Why mirrors reverse left and right, but not up and down

An old chestnut asks why mirrors reverse the directions LEFT and RIGHT, but maintain UP and DOWN.

Actually, it's not a question about mirrors, but a question about the different concepts we have of direction. Think of yourself standing in front of a mirror. Your left hand is opposite your image's right hand, your right hand is opposite your image's left hand, your head is opposite your image's head, and your feet opposite your image's feet. You could equally well look at somebody else, and ask why your head and feet are opposite theirs, but your left and right hands are reversed compared to theirs. So let's do that, instead.

Now look at how you transfer your notions of directions to the other person. To transfer left and right, you pretend to rotate yourself by 180^o about a vertical line between the two of you. Naturally, after rotation your left goes to the point opposite your right.

Suppose you wanted to transfer you up and down in this manner. You'd pretend to rotate yourself by 180^o about a horizontal line between the two of you. Lo and behold, you're now standing on your head, with your feet (after rotation) in front of where your head started off. But that's not how you transfer these directions; instead, you use the same rotation, about the vertical line, for all 3 directions

Your front is also opposite the other person's front. It's all due to the screwy notion we have of how to transfer left and right!

Interestingly, a combination of two mirrors at a right angle does not reverse left/right. In addition to front/back, it reverses the sides. The net effect is like (-1)*(-1) = 1, and the notions of left/right are unchanged.

I will probably not be the first person in this debate to say that everybody else was wrong. :) The real reason is, of course, the relative symmetry of humans. We look horizontally symmetrical, that's what makes it possible to say that a reflection of our hand or face is still a hand or a face. Imagine that all humans looked like a giant @ symbol. The reflection in the mirror would look pretty weird to us then. :) The question would not be why mirrors reverse this or that, but why mirrors turn a normal human into a wicked alien creature, or actually "who is this monster behind the glass wall?" :)

The left hand in the mirror is still our left hand seen reflected. Our head is still the head seen reflected. You need to be in a really bad state to mistake your head for a pair of legs, but you can easily persuade yourself that a hand or an eye in the mirror somehow changed their affiliation.

Future Research

While I believe that our findings are extremely valuable and useful, still we have only begun to uncover the mysteries of the mirrors. To stimulate further scientific inquiry into this phenomenon, I suggest several experiments that may greatly benefit human knowledge and further enhance our understanding of the psychological, logical, political, geographical or other effects of mirrors.

• check if mirrors reverse the polarity of the magnets
• investigate the claim that mirrors reverse the aging process. Some researchers suggest that mirrors actually accelerate it.
• check whether mirrors reverse North and South or East and West in terrestrial globes. What effect, if any, can be observed for globes of Moon or Mars? For a featureless white sphere? For a mirror glass ball (hold near the mirror)?
• check if mirrors reverse any latin letters or arabic numbers
• attempt to devise a text string the meaning of which will be reversed in mirror
• is it possible to achieve the same or better effect with kanji
• try to devise a mathematical theorem the reflection of which would be its own proof
• find out whether one-handed researchers observe the same effect?
• do the same for one-eyed researchers
• try to explain the problem to blind researchers (preferably those blind from birth)
• try to do the same with a deaf researcher (ask him not to look at you directly, but use a mirror instead)
• form a focus group of Siamese twins and dicsuss the problem with them. Analyse the effect that their relative positions has on their opinions. Of particular interest is the opinion of twins adjointed at their occiputs
• evaluate the feasibility of using mirrors as input devices in optical quantum computers
• is the behaviour of animals affected by the regular mirrors and angular double-mirrors that do not "reverse left and right" differently? Non-symmetric animals like certain crab species are especially interesting in this regard

Please feel free to add the results of the experiments that you perform below or suggest other ones.

The answer is: mirrors don't reverse left/right any more so than up/down. When you look at yourself in the mirror, your right hand side is on the right, and the left is on the left. We're more easily confused about left vs. right than top/bottom because the determination of left/right is more ambiguous than top/bottom: left/right is determined relative to the Self, whereas up/down is determined relative to the landscape. Because we are accustomed to facing others, when we face our reflection we project left/right in terms of the other's self. The point of confusion occurs as we witness and re-identify the reflection with ourselves, while hanging on to our projection to the other. Up/down is less ambiguous because we are strongly oriented by gravity, and identification of up/down is reinforced by association with distinctly different parts of the body (head/feet).

To put it succinctly, this conundrum is a confusion of identities.

This specific case is interesting because the concern is wholly a matter of language, while the presence of the mirror works as sort of a red herring that nicely leads consideration of a solution away from matters of linguistics toward physics, and as such is representative of confusions present in zillions of other highly significant matters, such as current (2004) doctrine about U.S. Foreign Policy.

[My distinction of language from physics is also an identity confusion when viewed from a certain level. ("Wowzy-wow-wow, Roxy!") suggesting important concerns for knowledge in general. See Science and Sanity]