2 + 2 = 5

"2 + 2 = 5" redirects here. For information about the song by Radiohead, see 2 + 2 = 5 (song)

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 usage originates from its inclusion in George Orwell's Nineteen Eighty-Four (Part One, Chapter Seven), where it is contrasted with the true, mathematical phrase "two plus two makes 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.

History

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 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 debatable hyperbolic display of loyalty to Adolf Hitler, declared, "If the Führer wants it, two and two make five!" In 1984, 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?

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".

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 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."

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).

Bernard Werber

Bernard Werber wrote in his novel Les Fourmis, that 1 + 1 becomes 3.

• Let a=b.
• Square both sides: a²=b²
• a²-b²=0 ... [1]
• (a+b)(a-b)=0 ... [2]
• a²-b×b=0
• a²-a×b=0 ... a=b, so substitute a instead of b.
• a(a-b)=0 ... [3]
• [2] and [3] are the same expressions: a(a-b)=(a+b)(a-b)
• divide both sides by (a-b): a=a+b
• a equals b: a=a+a
• divide both sides by a, 1=1+1
• 1=2
• Therefore, 1+1=1+2=3

However, this does not work because if you divide by (a-b), since a = b, you are dividing by 0; and division by 0 is undefined.

Popular culture

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!").

Songs

• 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 on Radiohead's 6th album, Hail to the Thief.
• 2+2=5 is an instrumental song by the Fourplay String Quartet released on their first album, Now to the Future

Similar concepts are explored in the following songs:

• Living Colour sings in "Cult of Personality," before directly naming Stalin, "I exploit you; still you love me. I tell you 1 and 1 makes 3."
• The Pet Shop Boys have a song called "one and one make five" on their 1993 album Very.
• In the song "Do What You Want" by Bad Religion the lyric appears "I'll believe in God when one and one are five".

Science

Significant digits

In measurement in physics, the number of significant digits is usually encoded in the way a number is written. That is, unless otherwise specified, "2" has only one significant digit, which means it represents a measurement with a margin of error of 0.5, which means the actual value may lie between 1.5 and 2.5. When adding such measurements together, the margins of error are also added, so 2 ± 0.5 + 2 ± 0.5 = 4 ± 1.0 . And since "5" actually means 5 ± 0.5, these margins clearly overlap and one could jokingly argue that the numbers are the same. When adding more precise measurements, for example 2.0 + 2.0, the margin of error is smaller and the maximum number that could be "reached" would in this case be 4.1. See also approximation.

Further reading

• Krueger, L. E. and E. W. Hallford (1984). "Why 2 + 2 = 5 looks so wrong: On the odd-even rule in sum verification". Memory & Cognition. 12: 171–180.

Internal Links

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

External links

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