Almost everyone is familiar with the experience of putting wires (e.g. headphones, chargers etc.) into a container untangled and you take them out some half an hour later, perhaps after a walk, and lo and behold, they’ve magically become very tangled. Now I’m familiar with the usual hand-wavey explanation of “there’s only one way for cables to remain untangled, but a huge number ways for them to get tangled”. I’m wondering if there’s a way to mathematically describe how they get tangled, how much they are likely to get tangled after some time, and if so, what’s the area of maths that underpins this?
A few thoughts for areas that could be involved were:
- a modified/approximate version of topology/knot theory, inspired by the above “explanation”, since we treat all untangled cases as equivalent
- stochastic calculus, if I understand correctly, is like the calculus of random kicks, which could approximate the shaking of a container
- group theory - related to the topology point, I’m just thinking about the braid group here
I’m not too sure though, so I’d be interested to hear if anyone has ideas about this, or even a sketch of a solution