Earphone tangled with Classical Mechanics

This what happen when you try to listen music while learning physics. At night while I was studying Chaos Theory from Classical Mechanics by Goldstein , I tried to take out my earphone from pocket to listen music. As usual they were tangled even though it was common case I tried to explain it by Classical mechanics

Its quite surprising that how a nonliving and headless pocket can mess up the cord of ear phone.This is one of those things that seem to happen rather more often than it should.

The possibility of wire to be untangled and remain as it is kept in pocket or bag is very less, as there is only single case which corresponds to untangled situation. In other way just picking one of those tangles is quite improbable but it doesn’t really matter. Any old tangled state will decrease the probability of untangle state.

To understand why there are more tangles state we need to
understand the Chaos theory first.

Chaos theory is an area of inquiry in mathematics, physics, and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.

In common usage, “chaos” means “in a state of disorder”, but the adjective “chaotic” is defined more precisely in chaos theory. Although there is no universally accepted mathematical definition of chaos, a commonly-used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:

1. it must be sensitive to initial conditions,
2. it must be topologically mixing, and
3. its periodic orbits must be dense.

Sensitivity to initial conditions is popularly known as the “butterfly effect“. For initial conditions all we need is something that will allow those wires to move within the pocket or 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. Force of attraction between the magnets of headphone, also contribute to mixing of wire. The chaotic dynamics create the randomness and knots, any uneven knots will do the tangle.