CH 41: Zeno Paradox in Time and Space
If you have ever wanted to consider the paradoxical nature of infinities, look no further than Zeno's Paradox. Zeno was a Greek Philosopher who posed a set of intractable riddles that illustrate effectively the paradox of infinity. This paradox is so confounding that in a sense it uses math to imply no one can ever get anywhere. Let’s dive into the specifics to see what craziness I speak of. Start by thinking about the classic problem of trying to get from point A to point B. The points themselves do not matter so it can be from wherever you are to the nearest door or Philadelphia to New York City, to offer two quick examples. Now, when you think about traversing this distance from point A to point B, it is a simple exercise to imagine that in order to cover this distance you first must go half of this distance. Now, imagine that of the remaining distance you have to go, you go half of that. You will continue to go half of each new remaining distance. This can be represented as the sum of the series ( 1 + 1 + 1 + 1 +….). This series is an infinite 2 4 8 16 number of ever-smaller values. But how can you go an infinite number of distances in finite time, regardless of how small those distances might be? While a branch of mathematics called internal set theory has come close to resolving the paradox, it remains a clever illustration of the problems inherent with infinity in a finite world.