Finals week is looming, and we’re all overwhelmed. Does it feel impossible to get to school or finish your work these days? It’s worth trying the following learned argument to convince your professors that it really is.
To get to school or finish an assignment, you have to complete infinitely many tasks. This assertion has been around since the ancient Greek philosophers. It’s called Zeno’s paradox, and applies to many situations, from running a race to walking into a wall. Most calculus classes discuss it, but Wikipedia also has less technical information for those who are interested.
There’s an argument that even reaching school is impossible. Let’s say there’s a mile between your home and the UW campus. Before you reach class, you have to walk the first half-mile. Then you must walk half the remaining distance, which is a quarter mile.
At every stage, you need to travel the first half of the remaining distance before you can begin the second half. This process carries out forever; you can always cut the next distance in half and make an even smaller one. This means you have an infinite number of distances to walk, just to get to school!
The same argument works for those impossible term papers. You have to write the first half, then the next quarter, then the next eighth, and so on. How can you possibly be expected to complete a paper that involves an infinite number of writing tasks?
Of course there’s a counter argument. You can tell your professor he or she is demanding infinitely many tasks that nobody could ever finish—this time of year, it certainly feels that way. However, the professor will undoubtedly point out that some irritating people show up to school and complete their papers, so it must be possible.
The explanation is that adding infinitely many things together doesn’t mean the answer has to be infinite. For example, to walk the mile you travel one-half, plus one-quarter, plus one-eighth, plus one-sixteenth, etc., of the distance. The more terms you have, the smaller they get. You are adding up an infinite series of really, really tiny steps, and the answer approaches a definite limited value of one mile.
This means that contrary to our feelings, it’s entirely possible to show up and finish schoolwork. However, if your professor has never taken calculus and doesn’t read this column, try sounding confident and mathematical when you say the class is definitely impossible. You might get away with it!
Is School impossible story.
