Where are we going?

“Zeno’s paradox goes like this: Suppose a student wishes to step to the door, which is 1 meter away. (We choose a meter here for convenience, but the same argument holds for a mile or any other measure.) Before she arrives there, she first must arrive at the halfway point. But in order to reach the halfway point, she must first arrive halfway to the halfway point – that is, at the one-quarter-way point. And so on, ad infinitum. In other words, in order to reach her destination, she must travel this sequence of distances: 1/2 meter, 1/4 meter, 1/16 meter, and so on. Zeno argued that because the sequence goes on forever, she has to traverse an infinite number of infinite distances. That, Zeno said, must take an infinite amount of time. Zeno’s conclusion: you can never get anywhere.”
– Leonard Mlodinow, The Drunkard’s Walk – How Randomness Rules Our Lives