November 9, 2012

Limits

In calculus, we define the limit of a function f(x) as the value L that f(x) approaches as x gets close to some fixed point c. We say as x->c, f(x)->L. This value L does not have to be a part of the range of the function; it's a value that you approach as you get closer and closer to c, without actually getting to c. 

I think about limits a lot. Not because I've had to formalize the definition of a limit in my Advanced Calculus class (over, and over, and over...). No, it's not because it's such an important reference from Mean Girls. It's because I think about how close I get to speaking up, approaching a guy, and get the courage to ask him out...

and never actually do it.

It's semiformal season, and I would like to ask somebody to come with me. But the sheer thought of going up to the person I like and mincing words together that make me sound like an intelligible human being gives me chills. I've sat in my room contemplating the worst forms of rejection I could potentially face, and every time, when I realize that I'm just wasting time and energy, I become a little more courageous and approach the limit that I'm interested in evaluating. Yet when it comes to the actual execution, I retreat, and move farther away from the limit.

I like to think I know my limits. I know who is and who isn't within my options, or so I think. Every person that I've liked recently falls within my "not gonna happen" category, due to the lack of faith I have in myself. Instead of attempting to move closer to my point of interest, I try and build an open set around my current location in my development and hope to capture my limit of interest. This open set seems closed from my perspective, and I shut out everybody because I find that I'm still not ready.

I've spent the past year "free-of-thinking-about-relationships" because I needed to take care of myself. Previously, I found my relationship function going on tangent curves and taking on indeterminate values because I did not have time to evaluate my personal limits when I was scrambling to find a boyfriend. My self-esteem was on an asymptote, heading for negative infinity and lacking any hopes for increasing. Once I started taking care of myself, my functions became bounded and smoother, and I have found myself at a stable equilibrium.

But now that I've worked on improving myself, taking time to evaluate my limits, I'm back to confusion at the limit of a potential relationship as I approach this guy. I want to make sure I'm avoiding an unstable point, and getting closer and closer to building up my courage.

I'm not content with approaching the limit and getting closer and closer.

I want to reach this elusive point.

The limit unfortunately does not tell us what the function is at this point. The limit gives the behavior as you get closer and closer, but often, as is life, the function is discontinuous, and the evaluation is not the same as the limit. This is a concern in prediction, because even if the limit seems certain, no matter how "confident" I think I will be rejected, as the limit tells me, there is still the opportunity for a disjunction, and I might be happily surprised.

The curve is status quo; it's reaching beyond the toolbox of limitations that makes this so much fun.

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