Two Plus Two! Really?

Apparently on Twitter, people have been arguing as to whether or not two plus two might make five. And you thought 2020 couldn’t get any stranger. While no one on Twitter can ever be sure that they’re supposed to be taking what people say seriously, but there were, what appeared to be a large number of people trying to argue that 2 + 2 didn’t necessarily have to equal 4 and that there were other ways of approaching the problem that are just as valid.

I wanted to say something about it, but life was getting in the way. In the most recent episode of his podcast, James Lindsay basically confessed that it was all because of something he said. He also wrote a long article over on the New Discourses blog he leads.

I listened to it at 2x speed so you don’t necessarily have to. But apparently it stems from an Instagram graphic series called “Woke Minis”. One of his followers appended it to a thread with Hannah Nicole Jones (of Project 1619 fame) and it set off a little kerfuffle.

What followed made every bit as much sense as you might expect it to given that this is 2020 and we all have too much free time on our hands.

But it does raise an interesting question. Who does get to decide what two plus two equals? Means? Represents? Who’s in charge of this thing anyway? The answer is simultaneously everyone and at the same time no one. Many people think of math as an abstract monolith that was delivered from on high. God created Adam and Eve, and also proclaimed that there would be universities subdivided into the following departments…

Math is that branch of human knowledge seeking that grows out of trying to be as clear and precise with language as possible. When every word, symbol and concept is rigorously defined and you try to make sure that everything works together without contradictions, what comes out is the field of math. The rules evolved over time based on what people (presumably the really smart ones) needed to do and found useful. So addition exists because it’s something that many people found to be a useful tool in their lives and wanted a common way to talk about it. And to be as useful as possible, it should be as general as possible. Take any objects, put down two of them, put down two more, count. Now there are four. This is an undeniable fact about the way our universe works. Addition is just a substitute for speedy counting.

Now the question comes, does it have to be this way? Must it always be four? Who decided that it was always four? For our universe, it seems to just be a property of the way things work. We’re not claiming ahead of time that it couldn’t be otherwise, but at some point we will be better off if we accept universe as it is, rather than trying to concoct weird alternative laws of counting.

The rules of math are somewhat arbitrary and somewhat not. The fact that we use the particular symbols we do. The fact that we write left to right, not bottom of the page to top. But at the end of the day, the rules have to produce answers that are useful to someone. (And the more broadly useful they are, the better they are.) A rule that puts two apples beside two apples and tells you you might have five apples just isn’t useful to anyone.

This is a shocking idea when you first encounter it. The rules of math are just made up? That seems unfair. Nobody consulted me. Forcing me to learn this has to got to be some sort of violation of my rights. If I don’t play along with this game, you’re going to give me bad marks that will shape my future education and career prospects? At what point does it stop being teachers trying to give you the condensed benefit of centuries of smart people figuring things out, and just plain dogmatic oppression? Yes, the rules are made up. But there’s a difference between rules just being made up, and rules being chosen for good reasons. And English doesn’t have a good way of making that distinction clear.

Could you make up your own rules? Sure. You can make up your own version of chess where Rooks move diagonally, Bishops move horizontally and Kings have teleportation powers on Wednesdays. But you would have to persuade people that your version of the rules was worth switching to. Maybe it’s more fun, maybe it’s more challenging. But changing the rules and then referring to the old rules as oppressive by itself won’t get you anywhere, except possibly made fun of. Take a more extreme example where everyone is driving on the right side of the road and you want to explore driving on the left. The real world consequences will manifest for you very soon. Math is the same way. Sure you could make up your own rules because you feel they’re more elegant, or they make your life easier, but there’s no guarantee anyone will give you a job to put your version of math into practice. It’s that you’re new at math, so the odds that you will come up with some useful new way of doing anything is infinitesimally small.

Eventually, the motivation becomes clear. Math is hard. But it also has very high value in the real world. But some people are not great at it. And it’s more or less accepted that we as a society suck at teaching it. There’s a fraction of kids for whom it comes naturally, but a much larger fraction that need to be dragged through it kicking and screaming.

As a society, we’ve already normalized being “not a math person”. If you’re willing to casually admit that you aren’t good at it, we won’t hold it against you. But at what point in your life are you permitted to make that opt out? At the end of high school? At the end of middle school? When memorizing times tables seems too challenging? On one hand, we don’t want people to hate school. But also, cutting off a subject like math too early closes real doors on your future education and career prospects. Then again… if they are so traumatized by math that they drop out of school altogether, that would be worse.

So really what I see in this protest against 2 + 2 = 4 is a poorly articulated complaint that math education is substandard. And for most large organizations, when the students aren’t performing well, normally what you do is publicly say that you’re going to improve your teaching methodology (re-write the curriculum, and so forth) and then just quietly lower the standards so on paper everyone is doing better.

And don’t get me wrong, math curricula are really in need of a re-write. Most high school programs would benefit instantly if they stripped out all of the trigonometry and replaced it with probability and statistics. And there’s an argument for less calculus and more linear algebra. But the way forward doesn’t lie in exploring “other ways of knowing” or designing ethnic math courses, but just finding teachers who know what they’re talking about and teaching consistently better across all grades.

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