Infinite Carrots on the Horizon

Hello, hello, and welcome to T.E.A. Time with Tayvin Bayless. To my returning listeners, it’s great to have you back. What is something you enjoyed about your language study this week? If you’re new here, hopefully you won’t be turned away by the strange topic I’ve chosen for today.

Earlier today, I was having a discussion with a student about the concept of infinity. Depending on how you think about it, infinity can be a truly mind-bending concept. It can take things that seem mundane, meaning everyday and ordinary, and turn them into insurmountable problems, problems that seem impossible to overcome. In our discussion, he brought up Zeno’s paradox of Achilles and the tortoise. It’s a famous thought experiment from an ancient Greek philosopher that we will get into in more detail in a moment.

But before that, I want to introduce the phrase the carrot and the stick.

This expression is about motivation. Specifically, it’s about two different tools for getting someone to do something, used together. The carrot represents a reward, something positive you offer to encourage the behavior you want. The stick represents punishment, a consequence you threaten to discourage the behavior you don’t want. Together, they describe a complete approach to motivation: reward the good, punish the bad. Carrot and stick.

Now, here’s something interesting. This phrase has drifted from its original meaning over time, and the culprit is a cartoon. A popular image began circulating that showed a donkey with a carrot dangling from a stick just in front of its nose. The animal keeps moving forward, always reaching for the reward, never quite getting it. The image was charming and intuitive, and people began associating it with the phrase “carrot and stick.” But the image actually changed the meaning. In the original phrase, the carrot is a real reward that the animal sometimes gets. In the cartoon image, the carrot is always just out of reach. The animal is being tricked, not rewarded.

That’s a pretty striking picture if you think about it. The carrot always in sight. Perpetually, meaning always and continuously, out of reach. The animal keeps moving, always reaching, never arriving.

Keep that image in mind. A goal that’s always visible but not quite reachable.

And that brings us back to Zeno’s paradox.

The story begins with Achilles, the greatest athlete of ancient Greece, deciding to race a tortoise. He has nothing to prove and everything to lose, so I have no idea why he would ever agree to this race. Whatever his motivations, he knows the tortoise is no match for his speed, so he decides to give it a significant head start. The tortoise will run 100 meters before Achilles leaves the starting line. The terms are set, the eager crowd awaits, and the race begins.

The tortoise was off like a rocket! Excuse me, I must have misread my script. The tortoise walked at a very leisurely pace, leisurely meaning slow, relaxed, and in no hurry at all. Once the tortoise had reached 100 meters, Achilles was off like a rocket! That is to say, he ran incredibly fast. He covers the hundred meters in no time at all. But when he crosses that 100-meter mark, the tortoise has moved another 10 meters. So Achilles runs those 10 meters, but the tortoise has crossed another meter. When Achilles covers that meter, the tortoise has crossed another 10 centimeters. And this continues forever. Because space is infinitely divisible, meaning you can break it up into smaller and smaller parts without end, Achilles is never able to fully close the gap. Or so Zeno argued.

You may be like me in thinking that this story is a bit ridiculous. Zeno was trying to prove that motion, or movement, is impossible. As someone who moves every day, I disagree with his conclusion. But I do think there is a real-world experience that feels very similar to what Zeno was describing.

In the summer of 2017, I moved to Japan. From day one, I was expected to go out and talk to people in Japanese. My skills were very limited, and so my early days in Japan were filled with a lot of stress, worry, and frustration. I wanted to express myself as well in Japanese as I could in English, but that just wasn’t possible. I studied every single day. I talked to hundreds of new people a week. And yet the progress felt agonizingly slow.

A few months passed, and my Japanese improved. I could hold simple conversations. But I remember thinking again and again, “If I just master this grammar point, or learn how to use this phrase, then I’ll be fluent.” It was a goal that always felt just a few weeks away. Those weeks would pass. I’d learn the grammar. And I’d still feel just as limited as before. It was like chasing a dangling carrot on a stick. The goal was in sight, but perpetually out of reach.

I have worked with many students who seem to feel the same way. Maybe you have felt that way too.

This is where I want to come back to the idea of infinity. When we think of infinity as a number, something to wrap our heads around, it is daunting, meaning intimidating and overwhelming before you even begin. It is so far from our everyday experience that it can seem impossible to understand. We end up reaching conclusions like Zeno’s: motion is impossible, progress is an illusion, and the gap can never be closed.

But infinity isn’t a number. It’s a process. And so is fluency.

As I mentioned in a previous episode, language is infinite. English is always changing and always evolving. If our goal is to fully understand English, to never make a grammar mistake, or to always know exactly the right thing to say, we will feel like we are never quite reaching it. Because we aren’t. That finish line doesn’t exist.

But here is the thing. That is not bad news. It is actually the most freeing idea in language learning, once you see it clearly. We will get to that in just a moment.

Let’s come back to that carrot on a stick.

I used that image in the story to describe what language learning can feel like. Always reaching. Never quite arriving. The goal perpetually in sight and perpetually out of reach. And I think that image is accurate, up to a point.

But here’s my problem with it. That donkey chasing a carrot it can never reach is a picture of futility, futility meaning effort that produces nothing, striving toward something that was never meant to be caught. The animal moves, but only because it’s being tricked. There’s no joy in that. There’s no growth. There’s only the endless, exhausting pursuit of something that can never be reached.

That is not what language learning is. And I don’t want to leave you with that image.

So I want to offer you a different one. Chasing the horizon.

The horizon is the line where the sky meets the earth, or the sky meets the sea. It is always visible. Always distant. And even if you spend your entire life traveling toward it, you will never reach it.

But here is what you will do. You will see things you never would have seen from where you started. You will cross mountains and oceans. You will meet people you never would have met. You will become someone you never would have become. The horizon is not a destination. It is a direction.

Fluency is the horizon. You can spend your whole life moving toward it and never stand on the line where the sky meets the ground. But along the way? You will read books that change how you see the world. You will have conversations that make you laugh, or cry, or think differently. You will understand a song, or a joke, or a moment of human connection that would have been invisible to you when you started.

The carrot on the stick is a trap. The horizon is an invitation.

So here is your challenge before the next episode: the next time you feel like fluency is out of reach, ask yourself what you can see from where you are now that you couldn’t see before. That’s not failure. It’s the view from the road.

Chase the horizon.

Zeno looked at Achilles chasing the tortoise and concluded that motion was impossible. But Achilles was moving. The gap was closing. The math said one thing and the reality said another. Zeno was right about the numbers and wrong about the world.

Language learning is the same. The math of infinity says you will never know all of English. And that’s true. But the reality is that people learn languages every day. They make progress every day. They have conversations they couldn’t have had yesterday, and understand things they couldn’t understand last year. The gap closes. Not all the way. But enough.

When I was in Japan, I didn’t become fluent in a moment. I went on a journey in that direction, and one day, I woke up and realized I was somewhere completely different from where I started. And I began to enjoy the view.

Don’t chase the carrot. Chase the horizon.

Every day, and enjoy the view along the way.

And with that, my cup is empty. Thanks for joining me for T.E.A. Time. Until the next pot.