Culture

This TikTok User Asked If Numbers Are Real, And Accidentally Started 2020’s Biggest Argument

Teen Gracie Cunningham accidentally stumbled into one of the oldest arguments in the philosophy of mathematics.

by Joseph Earp  28 August 2020
Gracie Cunningham TikTok numbers real

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Earlier this week, TikTok user @gracie.ham — real name Gracie Cunningham — recorded a short video in which she accidentally hit upon an ancient debate in the philosophy of mathematics.

Applying make-up, chatting conversationally to the camera, the teenager explained her belief that maths “isn’t real.”

“I know it’s real because we all learned it in school or whatever,” she says. “But who came up with it? … How? … I get addition. Like hey, if you take two apples and add three, you have five, or whatever. But how would you come up with the concept of like, algebra. What would you need it for?”

In the hours after the TikTok went live, the clip gradually migrated to Twitter, where Cunningham was condemned for posting “the dumbest video” anyone had ever seen. Before too long, the TikTok user was being roundly mocked, with some suggesting that her video only proved that she failed algebra.

But here’s the thing. I spent years of my life studying the philosophy of maths, which means I spent years of my life sitting in a classroom asking precisely the same questions as Cunningham.

Her video doesn’t display an ignorance of mathematics. It displays a great insight into one of the most pressing questions of our time, an issue so vast and complicated that esteemed philosophers remain deeply divided on it up to this very day — are numbers discovered, or created?

Let’s dive in.

Where Do Numbers Come From?

Like all the great debates in philosophy, the rift over the existence of numbers forces you to support one of two equally bizarre alternatives. Either you are committed to believing that numbers are real objects that we discover, rather than create — non-physical entities that we come into some kind of contact with when we do sums. Or, you are committed to believing that numbers are not real, and that we have merely collectively hit upon a shared, totally artificial system that everyone somehow agrees on.

Let’s examine the first point of view. People who believe in “real” numbers refer to themselves as Platonists, so-called because of the ancient philosopher Plato, who popularised the idea of non-physical, idealised realms.

For Platonists, on a planet with no human beings, the concept of “5” would still exist.

Platonists believe that numbers are real objects that exist outside of human thought and language. That means, for Platonists, on a planet with no human beings, the concept of “5” would still exist. Would it be called by that name? No. Would it be represented by the symbol “5”? Not necessarily. But the concept of 5 as we know it would exist.

Platonists have lots of arguments to back up their position. The most obvious, probably, is the fact that we all seem to agree on mathematics. Maths isn’t a matter of opinion, in the way that cultural norms or ethics seem to be. I can show you that 2 plus 2 equals 4, and if you don’t think so, then you’re wrong.

That’s not true, many people think, of other kinds of arguments. If I like Rambo movies and you don’t, it doesn’t seem that I can say you are “wrong” in the same way that people who don’t think 2 plus 2 equals 4 are wrong. That’s as much as I would like to say you’re wrong, given the Rambo movies are great.

Moreover, mathematics helps explain the world around us. This is called the “indispensability argument.” The basis of science is mathematics. When we shoot a rocket into space, we calculate all sorts of sums to do so. And those sums work — they help us understand and explain the world in all sorts of ways. Maths is indispensable to science. Therefore, anyone who gives up on maths must also give up on science. Or so the argument goes.

Platonists also have more exciting versions of this argument. My favourite concerns the hibernation patterns of a certain species of cicada. Creatures that emerge from hibernation at a different time to their predators live longer — animals are vulnerable when they emerge from hibernation, and need time to recover. Therefore, emerging from hibernation at a different time to predators is an evolutionary advantage, the same way that having wings is an evolutionary advantage if it means you can fly away from your enemies.

This particular species of cicada hibernates for 7 years. 7 is a prime number, meaning it is only divisible by itself and one. That means that hibernating for 7 years is evolutionarily advantageous to the cicada — the cicada will only emerge at the same time as predator species if those species also hibernate for 7 years, which is unlikely, or only hibernate once a year, which is rare. Contrast that to a creature that hibernates for 12 years. The creature that hibernates for 12 years will emerge from hibernation at the same time as predator species that hibernate in 1 year, 2 year, 3 year, 4 year, and 6 years cycles.

The number 7 and the rules of prime numbers are useful to the cicada. Not because the cicada “knows” what numbers are. But because numbers are a fact in the world that provide evolutionary advantage to the cicada.

Of course, no Platonist thinks that numbers physically exist. They don’t think that you can point to the number 5, for instance. Instead, they think that numbers are abstract, non-physical entities.

If that sounds weird, it’s because it is, and pretty much every Platonist admits so. Believing in a realm of non-physical entities is wild — it’s essentially like believing in a “number heaven”.

Wilder still is the question of how we’re meant to access this number heaven with our brains, when our brains are made with physical stuff. How does the abstract material of numbers influence and get involved with the material of our heads? It can’t be through the regular method of causation, because we know causation only occurs when two physical things come into contact.

Most Platonists don’t actually have a theory of how we are meant to “know” mathematical objects. But they don’t need a theory, because the argument they oppose, that we just made up numbers, is also super fucking weird.

Super Weird Shit

Maybe Platonism sounds obviously wrong to you. But the alternative, that numbers are created, seems even stranger to most. If you believe that numbers are merely invented, then how do you account for the fact that different ancient societies across history developed unbelievably similar systems independently of one another? Coincidence? That seems odd.

Odd, but not impossible, for the record. But what seems even harder still is making an argument for how science works when you’ve given up on the existence of numbers. Most of us want to defer to science as a special way of understanding truths — truths that exist in the world. Science uses numbers to do this. So if numbers are just constructed, then science doesn’t get to have this special insight into the “real” world.

Therefore, if you believe numbers are created, you have a couple of choices. You can either give up on using science as a way of understanding the world. That would be a big bullet to bite. Or, you can try to develop a science that doesn’t use numbers.

Some people, insanely, have actually tried to do this latter option. The most famous attempt was by Hartry Field, an American philosopher and mathematician. Field is a proponent of mathematical fictionalism, the belief that numbers are “useful fictions” that should not be taken as literally true.

But though Field’s attempts have impressed some, the debate is far from over. The philosophy of mathematics has reached nothing like a consensus in a long, long time.

Which is why it’s extraordinary that Gracie Cunningham, a young TikTok user who dropped one, short, sharp video, stumbled into one of the most fascinating debates of our time.