TedEd: Exploring other dimensions

A TedEd by Alex Rosenthal and George Zaidan

We live in a three dimensional world, meaning we have length, width, and height. But what if we were squished flat onto a two dimensional plane? Edwin Abbott wrote a novella called Flatland in 1884 on these premises. It details the experiences of a square that has been exposed to the 3D world. But before we talk about that, what is a dimension? It is a direction, basically a line, that is perpendicular to others. A one-dimensional world is a line, 2D is two perpendicular lines, and we live in a 3D world with a third perpendicular. But what about higher dimensions? Flatland can help us explore these possibilities. In Flatland, the flat objects see a line. Closer objects are brighter than those far away, helping them see depth. This makes them unable to see the third dimension. However, a sphere visits one day, and the way a square sees it amazes him. Then, the square is lifted into the third dimension by the sphere, allowing him to see what no one else has ever seen before. The square wants to see the fourth and higher dimensions, but the sphere can't accept this, which is understandable. It would be very hard for us to imagine a fourth dimension. We can look at it the way the square saw the sphere. 2D cross-sections of a 3D object, replaced by the third and fourth dimensions. Or, we can take a point and extend it in all directions and eventually get a 4D hypercube (see video at 3:42 for better explanation). There could be entire 4D worlds that we can't see because of the way we see things.