Perhaps you’ve seen the problem on Facebook or another forum:
6 ÷ 2(1+2) = ?
It’s one of several similar math problems popping up on social networks recently. Perhaps you, too, thought, “Duh! That’s easy,” and then, as I did, became embroiled in an epically long comment thread while your blood pressure steadily rose because you could not possibly understand why the others doing this problem could not get the right answer.
Perhaps, if you’re a nerd like me, or you teach math as I do, you even fell asleep thinking about this problem, baffled and frustrated about why you were unable to convince intelligent, educated friends that your calculation of this deceptively simple problem was accurate.
So, did you get 1 or 9? We’ll get to the “correct” answer in a moment.
But first, why do we get so riled up about these problems? People don’t usually get into fistfights at the bar over arithmetic, but these math threads are spectacularly vitriolic. A couple of factors are at work in these math debates, according to Robert Glenn Howard, a social psychologist at the University of Wisconsin–Madison who specializes in Internet communication and folklore.
For one thing, the whole point of Facebook and other forums is to provide a place for discourse and debate. Yes, there are your cousin’s new-baby pictures, and the opportunity to stalk a crush, but really, people go to social sites to say stuff. And argue about it. “People are already primed to engage in pretty intense deliberations, and that can bleed over into the way they play games,” Howard says.
And that’s exactly what these problems are: games. “Humans have used riddles as a form of play since ancient times,” Howard says. “And sometimes people can get competitive and wrapped up in it.” People use puzzles to show off their smarts, make others feel subordinate, and enjoy telling the story of the game later (as I’m doing right now).
Of course, the fervor with which some people debate basic arithmetic may be a proxy: There’s less at stake in a math debate than a potentially friendship-ending political debate. Arguing over multiplication may even be a way to make a subtle political point, using others’ “wrong” answers to reinforce a broader worldview, such as that the United States has poor math education.
But why do the debates often go on so long? One reason is psychological, another mathematical.
Math is already a source of anxiety for many people, and adding an audience ups the ante. “When there’s an audience, your performance can change,” says Sian Beilock of the University of Chicago and author of Choke: What the Secrets of the Brain Reveal About Getting It Right When You Have To. Emotional stress can overtake our limited reserves of “cognitive horsepower.” “Often people feel the most stressed when the audience is made up of people they know. It’s very painful to fall on your face in front of your friends and family.”
So people dig in, not realizing the other reason these debates drag on—a mathematical one. We are taught to think of math as an absolute discipline without ambiguity. To an extent, that’s true: Two plus two is always four. But while the math itself lacks ambiguity, the way we express that math requires a system of symbols—otherwise known as language. Consider how often people debate grammar. Math has syntax just as language does—with the same potential for ambiguities. And just as word-based riddles exploit the ambiguities of language, so do these math problems.