In the late 1990’s and early 2000’s, there was a fictional boy band called 2Gether. They had their own MTV television show, released a couple of moderately successful albums, and even had some hit singles. Their debut single, which expresses the level of glorious cheesiness and mockery in their music, was called U + Me = Us (Calculus), whose chorus proclaims: “I know my calculus. It says you plus me equals us.” Clearly, this was not a song written by someone who was successful at higher mathematics. That said, the song succeeds on the level of being catchy and humorous, and since most people don’t know their calculus, there is no harm in making a bit of lighthearted fun about calculus, because those people who would be inclined to point out that the sort of calculus that is being mentioned is so simple that it does not deserve to be labeled as such might find themselves feeling a bit excessive in making fun a piece of disposable pop music.
Last night I received a similarly lighthearted discussion of mathematics making at least somewhat more of a substantial point in my e-mail. One of the readers of my blog, after having read an entry I wrote on very basic questions of calculus in the Bible , sent me a visual representation of the very basic principle of there being no shadow of turning, or no derivative, of Jesus Christ (calculus). I thought it was a pleasant picture, and the fact that the gentleman who sent it to me stated that it was inspired by a kid from his congregation makes it even better, since it provides a way of making sense of a biblical truth in fairly simple and straightforward mathematical language. The addition made from my original discussion was that Christ = infinity, as well as the derivative of Christ being zero, which implies an interesting set of biblical principles as to both the consistency of God and the fact that it is far above our own understanding and ability to grasp. In the hands of less skilled people, these ideas can be seen in contradiction, when they create instead a rich tension between consistency and incomprehensibility, that God never changes but we aren’t able to fully grasp what He is about despite that lack of change in what He is about.
When I was in the tenth grade I took a semester of physics, where we memorized the three basic equations of Newtonian physics for acceleration, velocity, and position. Since we had not taken calculus yet, we learned these as three separate equations, not realizing that the acceleration was the derivative of the velocity and that the velocity was the derivative of the position. To be sure, it would not have taken a great deal of calculus knowledge to understand this relationship, and it was clear even without knowing the calculus that the three equations were connected somehow, but it was a reminder that there are operations that serve to measure rates of change and that there are transformations beyond the standard operations that people grow up knowing. To be sure, I do not think that I have ever been a spectacularly able student of mathematics , despite my interest in the subject, but despite this general lack of confidence in my in-depth knowledge of higher mathematics, there are insights to be gained not only from knowing equations, but also knowing the connections between them. It is in the connections that we gain a sense of context and a sense of place for the knowledge that we have, and just as equations based on biblical truths as well as equations based on science tend to have connections with other equations and thus form a field of knowledge that we can use to draw further conclusions by deduction and implication, so too we can find that knowledge improves our understanding when we grasp and use the power of connection.
And even though the song by 2Gether was an immensely silly one, even so it grasped a great truth about mathematics that is forgotten all too easily by teachers and students to whom math seems to many to be an area of thankless and pointless drudgery and toil. At its core, mathematics involves connections and operations, tying together aspects of our world through symbolic language and understanding reality by virtue of recognizing how something can be understood in a different perspective and placed in a relationship with something else. Whether we are looking at Fibonacci’s sequence and examining its connection to the golden ratio  or whether we are using the equations of an obscure French mathematician of the revolutionary period to examine the worth of human beings , there are connections and parallels to be drawn between mathematics and other areas of knowledge. Sometimes we have to recognize that calculus, and other areas of mathematics, are not about setting some people up as a sort of technocratic elite over those who find the subject matter daunting and frustrating, but it is about connecting the disparate fields of knowledge together, and making sense of the world in which we live, and little is more practical than those things, however clumsily we may go about them.
 See for example: