A Thought Experiment: Is Infinity Real?

This morning, I found myself in a "dreamy" state of mind and stumbled upon a thought experiment regarding the strange nature of infinity. There is something about the concept that makes it feel almost "unreal," specifically when you consider that there are multiple types of it.

Dimensional Infinity ($D\infty$)

Imagine a simple strip of paper. On the front side, we mark a plus sign (+); on the back side, a minus sign (-). Usually, these are two separate surfaces. however, if we connect the (+) side to the (-) side, we create a spiral loop (a Möbius strip).

If you take a pen and begin drawing a line along this surface, you can continue infinitely without ever lifting the tip from the paper. Your path has no end, yet it exists within a contained object. Let’s call this Dimensional Infinity.

Numeric Infinity ($N\infty$)

Now, consider a different kind: the infinite digits existing between the numbers 0 and 1. Mathematically, there is no end to these numbers. Theoretically, we could begin typing these digits into a computer to catalog them.

However, we eventually hit a physical limit. If we actually attempted to record every digit, we would eventually reach a point where all the available space in the universe was filled with the data from those numbers.

The Synthesis: $D\infty = N\infty$

I believe these two infinities are actually the same: $D\infty = N\infty$.

Just as our digits would eventually fill the universe and "hit the end," I propose we would come right back across the 0 we started from. I think we live in a Dimensional Infinity exactly like this.

When we zoom in further and further into an atom, we aren't just looking at smaller "stuff"—eventually, we would find our own universe inside of it. Just as every atom is contained within the universe, the entire universe is contained within every atom. It is a perfect, infinite loop.