Are Phenomena on Two Axes in Three Dimensions Strange?

There is a problem known as the Kochen-Specker theorem, this theorem is often trivially represented as the SPIN theorem. You can measure a 1-particle on three axes, and observe that the spin is parallel to the direction (+1), perpendicular to the direction (0), or anti-parallel to the direction (-1). The SPIN axiom states that the square of the spin is a permutation of (0,1,1), something is happening on two axes.

A particle being measured from three orthogonal directions

I really don't know what is going on here, but let's ask another question. Is it strange to observe something on only two axes in three dimensions? The answer: No!

Imagine you throw a ball against a wall, or bounce a fluid in space. If you look at it from three axes, where two axes are parallel to the wall, it will alternate between a flattened and stretched circle on two of them and on the remainder axis it'll look like a shrinking and expanding circle. If you assume that it is easy to observe the flattening/stretching, but not the shrinking/expanding, you end up with the SPIN axiom. If you assume that it can only fibrate alligned to the spin, you don't need to square. (In the picture you'ld bounce in the 0-axis direction.)

Note that this is the reverse question, it says nothing about the paradox or the spin axiom. It is a model which just satisfies the axiom, nothing more. Though now I am wondering if people are actually measuring spin...

The essence of QM: Its damned hard to get periodic behavior out of linear transformations? Or just a gimbal lock?