updated 23-Mar-1997 by Phil Gibbs and David Richards
updated 04-MAR-1994 by SIC;
original by Scott I. Chase
Trimotio: Hey Fineas, Tell me this, why do mirrors reverse left and right?
Fineas: The simple answer is that they don't. Look in a mirror and wave your right hand. On which side of the mirror is the hand that waved? The right side, of course. But look again Trimotio, mirrors do reverse in and out. Imagine holding an arrow in your hand. If you point it up, it will point up in the mirror. If you point it to the left, it will point to the left in the mirror. But if you point it toward the mirror, it will point right back at you. In and out are reversed.
Trimotio: I don't agree. Look, I have a mole on the right side of my lip. However, The guy in the mirror has a mole on the left side of his lip. I wave my right hand. He waves his left hand. This happens precisely because he is facing me and my right becomes his left. That a mirror preserves our own left and right is trivial. But the point is that it reverses the left and right of our reflected image. So there is this obvious question: Why doesn't it also reverse top and bottom? I pat the top of my head, so does the guy in the mirror. He does not pat the soles of his feet.
Fineas: What you are saying now is that a mirror changes a right handed co-ordinate system into a left handed system. If you take a three-dimensional, rectangular, co-ordinate system, (X,Y,Z), and point the Z axis such that the vector equation X x Y = Z is satisfied, then the co-ordinate system is said to be right-handed. Imagine Z pointing toward the mirror. X and Y are unchanged (remember the arrows?) but Z will point back at you. In the mirror, X x Y = - Z. The image contains a left-handed co-ordinate system.
This has an important effect, familiar mostly to chemists and physicists. It changes the chirality, or handedness, of objects viewed in the mirror. Your left hand looks like a right hand, while your right hand looks like a left hand. Molecules often come in pairs called stereoisomers, which differ not in the sequence or number of atoms, but only in that one is the mirror image of the other, so that no rotation or stretching can turn one into the other. Your hands make a good laboratory for this effect. They are distinct, even though they both have the same components connected in the same way. They are a stereo pair, identical except for "handedness".
Trimotio: I know all that, and you still have not answered my question. You can turn a right handed system into a left handed one by reversing any one of the three axis, or even by reversing all three at once. Yet the mirror reverses left and right, not top and bottom. Perhaps the effect is due to the fact that our eyes are aligned horizontally on our faces.
Fineas: So look at the mirror with one eye closed. Does it make any difference? No! I think it is gravity which is at work. Doesn't that define "up" and "down" for all?
Trimotio: Rubbish! I lie in bed and look in the mirror. The guy in the mirror is lying down. His right is my left, but the top of his head is the top of my head. That ain't it.
Another phenomenon unrelated to mirrors, but which sheds some light: I am in a crowd. "Up" and "down" are the same for all of us. "Left" and "right" is entirely personal. Floating in space, of course, it all becomes personal. I read once that when astronauts go up there they get used to the idea that their personal "up" is "up", whatever their orientation. But when they look in the mirror, astronauts see the same thing we do: left and right are reversed, but not top and bottom. How could it be anything to do with gravity?
Human beings are creatures with bilateral symmetry. We are symmetrical, our left and right halves being (more or less) mirror images through a plane defined by the vertical axis and the dorsal/ventral axis (perpendicular to the mirror). Our left sides are mirror images of our right sides. Not so with top and bottom. I think this is why we have local left and right and a shared top and bottom in the mirror, as elsewhere.
I figure the beings on the ocean planet of Skyron who are symmetrical around two axes (they are X-shaped, with four similar arms sticking out and one eye in the center) and have nothing other than a local sense of "up" and "down" as well as "left" and "right" look into the mirror and see things reversed for either axes.
Fineas: I see your point, but what about our ugly alien friends from the planet Torsor. They have no symmetry at all. Yet tell them to turn left and they shuffle round to the left while their mirror image shuffles round to its right. They would agree the mirror reverses left and right even though they have no symmetry. In space they lose all ideas about turning left and right. So you see it is something to do with gravity! Actually I think it is a bit of both symmetry and gravity.
Trimotio: Perhaps, but for the case of humans I think you will find that it is symmetry which counts most.
Let me see if a got this straight. Physically, the mirror reverses in and out. That will turn a left handed co-ordinate system into a right handed one. We might equally well say that it changed a top-headed co-ordinate system into a bottom-headed one. But when we look in the mirror we place ourselves mentally in the position of the reflection. We would do that by turning 180 degrees round a vertical axis, partly because that lines us up with a symmetrical image, and partly because we are used to turning round a vertical axis as we walk. The combination of the in/out reflection in the mirror and the 180 degree rotation in our head is a left/right reflection. The only creatures which would not perceive left/right reversal in a mirror would be those with radial symmetry like the Skyronians and those with no symmetry like the Torsions, but only if they lived in the absence of gravity too. Right?
Fineas: Well, I was just thinking. Our brains are divided into left and right halves. I wonder if that could have anything to do with it. The left half of the brain controls the right half of the body while the right half controls the left. They have very different functions in our mind. Our speech comes from the left side while visual recognition is in the right. Although we look symmetrical externally, our psyche is very asymmetrical. Perhaps that is why the change from left to right stands out so strongly.
Trimotio: I don't see what that has to do with it. You can't see your psyche in the mirror. On the other hand there does seem to be an element of psychology in it. The mirror just reflects light back. The way we interpret what we see is in the mind. I think different people could have different, equally good, answers to this question. It will all depend on their interpretations which may depend on their own experiences and world-view. Cool.
References:
The Left Hand of the Electron, by Isaac Asimov, contains
a very readable discussion of handedness and mirrors in physics.
The Ambidextrous Universe, by Martin Gardener is
another book which covers this subject.