Interestingly, though right and left and forward and backward are reversed when looking in a standard bathroom mirror, up and down are not. Why is that?
Though the problem seems trivial, asking someone why up and down are so inherently different from right and left produces many strange looks and not a lot of comprehension. I have heard only two explanations (from exactly two people) that actually make a modicum of sense, though each carries with it many flaws.
- Up and down are defined relatively to the planet, whereas left and right are relative to the individual; that is to say, my right might well be your left whereas my up is always also your up. Therefore, when the mirror reverses the individual, it flips his right and left, but since its focus is not on the planet, it leaves up and down well enough alone.
- When a mirror is oriented vertically (as is the case with the standard bathroom variety), it reverses all directions save that of verticality. If one were to lay a mirror on the ground and gaze downward into it, one would behold the sky; thus, the mirror would have reversed down and up. Moreover, in such a position, the observer's right and left and forward and backward would remain in tact.
Obviously, there are flaws in both arguments. In the first explanation, how does the mirror know that we intend it only to flip the individual? Why does it not indiscriminately include the world and the stars in its irreverent flipping? In the second explanation, why are two axes (left-right and forward-backward) reversed when the mirror is vertical but only one axis (up-down) when the mirror is horizontal? Physicists will tell you all about the nature of light waves, incident angles with respect to normal vectors, and so forth, but it really misses the point. The dichotomy comes with our definitions of left and right, up and down, forward and backward, concepts which appear to be internally consistent yet are extremely difficult to explain articulately when presented with the above quandary.
Note that I do not attempt to explain why mirrors reverse (in the conventional sense of the word) left and right but not up and down; a very articulate node has already been written on that very subject: why mirrors reverse LEFT and RIGHT, but not UP and DOWN. The purpose of this write-up is to identify the flaws in the two most common explanations I am given; no more, no less.