You are the Center of the Universe

What is the center of the universe? Scientifically, we are. That’s where we started millennia ago, then we learned that the sun was the center (of the solar system), then we discovered galaxies with their own centers, then clusters of galaxies, and now, we’re back where we started.

General Relativity describes the geometry of our universe as a three-dimensional surface in a four (or greater) dimensional universe. It’s very difficult—impossible for me—to visualize more than three dimensions, but it’s simple mathematically, and I can use lower dimensional analogies to get the idea and identify its center.

But what is a center?

A center is a midpoint. If you have a line that is twelve miles long, the midpoint is six miles from the end—from both ends actually. That tells us what we mean by a center. We can define it as the point from which if you travel, it will be the same distance to the end in any direction. For a line, that’s only two possible directions. For a plane figure, it’s more.

For a disk, the center is that point from which you would travel the same distance to the edge in any direction. The edge is defined by a circle surrounding the disk, and the disk’s center is in the middle of the disk.

Going back to the line, let’s bend the line around on itself to make a circle. The line still has only two directions that you can travel on it, but now those directions are curved in a 2^{nd} dimension. Using a familiar trope, if we are tiny one-dimensional beings traveling on a large circular line, we will have no awareness of the 2^{nd} dimension. If we travel far enough, we will come back to where we started with no understanding of how that happened. We will have gone in a “straight” line for twelve miles and should be twelve miles away! This is mind blowing.

So where is the center of the line now? I don’t mean the center of the disk defined by the circle; that is beyond our one-dimensional awareness. I mean the midpoint of the line itself that used to be six miles from the ends. You could easily say it has no center, since you can travel forever in either direction and never reach an edge, but it’s more interesting, and perfectly reasonable, to think of it another way. The point of return, your origin, functions as an edge for our purposes, so the center of the line is that point on the line from which you would travel exactly the same distance in either direction to return to that point. But that is true of any point on the line. Every point on a circular line is the center of that line.

The same thing would happen with two dimensional beings on the surface of a sphere. Small beings and a large sphere mean we could travel in a “straight” line and eventually end up right where we started with no understanding of that. We’re familiar with this because we live on the approximately spherical Earth. We are used to the idea that if we travel continuously in one direction on the surface, we’ll go around the world and end up where we started. The difference is that we are three-dimensional beings, so curvature of the two-dimensional surface of the Earth through the third dimension is completely understandable to us. Still, we should realize that every point on the Earth’s surface fits the definition of the center of the surface—not the center of the spherical earth, deep inside the earth, but the center of its two-dimensional surface.

But two-dimensional beings on a spherical surface could have no awareness of the curvature in the 3^{rd} dimension. For them, it would be pure, and scary, magic to return to where they started by traveling only in one direction. (It wouldn’t be magic to their mathematicians, who would have discovered the concept of higher dimensionality, and could deduce how this might happen even though they couldn’t perceive it.)

Now we come back to the universe as a three-dimensional surface in a higher dimensional space. We can’t visualize that. To us, if it’s three-dimensions, it’s just a volume, not a surface, too. That is no different from our one-dimensional beings on the closed circular line defining a two-dimensional disk, or our two-dimensional beings on the closed two-dimensional surface defining a three-dimensional sphere. Similarly, a four-dimensional sphere (called a hypersphere) has a three-dimensional surface. As three-dimensional beings, we live on that surface. That is our universe. If you travel far enough (it’s a long way) in a straight line in any direction from where you are now, you will return to where you started.

On our three-dimensional surface in spacetime, you (and I, and everyone else) are the center of the universe.

Hugh Moffatt

Waltham, Massachusetts

September 2, 2019