Why some claim that 2+2=5 (and the logic behind it)

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Does two plus two equal four? Well, the answer that there are five has a long, charming and sometimes controversial history. There is a saying in English that goes ‘he put two and two together and came to five’, which indicates that someone has come to a completely wrong conclusion. Getty Images via BBC There are indisputable truths, such as 1+1=2. Unless to 1 pile of dirty clothes you add 1 pile of dirty clothes and you have 1 pile of clothes to wash. Or you’re mixing paints, and 1 color + 1 color = 1 new color, as an art student told mathematician Eugenia Cheng, who included several of these examples in her book Is Math Real?: How Simple Questions Lead Us to Mathematics’ Deepest Truths (“Is mathematics real?: How simple questions lead us to the deepest truths of mathematics”, in free translation). Of course, this does not mean that 1+1≠ 2. It just means that even what is best known invites us to think, that everything deserves a certain degree of questioning and that a lot depends on the context. READ ALSO: What science already knows about cats’ grimaces – and what they mean The mysterious case of the 600 American planes that crashed in the Himalayas in World War II Does running hurt the knee? Does running dressed up make you lose more weight? See 7 myths and truths But a sum similar to the previous ones has a long, prestigious and even controversial history: 2+2. If you think the answer is always 4, I’ll tell you that there are those who argue that this isn’t necessarily right. Let’s start with René Descartes, in the 17th century, although we can follow this story even further back. The French philosopher who questioned everything in search of truth asked himself why it was not doubted that two plus two equals four, if even our existence was doubted. Doubting that 2 + 2 = 4, he noted, was not logically incoherent, since, after all, numbers were abstract ideas that we could not find in nature. But saying “I doubt I exist” was, yes, logically incoherent. The mere capacity to doubt, he observed, reaffirms our existence, hence the fundamental approach of Western rationalism: cogito ergo sum or “I think, therefore I am.” He was not, however, questioning whether if two things are added to two things, it will give four; he used precisely that sum, as it was an obvious truth. And questioning it was so absurd that the Englishman Ephraim Chambers used the expression 2+2=5 as an example when explaining the meaning of the concept in what was one of the first encyclopedias in history. In the Cyclopaedia, or A Universal Dictionary of Arts and Sciences (1728), the subtitle of which indicates that it “contains an explanation of the terms and an account of the meanings of things in the several arts, both liberal and mechanical, and several sciences, the human and divine” , observes: “Thus, a proposition that affirms that two and two are five, or that denies that they are four, would be absurd.” From enchanting to frightening A historically controversial sum. Getty Images via BBC Sum continued to be present, and not just in philosophical and mathematical writings. In 1813, the famous English poet George Gordon Byron evoked her in a letter to his future wife, Anne Isabella Milbanke. He called her his “princess of parallelograms”, for the fascination that mathematics aroused in her, a subject that, Byron wrote, “I must be content to admire from the distance of incomprehension”. “I know that two and two are four, and I would be glad to prove it too if I could, although I must say that if by any kind of process I could convert 2 plus 2 into 5, I would have much greater pleasure.” The great Russian writer Fyodor Dostoevsky went further. In Notes from the Underground (1864), the protagonist accepts the falsehood of 2+2=5 and considers the consequences of denying the truth that 2+2=4. However, he thinks that what makes humanity human is the ability to choose or reject the logical and the illogical, and the incessant process of wanting to achieve a goal, “in other words, life itself, not particularly the goal that, Of course, it must always be ‘two plus two makes four’.” This goal, in his opinion, “is no longer life, but the beginning of death.” So he concludes: “I admit that two and two are four is excellent, but, if we are fair, two and two are five also has a lot of charm.” It didn’t seem so charming to French writer Victor Hugo. He was one of those who used sum as a political metaphor, criticizing the abandonment of the liberal values ​​that inspired the French Revolution when Napoleon III installed himself as emperor. In the pamphlet Napoléon le Petit (“Napoleon the Little”, 1852), he undermined the system’s credibility by writing: “Now get 7,500,000 votes to declare that two and two are five, that the straight line is the quickest way long, that the whole is less than its part.” A century later, French Nobel laureate Albert Camus would write in The Plague that “no one congratulates a teacher for teaching that two and two are four”, as he does not appear to be risking his life by doing so. “But there is always a moment in history when whoever dares to say that two and two make four is condemned to death. The professor knows this well. And the question is not knowing what will be the punishment or reward that awaits this reasoning. The question is whether or not two and two are four.” ‘In the end, the Party would announce that two plus two make five and you would have to believe it’ (1984, George Orwell) Getty Images via BBC But perhaps the one who gave the most repercussion to 2+2=5 for denouncing absurd and dangerous dogmas was the journalist and writer George Orwell. He raised the idea several times, in essays and BBC broadcasts during the Second World War, to illustrate the illogicality of Nazi propaganda. In a 1944 letter, responding to a question about the rise of totalitarianism to someone named Noel Willmett, he explained his fears: “Hitler may say that the Jews started the war, and if he survives it will become official history.” “You can’t say that two and two are five, because for the purposes of, say, ballistics, they have to add up to four.” “But if we get to the kind of world I fear, a world of two or three great superstates that cannot be conquered from each other, two and two could become five if the Führer so wished.” “That, as far as I can see, is the direction in which we are actually moving, although, of course, the process is reversible.” Five years later, his novel 1984 would be published, which would attract the attention of generations as one of the most eloquent fictional statements against a world reduced to superstates. A world saturated with “emotional nationalism”, complacent with “dictatorial methods, secret police and the systematic falsification of history”, and with the desire to “not believe in the existence of an objective truth because all the facts have to fit the words and prophecies of some infallible führer”. In this dystopia, the novel’s protagonist, Winston Smith, wonders whether oppression could become so strong that if the State asserted that “two plus two equals five,” it would immediately become true. The answer is given by his torturer, O’Brien, when Smith says that it is impossible for him to conceive of anything else, as he knows that two plus two make four. “Sometimes yes, Winston; but sometimes it’s five. And sometimes it’s three. And sometimes it’s four, five, and three at the same time,” is O’Brien’s chilling reply. In 2003, inspired by 1984, the English rock band Radiohead released the song “2+2=5”, questioning the choice of staying in the comfort zone instead of fighting the absurd. “Are you such a dreamer To put the world in order? I’ll stay forever at home, where two and two always add up to five” The charm of 2+2=5 The result depends on what you’re adding: apples + oranges = impossible; fruits + fruits = yes. Getty Images via BBC But even the self-evident truths of mathematics are controversial. Although 2+2=5 has been widely used as an example of an evidently false proposition and to warn mathematics students about the risk of fallacies, there is a countercurrent. Interestingly, this sum, which for many illustrates what an absurd belief or dogma is, for others is a symbol of breaking chains. Many adhere to the theory of Critical Social Justice (JSC), which is based mainly on postmodern notions of power, knowledge and language, and think that society is built on oppressive systems of power and privilege that legitimize some forms of knowledge about others. For them, mathematics is not an objective or value-neutral science, nor merely instrumental; nor is it a pure abstract truth existing beyond the concrete world. From this point of view, 2+2 is not necessarily 4, but it could be 5. Have you lost your way? Perhaps it’s worth mentioning the most cited: Kareem Carr, doctor in biostatistics from Harvard University, who gained social media fame in 2020 with a post on Twitter titled “Everything you need to know about 2+2=5”. He began by saying that “statements like 2+2=4 are abstractions, which means they are generalizations of ‘something’.” “Literal-minded people may sometimes say things like ‘if I put a rooster and a hen together and come back the next year and there are three of them (1+1=3) or say, ‘if I leave a fox and a hen together , I come back later and there is only one (1+1=1).’ “People will think this sounds stupid, but they are making a tremendously profound point,” he said. He later declared that “the mere act of transforming something in a number is an assumption.” And, over time, he continued to find examples, such as adding 200ml of water to another 200ml of water in a container, which would then have, according to arithmetic, 400ml. But, he clarified , as the temperature of the first 200ml was 20°C and that of the others was 40°C, by combining them the quantity was reduced. His point was, and still is, that in a world where so much knowledge is generated from “So when someone tells me ‘2+2=5,’ I always ask for more details instead of thinking they’re stupid.”

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