In the 18th Century, the foremost debate in philosophy was between rational and empirical knowledge. The Rationalists had believed that all our knowledge came from an innate, inbuilt reason. Their favorite example of this was mathematics, a field they were rather besotted with. The empiricists, on the other hand, believed that all knowledge starts as sense data. As for mathematics, they believed that the "truths" of mathematics, so inspiring for the rationalists, were nothing but a pack of tautologies. Three times three equals nine is not a sign of universal order, but rather just restating something a different way.

Into this scene stepped Immanuel Kant. I will focus on just one statement that Immanuel Kant made, in what was a gigantic, unsurpassed effort, to describe the sources and limits of human knowledge. On the subject of mathematics, he wrote that "there is nothing analytic in the concept that 7+5=12, for there is nothing in the concept of 12 that leads to the concepts of 5 and 7". In other words, Kant didn't believe that even basic mathematics were purely analytic, or purely tautology. Even something as simple as 7+5 was the result of a synthetic attempt by the mind to apply universal concepts to numbers. Although, I admit that the first or maybe even the fifth time I read the sentence, I thought that Kant was overreaching or saying something counterintuitive. After all, all it takes is a six year old with a pile of 12 walnuts and a little bit of time on their hand to figure out that they can be broken into piles of 7 and 5.

But lets rephrase this a different way, and in fact in an even simpler way, 7+5=5+7. This is a simple law, known as the commutative law. Numbers in any order equal those same numbers in the any other order. It is one of the basic laws of arithmetic and again, nothing beyond first grade understanding. But to explain Kant's point, while it might seem obvious how well the commutative law is inherent in the above equation, the commutative law is not actually found hiding inside of those numbers. Try as you might to analyze numbers, even the basic laws of mathematics, such as the commutative law, the associative law, and the dissociative law (The last being the key to all sorts of abstract, mind blowing math), can not be analyzed out of them.

So how does 15 become 17? By adding 2 to it. But the magic that turns 15, and 2 into 17, isn't analyzable from those numbers. It is based on laws that are outside of the numbers themselves. Stare at those numbers as long as you can, you will not find those numbers in them.

But what type of philistine am I to talk about the cognizance of numbers when the original topic was the ineffable and bittersweet changes that occur in us and the people we know? The answer is, I am taking the long road to relevance. Because if the laws that allow 15 to turn into 17 by the simple addition to 2 are such a matter of hazy debate in mathematics, what can we say about being a complicated human being at 15, the complicated process of two years passing, and the "end result" of being 17? Since staring into the numbers didn't allow us to figure out the laws that guide them, how can we ever guess the same thing from staring into people? And I could explicate this with points, maybe some of them involving the fact that 16 years later, I still kick myself for overlooking the shy, nerdy girl who one day showed up beautiful. Or I could tell a long rambling story about being lost in Yamhill County. But all I can say is that since the rules that allow numbers to change: to allow x to become non-x are so ephemeral, what does that say about the rules that make people change, for better or for worse?