2 + 2 = 5  

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Kunstformen der Natur (1904) by Ernst Haeckel
Kunstformen der Natur (1904) by Ernst Haeckel

The phrase "two plus two equals five" ("2 + 2 = 5") is a slogan used in many different forms of media, most notably in Part One, Chapter Seven of the book 1984 by George Orwell. In the novel, it is used as an example of an obviously false dogma that one may be required to believe, similar to other obviously false slogans promoted by the Party in the novel. It is contrasted with the phrase "two plus two makes four", the obvious—but politically incorrect—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 one's 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").



Self-evident truth and self-evident falsehood

The equation 2 + 2 = 4 has been proverbial as the type of an obvious truth since the 16th century, and it appears as such in Johann Wigand's 1562 De Neutralibus et Mediis Libellus: "That twyce twoo are foure, a man may not lawfully make a doubt of it, because that manner of knowledge is grauen [grown] into mannes [man's] nature."

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 (1641), the standard of truth is self-evidence of clear and distinct ideas. However, Descartes questions the correspondence of these ideas to reality.

In his play Dom Juan (1682), Molière's title character is asked what he believes. He answers that he believes that two plus two equals four.

The mirror-image of this -- that 2 + 2 = 5 is the archetypical untruth -- is attested at least as early as 1728. Ephraim Chambers' Cyclopædia, or an Universal Dictionary of Arts and Sciences, published in that year, follows its definition of the word absurd with this illustrative example: "Thus, a proposition would be absurd, that should affirm, that two and two make five; or that should deny 'em to make four." Similarly Samuel Johnson said in 1779 that "You may have a reason why two and two should make five; but they will still make but four."

The first known sympathetic reference to the equation 2 + 2 = 5 appears in an 1813 letter by Lord Byron to his soon-to-be wife Anabella Milbanke in which he writes, "I know that two and two make four—& should be glad to prove it too if I could—though I must say if by any sort of process I could convert 2 & 2 into five it would give me much greater pleasure."

Abbé Sieyès, Victor Hugo, and Fyodor Dostoyevsky

Although the phrase "2 + 2 = 5" had earlier been used to indicate an absurdity in general, its use within a political setting is first attested at the dawning of the French Revolution. Abbé Sieyès, in his What Is the Third Estate? (1789), mocked the fact that the Estates-General gave disproportionate voting power to the aristocracy and the clergy in with the following analogy: "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."

Victor Hugo used this phrase 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. In his 1852 pamphlet, Napoléon le Petit, he writes: "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."

In Fyodor Dostoyevsky's Notes from Underground (published in 1864), 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." f Dostoyevsky may have been aware of Hugo's use of this phrase. 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 such that they would fit no conventional labels.

The idea seems to have been significant to Russian literature and culture. Ivan Turgenev wrote in Prayer (1881), 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. Russian anarchist Mikhail Bakunin in God and the State (1882), 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." In The Reaction In Germany (1842) Bakunin compares the behavior of Compromising Positivists to the one of Juste-milieu at the beginning of the July Revolution quoting a French journal: "The Left says, 2 times 2 are 4; the Right, 2 times 2 are 6; and the Juste-milieu says, 2 times 2 are 5".

Soviet planning

The Soviet Union began its first five-year economic plan in 1928. Its goals were ambitious from the start, seeking the immediate transformation of the USSR into an industrial nation. The consequences for underperformance during the plan were severe; managers who admitted missing their targets, even as those targets were revised upward, could be charged with economic wrecking. After statistics from the first two years indicated that the plan was ahead of schedule, Joseph Stalin announced that the plan would be completed in four years. Propagandist Iakov Guminer supported this campaign with a 1931 poster reading "2+2=5: Arithmetic of a counter-plan plus the enthusiasm of the workers." Stalin declared the plan a success at the beginning of 1933, noting the creation of several heavy industries where none had existed. George Orwell could have been influenced by this poster.

George Orwell

George Orwell had used this concept before publishing Nineteen Eighty-Four in 1949. 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", that referred to Guminer's slogan.

However, Orwell spoke of the Nazis, so he may have been making reference to 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?

See also

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