First, let me say this. Your topic is golden. Do not let anyone take this away from you. I'm a philosophy major who also has great admiration for maths and you've got a simmering idea here that is ripe for discussion and good reading.
After seeing your initial response for why you couldn't answer whether one plus one is equal to two, I was a bit let down to be honest, since I assumed this might be a creative essay involving departures from a base 10 number system but you've got something equally interesting, namely, the "why in between".
Correct me if I'm wrong here. From why? We are led to reason towards that which is true. From why not? We are led to reason towards the negation of why? That is, what makes a true statement false given that we assume the truth of the first statement. Yet, in many cases, we are not ABSOLUTELY sure if the answer to why? is true, and likewise, whether the answer to why not? is true. We only know that IF THE ANSWER TO WHY? IS INDEED TRUE, THEN IT'S NEGATION, THAT IS, THE ANSWER TO WHY NOT? SHOULD BE FALSE. VICE/VERSA.----This type of definitional anxiety is a perfect example of why we need to define validity which I think might help your essay out a lot. You can pick up an intro-to-logic textbook just about anywhere these days or just google "deductively valid argument" for a primer on what precisely makes an argument valid and take it from there.
Now, let's say the conclusion to our reasoning of why? is true, it is only true if the premises are taken to be true and makes the conclusion necessarily true. Otherwise the argument is invalid. Without going into all the craziness that is logical theory, I think your essay begins to make the case for necessity, causality, and the unknown. That perhaps because there is so much in this world that is uncertain, it is difficult to answer a question within a why / why not paradigm without ending up somewhere in the middle. Not to say that there
isn't knowledge that
is pretty much certain. Basic laws in physics are an example:
In a natural state, why do our bodies stay grounded on earth?
Gravity
Should our bodies not stay grounded on earth, Why would this be?
The absence of gravity.
I mean, there isn't really much in between there unless you depart or misinterpret the natural state condition. One could say Hey! I'm in hot air balloon, floating, and therefore not grounded on earth with gravity obviously still present and laugh his way out of the argument, but that would just be ridiculous and I would probably try to give the guy a bad day by shooting an arrow through his balloon. The sciences are really the disciplines in which you'll find causal relationships to be abundant and things that are true because there hasn't been anything discovered to prove them otherwise.
Yet I think when you're dealing with human action, which is what I'm assuming your essay is focused on, what is "in between" the answers to why? and why not? becomes more pronounced because human nature and nature are different. Aristotle in his Nichomachean Ethics described virtue as the mean between two extremes. For example, courage was the mean between fear and confidence, temperance the mean between pleasure and pain, and so on..I think your essay captures the human tendency to gravitate towards the extremes rather than the means. That this tendency manifests itself in our decisions and views about the world resulting in a certain weakness. This weakness comes in the form of not being able to make compromises, or even worse, compromising when we don't even realize it. It speaks to a human need for more clear and straight thinking and likewise, action that reflects such thinking.
The ending is nice, the possibility that maybe all that we know is merely an illusion. That there is no such thing as truth. I mean, one would have to first define what exactly truth and knowledge are before attempting to assert that they don't exist, but can one define something that doesn't exist in the first place? hahaha funny.... And are we slaves to ideas? Or seekers of truth?
Again, you've got a great topic but you might want to organize your thoughts a bit more, especially when moving from the abstract to concrete examples..... Try thinking about what the core argument you are trying to make is. Creative writing is so much different than philosophical writing which demands a type of precision and rigor that I don't think the admissions committee for a college will expect you to have. That is, they shouldn't expect you to have.
Best of luck and hope this helps.
Jason J Rhee