A spinor is like an electron! If you turn an electron by 360° it's orientation somehow becomes negative. Only when you turn it another full round its orientation returns to the starting position.
Attach a ribbon to your electron, and to the ground. As a reminder of the EM field that connects the electron to the universe. Turn it once, and you get a twist. Twice and... well, did you know: you can undo a doubly twisted ribbon by itself!
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