Why do wires tangle?

We put this question to Mike Pearson, from Cambridge University's Millennium Mathematics Project...

I hear that someone has called in asking about the fact that their headphones get in a mess whenever they put them into a bag.

This is one of those things that seems to happen rather more often than it should. It's kind of surprising what damage a mindless bag can do.

There are many more tangled possibilities than there are untangled possibilities if you think of the wires in the bag. In a way, just picking one of those tangles is quite improbable but it doesn't really matter. Any old tangled state will do, so the probability that one of those tangle states appears when you put your hand into the bag to get your cables out is actually quite high.

All we need is something that will allow those wires to move within the bag. We need them to pick up some energy from somewhere - and jiggling those headphones around is going to be exactly what we need - in order to generate the randomness - the chaos - that we need in order to create all these knots. Any old knot will do.

An analogy we might look at is the cells of our body: tThere's an enormous problem that they have keeping all the DNA that they have organised inside the nucleus. You can think of the nucleus as being a tiny, tiny little bag. It's only about 20µm big. The DNA is a big, long string or wire about 3m long. That's the equivalent, if you imagine it, of having an iPod cable 30km long stuffed into a 20cm bag. How this all happens is quite a problem, which has puzzled both biologists and mathematicians a lot.