If you took calculus in high school or college and did not go on to become a STEM (science, technology, engineering, and math) major, you might have found yourself wondering about the real-life relevance of what you were learning.
I personally quite enjoyed calculus in high school and college, and while I don’t use any of my calculus knowledge on the job, I have found some of the concepts to be useful in my personal life. As of late, I have found calculus to be especially useful in one particular area of my life — coping with heartbreak.
At some point in our lives, almost all of us have dealt with heartbreak in some way shape or form, be it the ending of a romantic relationship or friendship, the death of a loved one, a political upheaval, rejection from a dream job, or anything else that may have left us feeling hurt, weak, or helpless. And anyone who has ever grappled with heartbreak would probably say that time heals all wounds.
So what does this have to do with calculus, you might be asking yourself. In calculus, there’s a concept called the Intermediate Value Theorem, or the IVT. Formally, the IVT states that if a continuous function f with an interval [a, b] as its domain takes f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point in the interval. In other words, assuming you have a continuous curve, in order to get from one end of the interval to the other, you have to pass through every other point in between.
Now what’s the relevance of the IVT IRL, particularly in relation to heartbreak?
Well, life is a continuous curve. f(a) might represent a heartbreaking event, and f(b) might be peace or acceptance or complete healing. Every point in between f(a) and f(b) represents the healing process. Per the IVT, there is no shortcut from f(a) to f(b). There’s no saying how long it will take to get from f(a) to f(b), but the only choice one has is to ride the wave and feel the feels. In this particular situation, the IVT could be translated as “time heals all wounds.”
It is important, though, that you allow yourself the opportunity to feel. Do not suppress your emotions. Avoiding any negative emotions will only intensify them in the long run, potentially leaving you feeling worse once you pass f(b). In real life, the IVT gives you permission to feel whatever emotions you need to so that you can reach f(b) and continue past f(b) a stronger person.
While there is no magical formula to reaching f(b) from f(a) without passing every other point in between, remember that f(b) is the end of the interval, so you will get there eventually. Each minute, hour, day, week, month, and year that passes brings you closer to f(b). Nothing in life is permanent, including whatever negative emotions you might be feeling. So just remember that every point that comes between f(a) and f(b) only serves to bring you closer to f(b), and no matter how long it takes, you will get there.
Sometimes the assistance of a professional may be necessary in getting you from f(a) to f(b). If you believe you need professional help, you should by all means seek it. Other tips for making the IVT a little more bearable when coping with heartbreak include the following (modified from a blog post I wrote for Konversai):
1. Personal care: This includes eating healthy, getting enough sleep and exercise, and attending to your personal hygiene. While it can be hard to motivate ourselves to take care of even our most basic functions when we are heartbroken, not doing so can compromise our physical health and in turn delay the process.
2. Talking to people: Whether it’s with someone you know well or a stranger, conversations with others are powerful in the healing process. Don’t be afraid to let other people in. Remember that everyone has experienced a negative event at some point or another. Any person you talk to can offer you a new perspective, help you process your feelings, provide you encouragement, or simply lend a listening ear or hug, all of which can help you on the journey to f(b).
3. Laughing or smiling: Even if it’s just a little bit, finding a way to laugh or smile sends dopamine to the brain, which puts you in a better mood. While this may seem counter to allowing yourself to feel negative emotions, doing at least one thing a day that makes you laugh or smile will have a long-term positive effect on your mental health.
4. Doing something you enjoy: Again, even if it’s just for five minutes a day, do not neglect doing the things that bring you personal satisfaction, even if it’s the last thing you want to do.
5. Practicing gratitude: While it can be hard to remember our blessings when things are rough, and doing so won’t just make the problems go away, keeping in mind the things that are going well can help you move forward and put any problems into perspective. It can also be helpful to contemplate the lesson in the negative event and find the silver lining if there is one.
Again, the above suggestions may not be quick fixes, but they can certainly help nudge you along the continuous curve.
While calculus hasn’t yet given us a magical cure for heartbreak, the IVT can provide us an alternative framework for approaching heartbreak. Instead of suppressing any negative feelings that might come along with our healing process, we should allow ourselves to feel them in any way we need to, keeping in mind that we will eventually reach f(b). And when we do finally get to f(b), we will get there stronger and wiser than we were at f(a) having allowed ourselves to pass through every point in between.