving that 2+2 IS 5. At the end of the episode, Croker storms out and says Hawkings is wrong, and says 2+2 is actually 6.
• The song Cult of Personality by Living Colour contains the line "I tell you 1 + 1 makes 3".

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, H. (1990), "The history of 2 + 2 = 5", Mathematics Magazine, 63: 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, Jun. 30, 1947