Tim Wilkinson reflects on an old question.
https://philosophynow.org/issues/114/Mirror_Mirror
Mirror, Mirror
Re: Mirror, Mirror
This is nonsense. Put your left hand on the Möbius strip and slide it around the strip to the starting point. I can guarantee that your left hand has not been transposed into a right hand.Consider the Möbius strip, which is formed by taking a length of paper and, after introducing a single twist, joining the ends together. Now, by rotating a left hand and taking it on a journey around the strip, it can be transposed into a right hand without the use of a mirror: