Rotational invariance is achieved for every 360° turn. If the frame of reference is a straight line and if the angular measurement is pivoted at one end then zero degree measure and 360° are both equivalent measures. Furthermore, both also indicate rotational or directional invariance. It implies that clockwise (CW) or counterclockwise (CCW) rotations are indistinguishable.
If each link of a double Hopf links are turning then with respect to each other there is no way one link can determine the rotational orientation of the other whether CW or CCW. However, if one link made the assumption that it is turning CW then as an absolute frame of reference it can determine whether other links are turning CW or CCW. This distinguishes the distinctive frames for both linear motion and angular motion. The first only needed one zero as a point of origin. In addition, the second needed one perfectly straight infinitely extended line as well. This dual simple-complex frames of reference (one zero one line) can provide the topology of understanding ½-integer and integer multiples of elementary particles’ spins for both fermions and bosons.


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