Ant Analogy

Figure 1

Figure 2

The concept of multiple dimensions is very difficult for people to grasp. This is due to the fact that we observe only 3 dimensions (4 if you count time). There are many analogies that can assist us in visualizing this, one of which we will explore here.

Imagine that there is a thin hose stretching across a canyon. Also imagine that there is an ant on this hose. From a distance of, let’s say, 50 meters, the pipe seems to be a one-dimensional object, in that the ant can only move forward or backwards. This is illustrated in Figure 1a. However, upon closer inspection, we see that the hose is not one-dimensional, since the ant can move around the hose, as shown in figure 1b.

You may be wondering how this analogy parallels our world, since the ant is obviously aware of and able to move around the circular dimension. The link is in the fact that the circular dimension is different from the horizontal one. The circular dimension is much more subtle, requiring a closer view to see. In fact, this is just like how our universe works. There is a smaller, curled up dimension that requires closer inspection (smaller than Plack’s length, and therefore beyond our capabilities to directly measure). Also, like how the circular dimension exists at every point along the hose, our circular dimension (referred to as a “curled up” dimension) is there at every point in our universe, as seen in figure 2.

While this is a very subtle idea, since it has no massive impact on our world as we know it, it does have astounding implications. One of these implications is the parallel between the curled up dimensions and our own. This would suggest that, like how the ant can go completely around the hose and end up right back where he started, that our 3 physical dimensions are circular. This implies that if you keep on going in one direction for enough time, you will end up back where you started, like circumnavigating our Earth.