The Calculus of Saying “I Love You”

Two weekends ago I was visiting a dear friend in New England. She has just started a postdoctoral fellowship in Chemistry at an Ivy League University. She has also just started dating an engineering doctoral student at said ILU. They are very smitten. It was disgusting.

During one of their goodbye smooch sessions (while I was attempting to melt beneath the floorboards on my way out the door), my dear friend, let’s call her Judy, accidentally said “I love you” to the Engineer.

This was cause for great distress and she immediately “took it back.”

A few days later, consumed by the saying, taking back, and woefully lack of saying and taking back in return, Judy broached the subject with the Engineer (I was thankfully hanging out with my 21-year old cousin, who attends a nearby Liberal Arts University).

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 have forgotten your calculus (or blocked it out, or, lucky you, never took it at all) let me explain: he will say “I love you” when the slope of the tangent to the growth curve of his love has reached zero. This indicates of a local maximum and means that the rate of growth (the velocity of love, as it were) has slowed to a stop.

As Judy and I were discussing his response, we found it concerning on several levels. Firstly, if the curve of his love is akin to figure (a) then after he says I love you, he will actually begin to love her less. Which bodeth not well for their long term relationship survival. So then, let’s be generous and suggest the curve of his love is better approximated by figure (b), where the plateau of zero growth might indicate the end of honeymoon/infatuation-type love (a bit late, but not a BAD time to say I love you), which then moves on promptly on to another growth phase, the build up of life-long-partnership-love and the having of babies.

But the second distressing aspect of the whole affair was that somewhere along the line Judy had also mentioned the term “second derivative.” And neither of us could actually remember what this was. We both recalled HOW to take a second derivative (indeed Judy and I took calculus together many years ago), but we couldn’t remember what it actually meant.

Enter massive calculus textbook from our 1st year class (Judy hates throwing away text books).

After searching in the index and finding some helpful examples, we remembered that AHA! the second derivative is akin to acceleration: the rate of rate of growth. And by solving for the second derivative - d2 (love)/dt2 - we could ensure that when d(love)/dt = 0, it is a local maximum (the greatest love), not a local minimum (not the greatest love of all). For when the second derivative is negative = local maximum, as in figure (a); when positive, it’s a local minimum, as in figure (c) (Refresh your memory here). All is happy.

But, you see, I have come up with a better solution. The first few weeks or months of a relationship often result in a very rapid growth of love. Indeed you could even say love is accelerating at a break necking pace (oh har, sorry) not merely speeding along in a linear fashion. Of course this psychotic rampage in love growth can only continue apace for so long and eventually the acceleration will drop to zero, though the absolute value of love is still growing - ie the velocity or d(love)/dt is still greater than zero. An exemplary graph of said derivative can be seen in figure (d).

Try this math teacheresque example; it’s like Judy and the Engineer have the pedal to metal, building up speed along the on ramp to the freeway of love. But once they merge on, and find a nice lane, they can continue traveling at a constant rate, save for pit stops (fights) and the occasionally passing of trucks (make-up sex).  Or better yet, let’s say that falling in love is really actually like falling, wherein the acceleration = 9.8 meters per second squared. When you finally slam into the ground (or reach terminal velocity, which ever suits your particular romantic scenario) and start acting like a normal human beings, instead of a driveling, love-crazed sociopaths, then you know its really time to start saying “I love you.”

In either case, the Engineer should in fact solve for zero in the second derivative to the love-time function and say “I love you” when love has stopped accelerating. This solves the concerning problem of having to wait until his love has stopped growing. Because zero growth in the love function is likely to make any woman, chemist, calculus enthusiast or otherwise, pretty goddamn pissed off.