In this situation, a spinor is a sort of polarized vector. In the adjacent diagram, a spinor can be represented as a vector whose head is a flag lying on one side of a Möbius strip, pointing inward. Initially, suppose that the flag is on top of the strip as shown. As the coffee cup is rotated it carries the spinor, and its flag, along the strip. If the cup is rotated through 360°, the spinor returns to the initial position, but the flag is now underneath the strip, pointing outward. It takes another 360° rotation in order to return the flag to its original orientation.
