ust in time for St. Valentine’s Day, a good friend of mine informed me of this article from Inkling Magazine, entitled, “The Calculus of Saying ‘I Love You.’” This humorous piece describes an episode in the life of a young woman (”Judy”) and her engineer boyfriend. After a passionate start to their relationship, the young lady lets slip those famous words, “I love you,” which the young man fails to return in kind. She quickly repeals the statement as being to premature… but pondering the situation for a few days, and curiosity getting the better hold of her, she later inquires why he didn’t say “I love you” back. To this, the young man replies that he wanted to wait until it was the proper time:

The Engineer, delightful and rational fellow that he is, made it clear that he would not be saying “I love you” until he was sure. Otherwise, he might waste this very important statement by saying it too early in the relationship, when his love was still growing rapidly, thereby taking away the significance in later weeks/months when his love was much, much greater.

Judy, obviously disappointed by this response, pressed and asked when exactly that would be. His response: when dLove/dt = zero.

For those of you who are a bit rusty with your calculus, the first-order derivative (dx/dy, or in this case, dLove/dt) is a way of expressing the slope of a curve at a particular point. For example, if one plots the change in position (s) over time (t), the rate of change (ds/dt) can be calculated. This corresponds to velocity, or speed. In essence then, what the engineering boyfriend was positing was that he would wait to say “I love you” until the upward ‘velocity’ of his love for her seemed to plateau.

Unfortunately for Judy, she knew her calculus. And she realized that if the slope of a function plateaued (dLove/dt = 0), it could mean that it was either a relative minimum (a pause before another spur of growth and a more ‘mature’ form of love, as in graph B, above)… but it could also mean that it was a relative maximum (a peak before the decline, as in graph A).

This humorous article continues to explore the meaning of the engineer’s cryptic statement, delving into the second-order derivative (d²Love/dt²), which is akin to the ‘acceleration’ of his love.

fter a few laughs, I returned to my senses and realized that the article was completely wrong. In fact, the mathematical proof was based on a framework that was considerably flawed.

You see, the article acts as if love “just happens” and you sit back and watch it. Truly, love is a matter of the will. That is, one decides whom to love. At the heart of this societal misunderstanding is confusion over the different types of love: eros (έρως; infatuation and sexual love), philia (φιλια; liking, or friendship love), storge (στοργη; affection or fondness) and agape (αγαπη; divine love).

Thus, perhaps the ‘love’ variable is better renamed ‘fondness’ or ‘affection’ or ‘liking’ (or perhaps even ‘infatuation’). One doesn’t choose whom to like… it just happens. But one chooses to love — and it is even possible to love those whom one dislikes.

If we rename the variable ‘love’ to ‘like,’ then it is totally permissible for dLike/dt (the velocity of liking) to plateau and d²Like/dt² (the acceleration of liking) to reach zero. After all, there may be a limit to how much we are able to like someone… and perhaps as we get to know others more, we learn about faults or character flaws that actually make us like them less.

Notwithstanding this change in liking, love, as a matter of the will, continues to grow indefinitely.

Thus, in the Christian sense, love is either on (we will to love someone) or off (we will not to love someone). The engineer, then, should be able to tell her that he loves her (or not) at any point in time, regardless of the level of their passion. Many couples may be passionate and yet not love one another. Others who grow in love may experience decline in passion. Love is or isn’t.

The moral of the story? This Valentine’s Day, be truthful to your sweetheart and to yourself.

And know your calculus.