(Essay 6/30) Calculus: sum your repetitions, outcome will follow

I'm a big fan of Steven Strogatz's writings.
He's an applied mathematician with Cornell & has a flair for making you love mathematics.

A concept from one of his books - 'Infinite Powers' stuck with me for a while.

"You can reach potential infinity but not completed infinity. Unless there's calculus."

It's a beautiful cheat code to re-wire your mind.

Here's how:

Let's start with a circle.
We put certain number of "equally spaced" dots along the circle.
Connect them sequentially, one after another with straight lines.

We start getting polygons inside the circle (look at the top cover image.)
3 dots -> triangle
4 dots -> square
5 dots -> pentagon
.. You get where it's going.

More the "number of equally spaced" dots, greater the number of sides for the polygon.

With this "spaced repetition" of dots, polygon gets closer & closer to a circle.

But it never truly becomes one.

As the number of dots approach infinity, polygon gets infinitesimally close to a circle.

Mathematically, we can say:
Polygon's sides reach potential infinity. A potential circle.

But, it never actually becomes one.

This small gap between potential infinity & circle (a.k.a completed infinity) is filled by Calculus.

Using calculus, we add all the infinitesimal segments of the polygon and get the best possible measure of the circle.

Something which is otherwise impossible.

That's how we touch excellence.

Only when we repeat a process, an action in a routinized rhythmic pattern, we get closer & closer to the utopian state.

As we never truly reach perfection, we have no way of knowing what a
perfect outcome looks like.

It's only when we draw parallel with calculus, sum up all the repetitions, we would have approximated the perfect outcome.

Calculus says - sum your repetitions, outcome will follow.