Mirror - Solution

Mirrors invert front to back, not left to right.

The popular misconception of the inversion is caused by the fact that a person when looking at another person expects him/her to face her/him, so with the left-hand side to the right. When facing oneself (in the mirror) one sees an ‘uninverted’ person.

See Martin Gardner, “Hexaflexagons and other mathematical diversions,” University of Chicago Press 1988, Chapter 16. A letter by R.D. Tschigi and J.L. Taylor published in this book states that the fundamental reason is: “Human beings are superficially and grossly bilaterally symmetrical, but subjectively and behaviorally they are relatively asymmetrical. The very fact that we can distinguish our right from our left side implies an asymettry of the perceiving system, as noted by Ernst Mach in 1900. We are thus, to a certain extent, an asymmetrical mind dwelling in a bilaterally symmetrical body, at least with respect to a casual visual inspection of our external form.”

Martin Gardner has also written the book “The Ambidextrous Universe.”

Casper has sent in the following:

‘The riddle isn’t 100% true. If one turns his head 90 degrees to the right before looking in a mirror, one will notice that up and down are being reversed! Left, right, up and down are relative expressions, therefore the meaning of these expressions depend on how they are used. In fact, the problem of the riddle is that the mirror seems to only change the image in one direction.

The reason for this phenomenon is quite easy. A mirror is a two-dimensional field and can change an image in two directions. But because a human has got only two eyes, the image is only mirrored in one direction. If a human would have three eyes (or more), the image would be mirrored completely in two directions.

Furthermore, I wonder what would be the effect for some of us who’ve got only one eye. If such a person is used looking with one eye, I expect that the image won’t change at all. Maybe someone else can give an answer to this.’

I don’t agree with him, especially on that one eye (try it out yourself, closing one eye). His way of thinking is however creative, so I thought I could not withhold his reaction.