Knots Fall Apart in Four-Dimensional Space, But Surfaces Remain Knotty
The article explains that in four dimensions a knot tied on a rope cannot stay knotted, because the extra dimension lets strands slide past each other; by contrast, two-dimensional surfaces such as balloons can still be knotted in higher dimensions. A guiding formula says you can knot an object of dimension d only up to dimension 2d+1; for a rope (1D) that means up to 3D, while a 2D surface can be knotted in up to 5D. The piece uses analogies (ants on a line, a movie-like sequence of 3D frames) to visualize 4D space and notes that knotted surfaces in 4D is a vibrant area of research linking geometry to our understanding of four-dimensional space.