Orientation entanglement
In the left half of this picture
vertical slices left to right correspond to the `plate trick':
The `hand' at the top rotates twice about the vertical axis
while the `shoulder' at the bottom remains fixed.
Horizontal slices top to bottom correspond to the `belt trick':
The twice twisted `belt' at the top is deformed to the
untwisted belt at the bottom without moving the ends.
The `orientation entanglement' demonstration from
Misner-Thorne-Wheeler's section on spinors corresponds
to duplicating the left half of the picture by reflection in
the final vertical slice. The top slice now represents the
twice tangled strings connecting the stationary cube (the
previously final, now mi ddle vertical slice) to the walls.
Horizontal slices lead downward to the identity at the
bottom corresponding to the untangled strings. Because we reflect
rather than extend periodically the tangles to the left and right walls
are oppositely oriented. This is necessary to perform the demonstration
physically, but the mathematical deformation works either way!
(Thanks, Dad, for imagining you'd seen this, and for everything else!)