# The Topology of Movement

In this second lesson, we use a novel movement-based approach to understand the shape - or topology - of orientation space, with the help of a simple puppet. I haven't seen this approach elsewhere, but I feel it leads to very useful insights, which are often skipped in standard treatments.

Without further ado, let's proceed to the first warm-up challenge:

Okay, the first challenge was hopefully not too challenging. Once you've completed it, you can proceed to the next video:

Have you completed your own wobble loop? Let's see how it compares with other wobbles:

Did you complete the third movement challenge? Then you're officially warmed up, and ready for the next puzzle, which involves a very important definition:

Remember, a loop in orientation space is a movement sequence that finishes where it began, at the base orientation. And a loop is trivial if we can enact a gradual deformation to the stationary loop: that is, perform the loop repeatedly with small changes each time, until we reach the stationary loop.

Have you completed the fourth challenge? Let's see how it compares with other solutions:

Once you've enacted the gradual deformation of one 360° rotation loop to another, you can proceed to the next challenge:

Did you find both the trivial and nontrivial loops that track the particle? If so, you can proceed to the next video:

At every instant of the time, as θ goes from 0 to 2𝝿, the trivial loop's orientation can be achieved via a composition of two rotations: Somehow, performing two nontrivial loops simultaneously results in a trivial loop. What's more, if we concatenate two nontrivial loops, performing one after the other, the result is once again a trivial loop!

I hope you were able to enact a gradual deformation of a 720° rotation loop to the stationary loop! There are many ways to do this, but we'll examine one approach in the next video:

Okay, but how do all these loops and deformations in orientation space relate to the string trick, from the introduction video? Let's conclude with a closer look at the string trick, and take it to its logical extreme: the foam mattress trick: