"Suppose you have a whole bunch of identical mice. You smash them at high velocity, and measure what's flying out. Reconstruct the design of a mouse from the measurements"
I thought of a different way to look at it.
Suppose you are a train driver. The most boring job in the world - you have only one degree of freedom. Now, you try to accelerate your train beyond allowed speed, maybe collide with other trains, to have fun. This way you can start learning about your real 3D world, the world beyond 1D railway.