At any single instant, a flying arrow occupies a space equal to itself.
Therefore, it is motionless. But if it's motionless at EVERY instant...
1. At any single instant of time, the arrow occupies a space exactly equal to its own size.
2. To move, an object must change position.
3. But in an instant (which has zero duration), there is no time for position to change.
4. Therefore, at each instant, the arrow is motionless.
5. Time is composed entirely of instants.
6. Therefore, the arrow never moves!
The arrow paradox reveals a deep confusion about the nature of motion and instantaneous states. There are several modern resolutions:
Motion isn't about position at an instant—it's about the relationship between positions at different times. Velocity is defined as a limit:
The arrow at an instant has a well-defined velocity even though it occupies a single position. Velocity is a property of the arrow's trajectory, not just its position.
Zeno assumed time is made of instants the way a line is made of points. But points have no length, and instants have no duration. You can't "add up" zero-duration instants to get time any more than you can add points to get length. Motion exists in intervals, not at instants.
Modern physics offers a surprising perspective: at the quantum level, particles don't have precise positions AND momenta simultaneously (Heisenberg uncertainty). The classical picture of an arrow "at a position" might be an idealization that breaks down at fundamental scales.
Zeno's paradoxes challenged mathematicians for 2,000 years. Their resolution required developing rigorous concepts of limits, continuity, and the real number system. They remain philosophically interesting even today, as they probe the nature of space, time, and change.