Zeno's Paradox

Almost 2,500 years ago, the philosopher Zeno of Elea set out to challenge the way we understand the physical world through a set of brain teasers that have stuck with us for millennia. The most powerful of Zeno’s paradoxes grapple with the concept of infinity while pitting observable reality against the scientific language we use to describe that reality, suggesting that elements of the everyday, like motion and speed, are actually illusory.

Over the thousands of years it took to finally wrap our brains around his most famous paradoxes, they revealed weaknesses in the tools we use to understand the basics of space and time. More than just riddles, they have pushed mathematicians and philosophers to be more rigorous and precise in the logic we use to describe the concepts at work in the paradoxical traps Zeno so cleverly set.

Calculus would finally explain the paradoxes, but even then it took hundreds of years to refine the math. The most recent major breakthrough in understanding the tension between the infinite and the finite, the core of Zeno’s paradoxes, is just a few decades old. And some people—philosophers, mostly—are still toying with the tricks the paradoxes play on our minds. Here’s a finite description of an infinitely frustrating set of questions.