02/28/2017
"Consider this line, just a straight line.
When we study things like this, it really excites mathematicians when they find out something is compact. Now ‘compact’ means exactly what it intuitively sounds like: it is captured in a bounded area, self-contained. This is the type of mathematical problem we really like to study. Let's go back to this line, and here is an obvious problem: it’s not compact. It’s going to be infinite. In other words, no matter how far you zoom out of the line, if you keep zooming out, you’re still only going to see a finite portion of this infinite line—precisely because it’s infinite. So how do you fix that? How do you make everything into a single thing so you can study it? If I draw this “point at infinity” here, I can pick up this end of the line, turn it around, and turn its end into the side of a circle. And the same thing to the other side. Now the entire line is connected to the point at the center. Why did we do this? There’s this notion of what it means for shapes to be equivalent, as in, they have the same kinds of properties that we care about. It might not be intuitive but it is a fact that this line—this infinite line—cannot by itself be transformed into some bounded shape, like a line segment. But what we’ve done here is taken this infinite line and found a way to form it into a circle by introducing this point.…This mathematical fact has been one of the pillars in helping me to see, at a concrete level, who God is. Think of this line. Think of ourselves as small points on this line, going along, left and right, doing our business, going about our lives and trying to figure out what is around us, but we only see what is locally around us. And it seems as if this world is held together by nothing more than chance. But the key thing is, once we look at ourselves not on this line but on the circle, it helps to see that the circle—as a perfectly compact shape—you can see that you are connected at this point at infinity, which naturally corresponds to God. Geometrically you can see how this point pulls the line together. It captures and makes the world some coherent thing so that, at any given point, even though you can only see yourself locally, and with the small things around you, you know that in the circular view, your relationship with God holds. As a result, your worldview—I believe—is completely different."
-Soonho Kwon, in "Infinity: Part II"
PC Christie Jiang & Rae Perez
