Topological Logic - a rod through one hole of a double torus can pass through both with some careful stretching of the surface. No tearing or pinching required. A fantastic video made by math professor Dave Richeson @divbyzero
Heh.
I'm not sure I'm ready to explain swing machines, topology is easier!
Sewing machines use two threads, as the thread on the needle moves in and out a second thread below threads through the first thread. I can almost see in my mind how it works but not quite.
I didn't make the connection until you pointed it out. It was more like how was I confused by sewing machines for so long while I found topology easy!?