Within our own domain

It is important to recognize our limitations and essential to understand how to accept them. For example, that old ad that ended with the slogan “No limits”: are we really sure that we want to reject limits, boundaries, and those clear-cut lines beyond which we cannot and do not want to venture?

I realize that I am not the ideal ambassador for a campaign to accept one’s limitations, since this year I published a book, The Second Proof (Einaudi), about my relationship with mathematics, my limit par excellence. For years, I was comically bad at it, despite tutoring and clumsy attempts to understand logarithms. And for years, I dreamed of that failure, the blackboard interrogations, and the in-class tests. Even as an adult, though I conveniently chose a career that had nothing to do with numbers. 

It’s just that our limitations follow us and haunt us: it’s not easy to pretend they don’t exist. So, one fine day, I decided to try again to reject this limitation that, at 36, was still in my nightmares. I re-studied the entire high school science curriculum, from beginning to end, even reuniting with my former professor, until I retook the high school graduation exam of all those years ago. It’s a good story — at least one with a happy ending. 

Except that math remains distant and cold to me: Frankly, while I succeeded this time, I confirmed my long-held belief that math just isn’t my thing. Some people are good at sports, music, ballet, or manual labor. I don’t know what I’m good at, but it’s not math. And that’s a start.

During my second study of the subject, I got the chance to get acquainted with a concept I had always underestimated: the domain of a function. I had a vague recollection of it: The domain is calculated at the beginning of the evaluation of a function, whether it’s fractal, irrational, or logarithmic — the first step. If the goal is to find x (or to find out what form the function you’re studying has), the domain doesn’t tell you much about the exact answer, but at least it clarifies where to look for it: the regions where it is and where it certainly isn’t. That’s no small matter.

Another mathematical concept — similar but not the same as domain — is that of “conditions of existence.” For example, when dealing with a fractal equation, you first look at the denominator, the lower part of the fraction. Let’s say the denominator is x – 4. Now, x must always be different from four; otherwise you would have a division by zero, and you cannot divide by zero. It’s forbidden. So x can be whatever you want, BUT NOT four: x ≠ 4. The rest remains to be seen.

People always say that “math never comes in handy in real life.” This is true in the sense that in everyday life, no one really needs to solve logarithms when they go to the supermarket or pick up their children from kindergarten. But it’s also a simplistic view of things because some things do come in handy if only to draw life lessons from the hundreds of repetitive exercises we’re forced to do in high school.

I believe that each of us has “our own domain,” a range of possibilities within which we exist and beyond which we do not go. Many of the questions we ask ourselves, and the choices we have to make, deal with just that: What do you want to do and with whom? Which job to choose? To go or not to go to that retreat in the mountains? Or to stay at home, yes, but to do what? The answer is within us, somewhere in our domain.