If we set a coordinate system for each space, the coordinate system of Euclidean space is a straight line, but the coordinate system of non-Euclidean space will be bent into a circle. In one dimension, Euclidean space is a straight line, and non-Euclidean space can be a circle. In two dimensions, Euclidean space is a plane, and there can be many kinds of non-Euclidean spaces.

Cobb's box world is actually a spherical non-European space. If we want to construct the escher staircase that Ariadne walked through, we must bend into a circle in the height direction of that space. In this way, the heights of the highest and lowest points of the stairs are the same, so they can be connected. In this space, there are still upward and downward directions, but the meanings are different. Up and down does not mean the increase or decrease of height, but refers to drawing a circle from two different directions.

For example, from one direction, it is clockwise up and counterclockwise down. So I keep repeating it when I go up and down. There are no such stairs in life, but many things, such as clocks and watches, work like this.