You ever heard that lame, over-used and under-understood aphorism, "think outside the box"? As if all our thought processes and ideas were contained in some kind of Pandora's box, and the really good ones were found just a few inches removed from our cardboard heaven--we just have to stick our hands (or our heads) outside of our box for three small seconds to see the bright, shiny ideas outside of it? The very idea that our own way of thinking isn't enough to solve problems is kind of an insult to human intelligence (not that I am generally incredulous of human stupidity).
However, if you peer at it closely enough, you'll find some truth to the statement (you may have to tilt your head and half-blink your eyes). While we don't have to do something new and unheard of to solve problems or have genius ideas, it is possible for us to put limits on ourselves--a combination of ideas, resignation, and/or general apathy that limits how far inside our little box we go to pull out the really good stuff.
Any high-school graduate (I hope) will remember what a limit is. It's a barrier; an impassable line or point past which a certain function cannot progress. Here's a nice little Google image to help you out (and to save you from Googling it in a new tab, which I know you were all about to do).
There are a couple of things you need to notice about this limit (pay attention, class): (1) In the early stages of the graph, the limit is non-existent, or at least non-influential. Notice how (close to the 0), the graph looks like it could keep on going up forever. Also, (2), notice how the line becomes flatter and flatter more quickly once the limit starts exerting its influence. The line doesn't stop all of a sudden and say, "Well, I've reached my limit. Guess I'm done now." Instead, it's a gradual curve, something that slows the function down over time, kind of like a plane landing and slowing down gently instead of all at once. Also, (3), notice that the line never actually hits the limit. It still goes up, always inching closer and closer to the limit (the number 12), but never getting there. It just goes incrementally slowly.
Compare that graph to your own progression--up represents you reaching more of your potential, and vice versa for down. At the beginning, I would posit that each of us starts with unlimited potential and the ability to soar upward endlessly. But as time goes on, something starts to slow us down, eventually making us reach a wall where we progress at a painstakingly slow rate towards our own limits or mediocrity. These limits can be anything, as intense and sudden as a tragedy or disaster, or as slow as general psychological heuristics--we just get used to something happening a certain way with a certain level of success, and lose the ability to imagine it any other (more profitable or successful) way. We lock ourselves inside our box, and see small improvements as big steps forwards, even though we are in reality trapped by our own standards.
This may seem like a stretch (especially to the non-mathematically minded #sorrynotsorry), but the manner of framing the issue with this mathematical model is quite understandable when we understand how to break free from those limits. How do we convince ourselves that we can surpass mediocrity? How can we return to our original, unbounded rate of progression, and reach our full potential? For that answer, we turn back to the wonderful world of mathematics.
Look at this new and improved guy. Again, we're going with the potential thing here. As you an see, he started off pretty slowly, but he really started taking off--that is, until he hit point A. At point A, he got complacent, cozy. His progression petered off until he began to approach his particular limit (the red line).
And then what? Something happened at point B that changed him--he suddenly left the limit behind; he soared right through it. What did he take right there, and how do I get some?
The mathematical definition of point B is a point of inflection, when a graph goes from being "concave down" to "concave up" (or vice versa, but we're trying to stay positive here). In that single point, the limit was forgotten. And what's so dang beautiful about it is that while the results happened gradually and over time, the shift from limit to no limit didn't; it happened instantaneously. In a single moment of time--a solitary point--we made the decision to get out of our box. To ditch our limit. And then, we did it.
So that's the inspirational part of all of this. Mediocrity may not be easy to leave behind--in fact, it's a steep, uphill climb. But that climb--and its success--comes from one single moment. The point of inflection. It could be as simple as a renewed determination to be better and improve. It could be the moment you sit down and plan what you will change to break your limits. It could be just saying "I've wanted to for all this time, and now, I'm really gonna do it." It could even be as simply as just identifying those limits. But it can be done.
So look for your limits. Figure out what they are. And get out of that box. Here's a clip that, while admittedly stemming from my least favorite genre of movies, will inspire you to do it.
And, just in case you were wondering...here's the secret to doing it.
There's my mathematical inspiration. Go reach your full potential! #Mathpiration #Itsathing