As I think about higher-dimensions, I usually pace around my home talking to myself, trying to stimulate ideas. So, I decided to teach an overview of higher dimensions to my future 6th grader in hopes that the Q&A would inspire something in at least one of us.
I could’ve just downloaded this video and fielded questions, but there’s no family fun in that. Therefore, I assigned my student the task of obtaining an ordinary sheet of paper, finding a ball among all our toys, and constructing several colorful 2-dimensional shapes.
The sheet of paper was a 2-dimensional world and the shapes were its 2-dimensional inhabitants. I then told my version of the Flatland story: how the 2-dimensional beings had no concept of a 3rd dimension, and how their interactions with the 3-dimensional ball can teach us how to think about higher dimensions.
I then went one step further with the visualization. We rolled up the paper into a 3-dimensional space and placed the ball inside. We imagined ourselves as 4-dimensional beings and, as the 2-dimensional shapes had no concept of the 3-dimensional ball, the 3-dimensional ball had no concept of our 4-dimensional existence.
However, just like how the ball could exist in Flatland as a 2-dimensional cross-section of itself, we could reach into 3-dimensional space and interact with the ball. From the ball’s perspective, a bodyless hand popped into existence from nothing. The rest of the body, still in a 4th-dimensional space, remained imperceptible to it.
My student then asked about how we can really experience higher dimensions, to which I replied that we can’t. However, we can use them mathematically. I went on to use the ball as a qubit, and I explained a little bit about how I am exploring higher dimensions with quantum computing.
Although I did not have the epiphany I was hoping for, the props attracted the whole family and we had a good ole’ educational adventure together.