infinities

“There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities”  – John Green

0.9999999999 (recurring) is my favorite number. It’s a number that teeters on the edge of becoming 1, requiring only something infinitesimal — something “equivalent to nothing” — to cross the threshold into reality. But is 0.0000000001 really “nothing” if it can make something superficial into something that exists? It’s a whisper of existence, a thread tying the theoretical to the tangible.

I recently came across an interesting concept in math: the sum to infinity of a geometric progression. It's really simple- say you have a sequence like 16, 8, 4, 2, 1/2, and so on. At first glance, it seems infinite — an endless cascade of steps stretching into eternity. Yet, with a single formula, you can calculate the sum of all its terms, no matter how far it extends. Essentially, the logic is that as the nth term of the progression keeps getting smaller and smaller, you can assume it becomes “equivalent to nothing” or zero.

This didn’t sit right with me. How can infinity, with its boundless, godlike nature, be tamed so easily? How can you reduce it to a finite sum with a touch of mathematics? Of course, I had to make it sit right with me to bag the occasional 3 marks, yet it didn’t– my mind wandered around the likes of this:

Imagine life itself as a geometric progression. Maybe you’re at the twenty thousandth term — far far along the way, at the last step before you reach the peak — a moment so small it feels insignificant, yet big enough to alter a lot of things, like 0.0001. Even the smallest term, 0.0001, adds to the whole, contributing to the sum of your existence. Each moment, no matter how fleeting, matters. And as these moments accumulate, they form something beautiful, something greater than the sum of their parts.

I still have infinite baby steps to finally grow wise enough to sit right with the quantification of infinity, as well as make peace with the equation of life, but I’ll leave you with this: 

Whether it’s arithmetic, geometric, or harmonic, let there always be progression in your life. And, most importantly, let there be love — for even the smallest bit of love is never “nothing.” It’s the thread that connects, the constant that defines, and the infinity that makes life real.

all is love.