At some point in high school, one of my favorite teachers had me read a book about math. The book was called Zero: The Biography of a Dangerous Idea. After reading it, I started to regard math as more than just a numbers game, but rather as philosophical in its own way.
One key idea that the book's author exemplifies is Zeno's Paradox of Achilles and the Tortoise. In a nutshell, this mathematical conundrum is premised on the idea that despite being much faster than the tortoise, Achilles can never overtake the tortoise in a race if it begins with a headstart. Logically, this checks out. Imagine that the tortoise is one hundred feet ahead of Achilles. By the time Achilles reaches that point, the tortoise has advanced another fifty feet. When Achilles advances another fifty feet, the tortoise advances another twenty five, and so forth. This goes on infinitely, and Achilles technically never catches up. As Charles Seife (the book's author) illustrates, the Paradox is explained with the concept of convergent series, which was not around in the days of the Greeks.
But I'm no engineer: I study the humanities, after all. So I bring this topic up for another reason altogether. Zeno's Paradox is important to me because of the way in which I think about my goals and time horizons, and how I'd like to change that. And more broadly, Zeno's Paradox suggests an important idea about the fleeting quality of life.
I try to run a healthy amount to stay in shape. In fact, it's a goal of mine to run six miles every week. When I'm not away from school, this works out numerically well for me, as one lap around my block at home is almost exactly one-third of a mile. So if I'm doing a two mile run, it'll mean six laps around my block. While this is useful when it comes to measuring exactly how much I need to run, I often find myself applying a kind of Zeno's Paradox framework in motivating myself to keep going.
After one mile, I'll begin to hear a nagging voice telling me that I just need to make it another half-mile (since this is technically an easier goal to achieve than completing another full mile). Upon reaching that point, the voice will start up about another quarter-mile. Then, an eighth-mile (lose yourself), and suddenly, my run will be over. When it comes to running a couple of miles, this kind of mindset isn't too problematic. But I think that the underlying idea it illustrates is.
To put it another way, I went to a high-stress high school. It was technically a seven-through-twelve grade school, so I experienced a total of six full school years there. Ultimately, high school was a good time: I made some great friends; I had some memorable experiences in New York City; and I learned so incredibly much. But just like on my runs, I often self-motivated Zeno-style, convincing myself all too often that I had x amount of time to go until y, at which point I'd be z of the way through my time there. Sure, it kept me going. But it also had me thinking all too far ahead. I was focused on getting out. I wanted high school to be over.
Between my summer job, final exams, and my occasional exercises, I've noticed that I do this whenever I need to wait something out. I think like this whenever I'm unhappy with a situation. I self-motivate in this way when my goal is simply finishing. But I realize that time is precious: especially at this particular stage in my life. It makes me consider how I've got to change my attitude when it comes to situations I'm not happy about.
You can always quit, but you shouldn't. That's the first step: choosing to commit. If you make it that far, the next important thing is to keep going (that's step two). But the final, most important step involves positive self-motivation. I'm not talking about Achilles and the Tortoise. I'm talking about finding something about the situation to love, or trying your hardest to discover something positive about it.
The next time I go for a run, I'm going to try and focus on the good weather, or how nice it feels to get active. If only he had stopped worrying about each increment of the race, I think Achilles would have beaten the tortoise in no time. Sure, it's true that calculus refutes Zeno's Paradox. But so does a better outlook.
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