I have never been and never will be a math person. I was confused by everything from division to algebra to probablity to trigonometry to calculus, and have stuck with it all this time merely to fulfill my obligations. However, I was thinking the other day about Math, and started wondering whether it counts as something we discover or something we create. I remember a funny yet extremely irritable Algebra teacher I once had walking in on the second day of class and saying “now all of you remember that these numbers you hate so much aren’t even real. They’re just concepts to describe abstract quantities.” The implication she gave us was that numbers don’t exist, it isn’t as if somewhere out there the number three is hanging in space just waiting to be discovered. The idea is that we have three of something, three apples or oranges or protons or electrons or born again Christians or Atheists or any other “thing” that can be described as a quantity, and then numbers like “one, two, three, four…” are just names to describe how many of these things there are.
However, Mathematics seems unique to me because we’ve invented these things we call numbers, which are abstract and don’t actually exist, and yet we can discover patterns in them that have led to math as we know it. After all, what are advanced forms of math such as calculus or differential equations except descriptions of extremely complicated and unexpected patterns in these numbers that we’ve invented? And what about the things we can’t describe? I laugh as I imagine the frustration of the first mathematician to discover that no equation could describe the pattern of prime numbers. How irritating it must have been to realize that these numbers and abstract concepts that we ourselves created could take on a life of their own! Most machines people invent or other creations are designed with the expectation that we can control them. Besides the occasional science fiction horror story, we don’t often here of an invention designed not to do what we instruct it to do, and yet we have invented math and numbers and they very often do not work out the way we would expect or desire them to. After all, imagine how much easier my math homework would have been if I could have simply invented equations that achieved the desired results! Math could have actually been fun! Yet numbers seem to live apart from us, but we have given them life. How could this be?
This then struck me a lot like the creation story and the idea of man choosing his own will over the will of God. Certainly numbers cannot “choose” whether or not to obey us, however, it is interesting to note the similarity of how we create these abstract things that suddenly achieve a “life” of their own, the same way the Bible says God created us and we achieve a life of our own. And yet the same we cannot force an equation to yield any answer we want (force 2+2=5 for instance) God cannot force us to do His will. Of course, we could all simply agree that from now on 2+2=5 and 4x+5=23 when x=7 and so on and so forth, but then what would be the whole point of mathematics? Math would become useless for all of its applications in science and business and life in general. Similarly, maybe if people couldn’t make a conscious choice about whether to love God or act righteously, our decisions would inevitably be worthless to God, and worthless for God, worthless for whatever purpose we are intended for.
On a side note, this question also makes me think about this one common objection I hear sometimes to God, the idea of whether values like charity and good behavior are rules set by God, or whether they are independent rules that God is the mere overseer for. The idea is that if God set the rules, then there’s also the idea that He could just as easily have set rape and murder and lying as good values, and we would live in a much different, much more horrible universe. If God didn’t set these rules, then that means God isn’t the ultimate high authority anymore, there are rules even he must abide by. However, I think both of the explanations miss the point. I think the point is that God is the rules, God is all those good values and good things that we associate with religious law. It isn’t that God sat back and was thinking one day “now…should I have all these little squirts be nice to one another? Or should I have them all be total jerks?” I think it’s just that thought never occurred to God, because I think that’s just how He is, and that’s just the way it is. It isn’t as if God had to decide what was good and what was bad, it’s just that what God is is good by definition. Becuase God is the be-all end-all of existence, it really isn’t possible that murder or rape or dishonesty ever could have been “good” values, because that just isn’t what God is, and God could never possibly be anything else. I don’t know, I’m having trouble articulating the philosophy today, but to me this suggests such beautiful hope. Maybe the idea is that somehow all this growth we see, both in nature and in us, is good, it’s positive. Maybe the final trend of everything is beneficial, not just abstract or bad the way we often think it is. Maybe this good trend is simply the final option, the only option, and while we can decide not to recognize it, our recognition can’t change it any more than our recognition that 2+2=5 can change the reality that 2+2=4.
How strange! I would never have expected to have so many revelations about God revealed from a school subject I was always so lousy at, and always disliked so much. My final thought is just that numbers are clearly only abstract concepts, but they have patterns, follow laws, and describe real, tangible objects. Similarly, to me it seems like God is quite an abstract concept, but He seems to have patterns, set laws, and has created real, tangible objects. What a strange parallel, don’t you think?