Existential Geometry: Don’t Be An Asymptote

Everything is made up of lines. As humans we spend our days drawing lines, crossing lines, walking lines, or signing on dotted lines. We drive inside of lines, we stand in lines, we argue over property lines, and lines of code make up how you see this blog entry. Lines are important. Lines give our world meaning it would not have without them. We live our lives in relationship to lines.

Today I was teaching geometry, which at first seems harmless enough, but when people wrote the book on analytic geometry something tells me what goes on in my brain isn’t exactly what they had in mind. Today when explaining parallel lines to a student it occurred to me how sad parallel lines would be if they had human characteristics. We know that parallel lines are always the same distance apart. They will never touch. They never get any closer than they were the day before. They point in the same direction. The old joke goes, “Parallel lines have so much in common! It is a shame they will never meet!”

The better existential question is do the parallel lines know each other exists? Do they whisper across the plane? Do they know just how congruent they are? They are always moving in the same direction, but will never share a common point. How many people do we pass in the halls at work or on the road in our cars and we might all be driving toward a common location, but we will never meet? We might be listening to the same radio station, eating the same breakfast, or drinking the same brand of coffee, all while never knowing this, and will never come to a point in our lives where we do know this. I think of this kind of line cinematically as The Lake House. In order for those two lines to meet, they had to move to an entirely different plane. I’m glad they did too, because what a frustrating plot otherwise!

There are also lines that intersect. You can have intersecting lines, and some of those intersecting lines happen to be perpendicular. I know I have met a lot of people that I have come into contact with at some point in my life, and I have no idea where they are right now. The geometrical reason for this is we weren’t perpendicular lines. Perpendicular lines are interesting, because they aren’t as tragic. Two lines are perpendicular when they are right angles to each other. Perpendicular lines meet. They meet at one spot. We know that when they meet at this one point, they form a right angle. There is hope there, right? They meet! And when they do, they form not just an angle, but a right angle. Intersecting lines are the Casablanca of the movie world, while perpendicular lines are more When Harry Met Sally. You do have to realize though that even Harry and Sally knew when the time was right to be perpendicular. For a while we were all on the edge of our seats.

There is but one winner for the saddest existence when it comes to lines. It goes to the asymptote. Asymptote derives from Greek meaning “not falling together.” These lines come as close as you can get and never intersect. They appear as though they might intersect, and as soon as they have you persuaded they are going to intersect, they run parallel all the way to infinity. I think of this kind of line as the movie Lost In Translation. I’ve also never forgiven the movie writers for that ending, but I digress.

Archimedes said, “The shortest distance between two points is a straight line,” but once you grow up you realize it is a lot more complicated than that. You see that rarely are lines straight, rarely are they what you imagine them to be, and you tend to want to color outside the lines just a bit. You also realize that the best of friends know how to read between your lines, and most importantly the most critical line is your smile. As long as you still have that, you have everything.

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