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.
