Things to Make and Do in the Fourth Dimension

by Matt Parker

We can explain the disjointed nature of the 4D monster by looking at what would happen if we, as 3D creatures, attacked a 2D creature. Being 3D means that the space we operate in extends in three different directions: side to side, backwards and forwards, and up and down. A 2D creature can move only in two directions: it’s constrained to a flat surface. Let’s imagine a hypothetical creature who is completely flat – a hypoflatical, say – living in a completely thin universe, so thin that it would appear as a piece of paper does to us. We could loom as close to it in an up or down direction as we want and, because the hypoflatical has no concept of a third dimension, it would have no idea we were there. The third dimension provides perfect cover. Time to mount our own terrifying attack on a lesser-dimensional being – and all it takes is a move in the third direction into its two-dimensional world. The 4D monster which came from Higher Space! Imagine it from the hypoflatical’s point of view. As our fingertips pierce its 2D reality, they appear as individual floating circles which grow, move and then merge together as our palm reaches the 2D world. If we pass our fingers through their flat universe, all the hypoflatical sees are shape-shifting 2D cross sections, like flying meat pancakes. Trying to hide won’t do it any good either: as 3D creatures, we can see the entire 2D world set out in front of us like a blueprint – which is exactly how the 4D creature in the Alan Moore st...