Let us replace the Pauli unknot arcs with the suggestive letters $i$, $j$ and $k$. Now we can carefully draw the unknot in three dimensions, making sure that each straight line segment follows a $45$ degree line with respect to a chosen set of axes. Thus one arc moves down the $45$ degree line, one moves up the $45$ degree line, and one moves along the $135$ degree line.
If the knot arcs were thickened to ribbons, the twisting moves would look like ribbon twists, one for each of the three planes in space, as in this paper.
6 years ago