There are incontrovertible truths, like 1+1=2… unless you add 1 pile of dirty clothes to 1 pile of dirty clothes and you are left with 1 pile of clothes to wash.
Or that you are mixing paint, and 1 color + 1 color = 1 new color, as an art student pointed out to mathematician Eugenia Cheng, who included several of these examples in her book “Is math real?“.
Of course that does not mean that 1+1≠ 2, it just means that even the most well-known suggests that everything deserves a certain degree of scrutiny and that a lot depends on the context.
But there is a similar sum that has a long, prestigious and even controversial history: 2+2.
If you think that the answer is always 4, I anticipate that There are those who argue that it is not necessarily true.
Let’s start with René Descartes in the 17th century, although we could trace this story further back.
The French philosopher who questioned everything in search of the truth, wondered why if there was no doubt that two plus two equals four, our existence was questioned.
Doubt that 2+2=4he pointed out, was not logically incoherent, since, after all, numbers were abstract ideas that we could not find in nature.
But stating “I doubt I exist” was logically incoherent.
The mere ability to doubt, he pointed out, reaffirms our existence, hence this fundamental approach of Western rationalism: Cogito ergo sum or “I think, therefore I am.”
I was not, however, questioning the fact that if you add two more to two things you will have four; He precisely used that sum because it was an obvious truth.
In fact, questioning it was so absurd that the Englishman Ephraim Chambers used the expression 2+2=5 as an example when explaining the meaning of that concept in what was one of the first encyclopedias in history.
In the “Cyclopaedia, or Universal Dictionary of Arts and Sciences” (1728), whose subtitle indicates that “contains an explanation of the terms and an account of the meanings of things in the various arts, both liberal and mechanical, and various sciences, the human and the Divine“, he points out:
“So, A proposition would be absurd which affirmed that two and two are five, or which denied that they are four.“.
From charming to terrifying
That sum continued to be present, and not only in philosophical and mathematical writings.
In 1813, the famous English poet George Gordon Byron He evoked it in a letter to his future wife, Anne Isabella Milbanke.
He called her his “princess of parallelograms” because of the fascination that mathematics aroused in her, a subject that, Byron wrote, “I must content myself with admiring from the distance of incomprehension.”
“I know that two and two make four, and I would be happy to prove it too if I could, although I must say that if by any type of process I could convert 2 plus 2 into 5, it would give me much greater pleasure“.
The great Russian writer Fyodor Dostoevsky went much further.
In “Notes from 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 equals four’.”
That goal, in his opinion, “is no longer life, but the beginning of death.”
So, he concludes:
“I admit that two and two make four is excellent, but, if we are fair, two and two make five also has a lot of charm.”.
The French writer Victor Hugo had not found it so charming.
He was rather one of those who used the sum as a political metaphor, criticizing the abandonment of the liberal values that inspired the anti-monarchical Revolution when Napoleon III was installed as emperor.
In the pamphlet “”Napoléon le Petit” (Napoleon the Little, 1852) he undermined the credibility of the system by writing:
“Now, get 7,500,000 votes to declare that two and two make five, that the straight line is the longest path, that the whole is less than its part“.
A century later, the French Nobel Prize winner Albert Camus would write in “The Plague” that “no one congratulates a teacher for teaching that two and two make four,” because he does not seem 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 teacher knows it well. And the question is not knowing what the punishment or reward awaits that reasoning. The question is whether two and two make four or not.
But perhaps the person who gave 2+2=5 the most impact in denouncing absurd and dangerous dogmas was the journalist and author George Orwell.
He raised the idea several times, in essays and speeches on the BBC during World War II, to illustrate the illogicality of Nazi propaganda.
In a 1944 letter, answering a question about the growth of totalitarianism to someone named Noel Willmett, he explained his fears:
“Hitler can say that the Jews started the war and, if he survives, that will become official history.
“You can’t say that two and two make five, because for the purposes of, say, ballistics they have to add up to four.
“But if we reach the kind of world I fear, a world of two or three great superstates that cannot conquer each other, two and two could become five if the Führer so desired..
“That, as far as I can see, is the direction we are really moving in, 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 will to “not believe in the existence of an objective truth because all the facts have to fit with the words and prophecies of some infallible führer.”
In this dystopia, the novel’s protagonist, Winston Smith, wonders if oppression could become so strong that if the State affirms that “two plus two equals five,” that would immediately become true.
The answer is given to him by his tormentor O’Brien, when Smith tells him that it is impossible for him to conceive anything else because He knows that two plus two is four.
“Sometimes yes, Winston; but other times it is five. And others, three. And sometimes it is four, five and three at the same time”is O’Brien’s chilling response.
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 against the absurd.
“Are you so dreamy
How to set the world right?
I will stay home forever,
where two and two always add up to five“.
The charm of 2+2=5
But even the obvious truths of mathematics are controversial.
Although 2+2=5 has been widely used as an example of a patently false proposition and to alert mathematics students to the risk of fallacies, there is a countercurrent.
Curiously, that sum that for many illustrates what is an absurd belief or dogma, for others is a symbol of breaking chains.
Many are adherents of Critical Social Justice (CSB) theory, which is based primarily on postmodern notions of power, knowledge and language, and think that society is built with oppressive systems of power and privilege. that legitimize some forms of knowledge over others.
For them, mathematics is not an objective or value-neutral science or a merely instrumental science; nor is it a pure abstract truth existing beyond the concrete world.
From that point of view, 2+2 is not necessarily 4, but could be 5.
You got lost?
Perhaps it is worth quoting the most cited: Kareem Carrdoctor in biostatistics from Harvard University, who rose to fame by lighting up the networks in 2020 for a thread on what was then called 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 thinking people can 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)’.
“It will seem to people that This sounds stupid but they are making a tremendously profound point.“, he assured.
He later stated that “the mere act of converting something into a number is an assumption.”
And, over time, he continued to find examples, such as adding 200 mls. of water to another 200 mls. of water in a container, which would then have, according to arithmetic, 400 mls.
But, he clarified, like the temperature of the first 200 mls. It was 20° and that of the others was 40°, when combining them the amount was reduced.
His point was, and remains, that in a world where so much knowledge is generated from data, it is important to make sure assumptions are accurate so that conclusions about reality are accurate as well.
“So, when someone tells me “2+2=5”, I always ask for more details instead of thinking they are idiots.“.
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