We assume it for granted. You walk from one corner of the room into another, cars pass along the street, the Earth turns upon its axis. In ancient Greece there existed the philosopher Zeno of Elea who created a sequence of puzzles (known as Zeno’s paradoxes) that call into question the very reality of movement itself. If the argument is sound, motion might very well not be what we think it is. Indeed, it might be impossible.
One of his most well-known paradoxes is the Achilles and the tortoise paradox. We have Achilles, the great fast runner of the day, running a race against a slow tortoise. To make the race fair, the tortoise begins a little ahead of the starting point. Before Achilles arrives at the starting point of the tortoise, the tortoise moves a small distance further. Before Achilles arrives there, the tortoise moves another step. No matter how fast Achilles runs, he must continually “catch up” to where the tortoise was, and the tortoise is one small step ahead every time, every single time. Zeno arrives at the conclusion that Achilles will never be actually able to catch the tortoise.
Another difficulty is the paradox of the dichotomy. You need to cross any distance first by getting halfway through it. Then you need to cover half the distance you just were covering, and half the distance you just covered, and so forth ad infinitum. The process is reduced to an infinite number of tiny steps. How can you ever complete crossing the room if there are infinitely many “halves” you need first reach?
At first blush, these paradoxes make movement impossible. Since movement of any kind involves taking an infinite number of steps, movement should never even begin at all. But we clearly move every day. So what is going on?
Scientists and mathematicians respond typically with the mental framework of infinite series. There are infinite steps and not infinite time. If, for example, each step is half the length of the one prior, the total time yields a finite quantity. The tortoise is overcome by Achilles since the number of steps is infinite, although the steps are increasingly tiny and quicker, summing up toward a finite quantity of distance. In such a manner, the math “resolves” the paradox.
Those of Zeno, however, are mathematical paradoxes with more than mathematical depth; they are also philosophical puzzles. They compel us to think about our assumptions about reality. Do we actually perceive movement, or do we mistake the way our mind distinguishes the intervals and the instants? Zeno might be uncovering that our conceptions of infinity, continuity, and division are more complex than we think them to be.
Some contemporary thinkers relate the paradoxes of Zeno to those of physics. Quantum mechanics, for instance, does not observe subatomic particles acting like small billiard balls moving along smoothly through space. They are probability until you see them, literally “jumping” through odd trajectories. Even time itself, some theories propose, could not be smooth continuity but a sequence of discrete moments, like frames on a motion projector. In such a world, the paradoxes of Zeno appear strangely pertinent again.
Even beyond physics, the paradoxes have a richer metaphorical content. Consider your own life: any goal can be divided and divided into ever-smaller steps, study before the examination, memorize before studying, concentration of mind before memorizing. You can never seem to reach it because the process is endless. But, in life, we consistently reach ends despite the endless sub-divisions of the thinking process. Life, just like motion, appears to transcend the endless sub-division of the thinking process.
Zeno’s paradoxes teach us the limitations of our reason. Our intellect yearns for clarity, but extremes, such as infinity, cause it to stumble. Motion is not an illusion perhaps, but our grasp of it is definitely unfinished. The deeper lesson is one of humbleness: the world is too rich for our conceptions of it. Then is motion an illusion? Maybe not in practice, you can still pace back and forth across the floor. But as Zeno teaches, what seems evident is not quite that evident. Motion might not be the clear-cut reality we think it is, but a mystery occurring right under our very eyes, executed every step we make.