mirror reversal

It is surprising how few people can give an intelligible answer to the question: 'Why are mirror images reversed sideways, but not up and down?' Even physicists, and experts in visual perception, can be shaken by this apparently simple question, and find no ready answer; though 'mirror writing', and lateral reversal of objects — including oneself — seen in mirrors is an everyday experience.

This is best seen with writing. For example, is quite difficult to read. It is inverted laterally — as in a mirror. Vertical inversion is: . Double inversion looks like this: .

Distinguishing left from right has been held, especially by Kant, to depend upon an observer, and not to be a physical distinction of the world. Kant uses this as evidence for his mental categories of knowledge (Prolegomena to any future Metaphysics, 1783).

The mirror reflects top as top, bottom as bottom, right as right, and left as left: the mirror does not reverse right to left or up to down. All this is entirely symmetrical, so where does the asymmetry come from? That there is no asymmetry of the mirror round the line of sight may be demonstrated by rotating the mirror (or rotating it in imagination) in its plane. Clearly it is optically the same for any angle of rotation: there is no asymmetry here. To explain horizontal but not vertical reversal with optical ray diagrams is doomed to failure, for they cannot distinguish horizontal from vertical, as they are symmetrical and equally valid when held in any orientation.

Is the asymmetry of 'mirror reversal' related to the fact that we have a pair of horizontally separated eyes? This is sometimes suggested; but close one eye, and the 'reversal' is unchanged. Consider also a man born blind in one eye: would he not suffer 'mirror reversal' as we do? Yes, he does. The reversals (both upside-down and right–left) of the retinal image by the optics of the eye cannot be relevant either; for this would affect all vision. (The inversion produced by the eye's image-forming optics is of no consequence, for the retinal image is not seen by the brain as a picture by some internal eye. Provided its — doubly inverted — relation of external objects remains unchanged, the inversions have no effect, and do not present any special difficulty for babies during perceptual learning. Experiments with inverting spectacles show that we can adapt to changed touch–vision relationships even when we are adult, which is remarkable, but this is not relevant here.)

It is sometimes said of 'mirror reversal' that it is 'merely verbal — how we speak of right and left' (Bennett 1970). But 'mirror writing' is difficult to read: it looks very different from 'normal' writing. If the difference is difficult to express, it is present before we attempt to describe it; so it cannot be due to the way we use words, such as 'left' and 'right'.

If 'mirror reversal' is not in the mirror, not in the eyes, and not due to how we use words — can it be some cognitive perceptual effect? This kind of explanation has been put forward (Gardner 1964). It is suggested that since we appear behind the mirror, facing ourselves, we make a cognitive rotation — as a mental perceptual act — selecting rotation around the vertical axis because our bodies are nearly symmetrical left–right but not vertically, so this is the easier mental operation to perform. It is remarkable that this explanation appears to have gone unchallenged. If true, it would be of the greatest interest as a dramatic perceptual phenomenon, somehow specifically associated with mirrors. Mental image rotation is possible, though it is slow and often inaccurate. It is very different from mirror rotation.

If mirror inversion were a cognitive rotation it would have to depend on knowledge that a mirror is involved. Suppose we hide from the observer the fact that he is looking in a mirror. He is shown a large, very clean, wall-to-wall mirror with no frame, so there is no information or knowledge that he is looking in a mirror — but the usual 'mirror reversal' still occurs. Consider, further, a photograph taken by reflection from a frameless mirror: the lateral 'reversal' still occurs in the photograph, and yet there is certainly no information here that a mirror was involved. We may also consider introducing false information that there is a mirror when in fact there is not — a typical mirror frame but with no reflecting glass. Does the world reverse when we look through what appears to be a mirror but is not? There is no reversal. Since absence of knowledge that there is a mirror does not remove mirror reversal, and introduction of 'false' knowledge that there is a mirror when in fact there is no mirror does not produce it, we may rule out such cognitive explanations. What then is the answer?

It is remarkably easy to forget that the reflected object has to be rotated, to face the mirror, for us to see it in the mirror. Now we generally rotate objects, including ourselves, around a vertical axis. This produces the right–left reversal. The 'mirror reversal' is not in the mirror; or in the optics; or in ourselves as a cognitive reversal: it is the rotation of the object from our direct view of it, to face the mirror, which produces 'mirror rotation'. What is odd about mirrors is that they allow us to get a front view of objects though we are behind them. But for this, the object must be rotated from facing us to face the mirror. The reversal of the mirror image is right–left only when the object is rotated around a vertical axis. It is entirely possible (though often less convenient) to rotate objects around their horizontal axis. When, for example, a book is rotated around its horizontal axis to face a mirror, it appears upside-down, and not in 'mirror writing'.

If we stand on our head before a mirror, then we are upside-down and not right–left reversed. But this is a confusing case because, quite apart from mirrors, the world continues to look its normal way up though we are upside-down. Here there is indeed a perceptual phenomenon; but this is quite different from mirror reversal, though it may be confused with it. In the case of a room seen laterally inverted in a wall mirror, we see the room from the point of view of the mirror, though we stand opposite to it. The inversion occurs as we walk round the room and so rotate to face the mirror.

It is worth pointing out that if we place a transparent glass sheet with writing on it in front of a mirror, we see the writing on the front of the sheet, and its reflection from its back from the mirror, and they both look the same. This is because we have not had to rotate the transparent sheet for the writing to be reflected from the mirror, as we do have to rotate writing on opaque paper for it to be visible in the mirror. In all cases, it is object rotation that produces these mirror reversals in plane mirrors. Mirrors are not even required: the same considerations apply to lateral reversal of type in printing, as the paper is rotated when removed from the type — so type is made left–right reversed.

There is another kind of reversal of mirror images. We see objects behind the mirror though we are in front of it. This does have an immediate optical explanation; though this is not quite the whole story. Optically, the light path is from the object to the mirror and back to the eye, so we see reflected objects (and ourselves) according to the total length of the light path, which is always longer than the distance of the mirror from the eyes. So it is not surprising that we see objects through the mirror: except that we continue to see this though we know intellectually that the objects (and ourselves) are in front of the mirror. So here our knowledge does not affect what we see. This is an interesting limitation of our cognition, which allows us to see ourselves through the mirror, as we are optically, though we know we are in front of it. Knowledge of the situation does not correct perception of where we are or which way round we are.

While driving, looking at the cars behind reflected in the mirror, their number plates appear right–left reversed; but what is physically rotated to cause this? It cannot be the cars, or the entire scene. What is rotated is the observer's head. The cars behind are seen with the eyes looking forward, into the mirror; so the head is rotated from direct view of the cars and their number plates. This is the cause. It is puzzling when we forget that we are looking forward but seeing backward!

Although we see ourselves in a different place from where we know ourselves to be, we seldom mistake our image for that of another person. This appears not to be true for animals, other than the higher primates and human infants in their first year of life (Gallup 1977). Almost all animals respond to their own images as to another individual of the same species. Gordon Gallup placed marks on one side of animals' faces, and did the same for infants, and found that even after lengthy experience with the mirror there was no tendency for the subjects to refer the mark to their own face. He suggests that this is an objective criterion for testing for awareness of self.

Somewhat similarly, tactile writing on the forehead may be read as from the outside or from the inside. It has been suggested that women tend to 'see' touch writing on their forehead from the point of view of an observer in front of them, while men generally 'see' the touch writing laterally inverted as though from inside their own head. Possibly this difference, if real, is because women spend rather more time concerned with their own faces and with how others see them while men look out.

(Published 1987)

— Richard L. Gregory

Bibliography
• Bennett, J. (1970). 'The difference between right and left'. American Philosophical Quarterly, 7, 3.
• Gallup, G. G. (1977). 'Self-recognition in primates'. American Journal of Psychology, 32, 329–38.
• Gardner, M. (1964). The Ambidextrous Universe.

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