Friend Functions
When I was young, there was a program on our Macintosh LC computer called “Biorhythm II.” It was filed underneath the Games folder, but it really wasn’t a game by any means. In fact, it was little more than an intellectual curiosity, but for some reason it appealed to me, and I frequently opened up the application. The theory behind it was to explain the seasons of the human body and mind by speculating that our physical, emotional, and mental processes went through regular cycles of peaks and troughs, times when we were feeling alternately strong and weak. Given a birthdate, it would plot out three sinusoidal curves stretching as far back or forward as you wished in order to plot out your (or others’) personal cycles. You could even compare two people’s together, and this gave me no end of entertainment. I was always curious to see if my biorhythm would line up with someone else’s. Sometimes, mine would be totally opposite another’s, but every so often, I’d fine another person’s biorhythm lined up ever so closely to mine. I guess, being ever the math geek then as I am now, I was perpetually entertained by this.
Recently, a similar thing happened when I was given a rather interesting project for our game. I had to model power lines in a way that resembled reality. With the help of a few physics texts, some equations, and a few helpful Internet sites, I found out that the proper equation to model a power line sagging under its own weight was a catenary. I had no idea what the graph of the resultant equation even looked like, and so when I graphed it, it looked pretty much like a parabola. In fact, I honestly couldn’t tell the difference! And so, thinking I was clever, I figured I’d try just replacing it. Well, much to my surprise, between the power poles, the parabola worked nearly flawlessly. Everything worked just as expected. But only when it came to the regions outside of the poles did I realize just how different the two graphs were. They diverged completely outside the interpolation zone, as shown below:
Blue is the catenary; pink is the parabola interpolated between the power poles.
The above examples might be a very odd segway into a seemingly disjoint topic of friendship, but so it goes.
I’ve always been a firm believer that friends come into people’s lives for a distinct reason. Part of this stems from my religious background, believing that there’s a greater purpose and plan guiding a few subtle strings of the cosmos; part of it stems from the fact that lessons can be learned anywhere and anytime if you are willing to take the opportunity to learn and grow. The beginning of a great friendship is a wonderful time. Such beginnings are joyful just like the birth of a new child; there is new life in the world, delicate and gentle, yet that life is a thing of blooming beauty, and those times are full of passion and excitement. The friendships, just like that newborn child, continue to grow up and take firmer shape, and the excitement grows up with it, taking hold of more and more energy.
However, there comes an age when growth stops and decay starts. Our human bodies are not made to last forever, and the mortality rate of humans is still hovering around 100%. However, death is not a popular subject to dwell on here in America, and so very little do we like to discuss the end of a life... just as we don’t like to dwell on the end of an era. We wish to retain and prolong such times as long as we can, artificially extending the beauty of something to far beyond its customary life cycle. Ends make us uncomfortable. It’s simply a product of our culture.
It’s why there’s very little advice out there on the “ends” of friendships. People love to discuss the beginnings, but never the ends. Sure, people will come into our lives for a reason, but sometimes, uncomfortable as it may be, sometimes people leave our lives for a reason as well. Or perhaps... there’s really no apparent reason at all other than natural separation. People drift, and so naturally some people will drift apart. Oddly enough, the fact that we don’t think about this much is weird given that most relationships (in the terms of being significant others) don’t go the distance, and often they end with bitter feelings that cause a somewhat permanent rift. But friendships are one of those beasts that almost seems to be always assumed as a permanent fixture in our lives, things that will always be there until the end of time. Perhaps I feel this way because most of my experiences have supported this belief; though many of my friends and I will sometimes take on a wanderlust and drift away from each other for one reason or another, whenever we meet up again, possibly years down the road, all of the strong feelings that we shared back when we had first met will just come out as if they’d always been there the entire time. It’s as if those years of wandering had never really happened, as if not a day had passed since we saw one another last.
But to accept such experiences means that there is the necessity to accept that separations do happen along the way, that there are at least minor endings along our journeys. Perhaps friendships are like concurrent Interstates; two differently-numbered highways will travel along a stretch of road for some time, but in the end they almost always veer away from one another, each going unto their own destinations. Like the catenary and the parabola, the two shapes are almost synonymous with one another for quite some time, but in the end, after a while, they end up going their own ways, doing their own things. Though two may skate together for a time upon the ice rink of life, passions, priorities, and motivations change, and suddenly our emotional inertia moves us in a different direction, thereby separating the duet.
Yet no matter how it takes place, separation is painful. No matter which side one is on, provided one truly is a friend, there is anguish and hurt whenever something is lost or let go. The word “betrayal” has easily come to mind in both situations, naturally for opposite reasons. And that pain that cannot be escaped except by confronting it dead on, and that is scary, nerve-wracking, humbling, and... despite its necessity, difficult.
But I do believe that friends who are honestly true, even though there is a relational drift between them, don’t stop caring for one another. An ending is not necessarily a full stop at the end of a sentence, nor is it just an opportunity for mourning. Sometimes, despite how odd and difficult it is to say so, sometimes endings are perhaps necessary in order to stop and take a full assessment of our lives, to question our momentum, to try something new, and to eventually prepare for yet another beginning, hopefully a better beginning, a better present, a better now. For every thing, there is a season, and each of our seasons eventually come to an end. But on the other hand, after a time, the long, deep winter will one day become summer once again. And there is always the hope that, next year, I might be able to dust off that old Frisbee or baseball bat that I hung up and get back on the old horse and maybe give it another try. Maybe it’ll be better next time. Maybe next year will be so much better.
Endings are tragedies; this much is true. Both ender and endee suffer from the death of the old, each in their own separate ways. It is hard to get past. But I do have hope for the future; I do hope for better days. And Dr. Carl Sagan states it best when he says, in his 1980 show “Cosmos: A Personal Voyage,” wonderfully recreated by this YouTube auto-tune, “A still more glorious dawn awaits-not a sunrise, but a galaxy-rise, a morning filled with 400 billion suns, the rising of the Milky Way.”
Recently, a similar thing happened when I was given a rather interesting project for our game. I had to model power lines in a way that resembled reality. With the help of a few physics texts, some equations, and a few helpful Internet sites, I found out that the proper equation to model a power line sagging under its own weight was a catenary. I had no idea what the graph of the resultant equation even looked like, and so when I graphed it, it looked pretty much like a parabola. In fact, I honestly couldn’t tell the difference! And so, thinking I was clever, I figured I’d try just replacing it. Well, much to my surprise, between the power poles, the parabola worked nearly flawlessly. Everything worked just as expected. But only when it came to the regions outside of the poles did I realize just how different the two graphs were. They diverged completely outside the interpolation zone, as shown below:
Blue is the catenary; pink is the parabola interpolated between the power poles.
The above examples might be a very odd segway into a seemingly disjoint topic of friendship, but so it goes.
I’ve always been a firm believer that friends come into people’s lives for a distinct reason. Part of this stems from my religious background, believing that there’s a greater purpose and plan guiding a few subtle strings of the cosmos; part of it stems from the fact that lessons can be learned anywhere and anytime if you are willing to take the opportunity to learn and grow. The beginning of a great friendship is a wonderful time. Such beginnings are joyful just like the birth of a new child; there is new life in the world, delicate and gentle, yet that life is a thing of blooming beauty, and those times are full of passion and excitement. The friendships, just like that newborn child, continue to grow up and take firmer shape, and the excitement grows up with it, taking hold of more and more energy.
However, there comes an age when growth stops and decay starts. Our human bodies are not made to last forever, and the mortality rate of humans is still hovering around 100%. However, death is not a popular subject to dwell on here in America, and so very little do we like to discuss the end of a life... just as we don’t like to dwell on the end of an era. We wish to retain and prolong such times as long as we can, artificially extending the beauty of something to far beyond its customary life cycle. Ends make us uncomfortable. It’s simply a product of our culture.
It’s why there’s very little advice out there on the “ends” of friendships. People love to discuss the beginnings, but never the ends. Sure, people will come into our lives for a reason, but sometimes, uncomfortable as it may be, sometimes people leave our lives for a reason as well. Or perhaps... there’s really no apparent reason at all other than natural separation. People drift, and so naturally some people will drift apart. Oddly enough, the fact that we don’t think about this much is weird given that most relationships (in the terms of being significant others) don’t go the distance, and often they end with bitter feelings that cause a somewhat permanent rift. But friendships are one of those beasts that almost seems to be always assumed as a permanent fixture in our lives, things that will always be there until the end of time. Perhaps I feel this way because most of my experiences have supported this belief; though many of my friends and I will sometimes take on a wanderlust and drift away from each other for one reason or another, whenever we meet up again, possibly years down the road, all of the strong feelings that we shared back when we had first met will just come out as if they’d always been there the entire time. It’s as if those years of wandering had never really happened, as if not a day had passed since we saw one another last.
But to accept such experiences means that there is the necessity to accept that separations do happen along the way, that there are at least minor endings along our journeys. Perhaps friendships are like concurrent Interstates; two differently-numbered highways will travel along a stretch of road for some time, but in the end they almost always veer away from one another, each going unto their own destinations. Like the catenary and the parabola, the two shapes are almost synonymous with one another for quite some time, but in the end, after a while, they end up going their own ways, doing their own things. Though two may skate together for a time upon the ice rink of life, passions, priorities, and motivations change, and suddenly our emotional inertia moves us in a different direction, thereby separating the duet.
Yet no matter how it takes place, separation is painful. No matter which side one is on, provided one truly is a friend, there is anguish and hurt whenever something is lost or let go. The word “betrayal” has easily come to mind in both situations, naturally for opposite reasons. And that pain that cannot be escaped except by confronting it dead on, and that is scary, nerve-wracking, humbling, and... despite its necessity, difficult.
But I do believe that friends who are honestly true, even though there is a relational drift between them, don’t stop caring for one another. An ending is not necessarily a full stop at the end of a sentence, nor is it just an opportunity for mourning. Sometimes, despite how odd and difficult it is to say so, sometimes endings are perhaps necessary in order to stop and take a full assessment of our lives, to question our momentum, to try something new, and to eventually prepare for yet another beginning, hopefully a better beginning, a better present, a better now. For every thing, there is a season, and each of our seasons eventually come to an end. But on the other hand, after a time, the long, deep winter will one day become summer once again. And there is always the hope that, next year, I might be able to dust off that old Frisbee or baseball bat that I hung up and get back on the old horse and maybe give it another try. Maybe it’ll be better next time. Maybe next year will be so much better.
Endings are tragedies; this much is true. Both ender and endee suffer from the death of the old, each in their own separate ways. It is hard to get past. But I do have hope for the future; I do hope for better days. And Dr. Carl Sagan states it best when he says, in his 1980 show “Cosmos: A Personal Voyage,” wonderfully recreated by this YouTube auto-tune, “A still more glorious dawn awaits-not a sunrise, but a galaxy-rise, a morning filled with 400 billion suns, the rising of the Milky Way.”