Quick Take
Zeno’s Paradox

How a centuries-old thought experiment taught me something important.



Zeno, an ancient Greek philosopher, is most well-known for his list of paradoxes trying to prove that motion was an illusion.

Here’s an interesting brain teaser to think about. My dad told me this a couple of years ago, and I still remember the gist of it.

Imagine yourself in an empty room. Your back is against the wall, and you’re facing a strangely blank wall across from you. 

Suppose you wanted to cross the room so that you could touch that other wall. In order to go all the way, you would have to cross half of the room to do so. And once you’ve crossed that half, you would have to cross the next half. And once you do that, you have to cross the next half, and the next one, and the next one…

Here’s when it gets tricky, though. If you follow this logic, then theoretically, you wouldn’t reach the other wall at all. You would only be going to each halfway point, no matter how minuscule the next one might be. You would get very close to the wall, but you would never touch it at all.

The story stuck around with me all this time mainly because it demonstrated the underlying concept so well. Your math teacher might have introduced this concept as an exponential function, a particular mathematical function that doesn’t touch the x-axis at all. This function, in fact, describes just one part of a larger set of theoretical problems, all of which are roped together under one name: Zeno’s Paradox.

I bring this up, however, only because of the effect this teaser has had on me. I remembered the whole idea behind exponential functions years after I had last seen and plotted one in my math class. And it’s because of this that I wish math was sometimes taught this way. Instead of through pages from textbooks and videos from YouTube, perhaps describing math through a fun, engaging story or mental experiment would make the concept stick around longer.

For, you see, I’m not exactly a math person. I can do math, and often correctly, but a month or two after the concept is introduced, it usually starts to fade from my mind. I’m often so busy moving from one type of math to the next that I forget to practice that certain math skill. 

My suggestion isn’t the be-all, end-all solution for teaching math (or just about anything) to students; there’s still a time and place for textbooks, YouTube, Khan Academy, and note-taking. It’s just that for me, and perhaps a few other students as well, this device would be very, very helpful if it were incorporated into classrooms.