Is change merely an illusion? In the Fifth Century BC,
Greek philosopher Parmnides proposed that the universe
was not made of “many” things, but rather, is a single, indivisible substance-
an eternal “now” that encompasses all time and all entities.
And if the universe is one- then all change is impossible. For the very idea of
change suggests something transforming from one state to another. But since according
to Parmenides, all states occur simultaneously, change is impossible.
After receiving heavy criticism from his contemporaries, Parmenides’s student
Zeno of Elea came to his defense by creating a series of paradoxes that seek to prove that
time and change are, in fact, utter nonsense.
Consider a situation in which a motorcyclist races a man on foot.
Lets assume the man is given a 50 meter head start. By the time the motorcyclist reaches the 50
meter mark, the man will have moved a small distance forward. And when the motorcyclist
catches up the ensuing spot, the man will have moved farther still. If there are an
infinite number of measurable distances between any two points, the man will always stay a
minute distance ahead of the biker. This, then, will go on indefinitely, and the biker
will never catch the man. But this is absurd. For our perceptions tell us the
motorcyclist would quickly overtake the man. Therefore, Zeno’s paradox tells us that
our perceptions are flawed and that a change in distance is preposterous.
In another of his paradoxes, Zeno talks of an arrow being shot at a target.
If it takes the arrow 1 second to travel 60 feet, it would take .5 seconds
to travel half that distance, a quarter second to travel half THAT distance and so on.
If this process continues, we will eventually reach a unit of time during which the arrow
will occupy a space at complete rest. Let’s call this unit of duration- less time a “moment.”
If the arrow’s trajectory is the sum of these stationary “moments’, then how will
the arrow ever reach its target? And thus, motion is nonsensical.
Zeno’s paradoxes have challenged scholars, philosophers, and mathematicians
for over 2500 years. If nothing else, they force us to continuously reconsider our
reasoning about the nature of space and time.