Why didn’t the chicken cross the road? According to the ancient philosopher and logician Zeno of Elea (c. 495–c. 430 BC), the bird simply found it impossible to get to the other side.
Here’s why: To cross the road, the chicken first has to strut to the halfway mark. That’s easy enough. But then, logically, the bird has to fly, hop, or flutter half the remaining distance to reach the three-quarters point. After that, it has to cover half the remaining distance. No matter how far the chicken goes, it still has half of an ever-smaller remaining distance to travel. Therefore, Zeno concluded, nothing can ever really get anywhere.
The scenario is the most famous of Zeno’s paradoxes, a set of logical riddles that have perplexed and infuriated philosophers for 2,000 years. The paradoxes are the most famous legacy of the Greek-speaking logician, who taught at a famous philosophy school in southern Italy.
Like the above dichotomy paradox, several of Zeno’s other paradoxes were also “arguments against motion.” One, the story of Achilles and the tortoise, asks whether a fast runner can ever catch up with a slowly moving tortoise that has a head start. The runner first has to reach the tortoise’s starting point. But because the tortoise will have crawled to a second location by then, the runner still needs to keep moving. By the time the runner reaches the tortoise’s second position, the tortoise will again have moved. No matter how speedy he is, the runner can never catch up.
Of course, as Zeno knew, runners do catch up with and pass slower objects. And sometimes, the chicken really does cross the road. The provocative question Zeno raised in his paradoxes is—how?
Little is known about Zeno’s life. His influence, however, was great. By challenging his students to ponder the underlying dynamics of motion, Zeno inspired thinkers who would make major discoveries in mathematics and physics.
Zeno came to a violent end when he was implicated in a plot to kill a local tyrant. Under torture, the philosopher refused to name his coconspirators, instead biting off the ear of his torturer—first halfway, then all the way—before he was executed.
ADDITIONAL FACTS
- Zeno was born in the southern Italian town of Elea, which is now known as Velia. At the time, the area was under the control of the Ionian Greeks.
- Another of Zeno’s famous riddles, the “arrow paradox,” questions whether an arrow can ever actually move. The scenario asks, If every object that occupies a single space is at rest, and if any object when in motion occupies a space at any particular moment, then how can an arrow move at all?
- Rudimentary calculus, which was developed in the Greek world after Zeno’s death, provided solutions to some of Zeno’s paradoxes. Others have been “solved” by rejecting the philosopher’s fundamental premises. For example, the arrow paradox presupposes that the arrow is “at rest” at a given moment, but that is not a condition that is ever actually met, since Earth is in constant motion.
