Saturday, July 2, 2011


Some animals never seem to learn that mirror images are illusions. A parakeet, for example, is endlessly fascinated by what it sees in the reflecting toys placed inside its cage. It is hard to know what goes on within a bird’s brain, but the parakeet’s behavior suggests that it thinks it is seeing another bird. Adult cats, dogs, and other mammals are curiously indifferent to mirrors. Perhaps they learn quickly that the images are not substantial because they have no smell. Young chimpanzees, on the other hand, become excited and thoroughly mystified the first time they see themselves in a mirror. If the mirror is vertical, in the middle of a room or grassy area, they keep jumping behind it to find the other chimp, then jump back again to look in the mirror and see the chimp who so mysteriously vanishes and reappears.

Older chimpanzees with play for hours with a pocket mirror. They make faces at themselves. They use the mirror for looking at things behind them. They will study the way an object looks when seen directly and ten compare it with how the same object looks in a mirror. They use mirrors to groom parts of themselves they cannot see, to pick food from their teeth, and so on. If an anesthetized chimp is painted around an ear with a bright-red dye that is odorless and nonirritating, on being awakened the chimp will see the spot in a mirror and try to rub it off. Apes who have been taught to use hand signs will make a sign that means “me” when asked whom they see in a mirror. Clearly they know that the image is not that of another chimp. All this strongly suggests that the great apes are to some degree aware of their own identity. True, a pigeon can be trained to peck at a spot of dye it can see only in a mirror, but pigeons can be trained to do all sorts of meaningless things.
Let me try to confuse you with a simple question. Why does a mirror reverse only left and right sides of things, not up and down? Think this over carefully. The mirror’s surface is perfectly smooth and flat. Its left and right sides do not differ in any way from its top and bottom portions. If it is capable of transposing the left side of your body to the right, and the right to the left, why doesn’t it also switch your head and feet? Each line in the reverse stanza of “Jabberwocky” reads from right to left. Viewed in the mirror the lines read from left to right, but why does the top line remain on top, the bottom line on the bottom? Since the mirror exchanges left and right, what happens if we give the mirror a quarter turn clockwise? Will it turn the image of our face upside down? We know, of course, that no such thing will happen. Then why this spooky, persistent preference for left and right? Why does a mirror reverse the room horizontally but fail to turn it topsy-turvy?
I hope these questions are beginning to make you feel a bit more like an intelligent monkey contemplating his reflection in a pocket mirror. They are indeed puzzling questions. Try them on your friends. Chances are they will be just as puzzled. You will get plenty of embarrassed laughs and stammering attempts at explanation, but it will be surprising if anyone gives a clear, straightforward answer. With respect to mirrors, adults are more like cats and dogs than monkeys. They take mirror reflections for granted without attempting to get clear in their mind exactly what a mirror does.

To make matters even more bewildering, it is quite easy to construct mirrors that do not reverse left and right at all. …..

As a chimpanzee no doubt says to himself, which he reflects on mirror reflections, the matter deserves further study. We begin such a study in the next chapter by taking a closer look at what a mirror does to geometrical figures in one and two dimensions. Before our study is finished, we will have explored many queer scientific truths, from frivolous, some not so frivolous. Two of the most stupendous scientific events of this century – the physicists’ overthrow of parity and the biological discovery of the corkscrew structure of the “genetic code” – are intimately connected with left and right and the nature of mirror reversals. In the end, our investigation will plunge us straight into some of the deepest, least-charted waters of contemporary science.

From: Chapter 1: “Mirrors”, The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings, 3rd edition, by Martin Gardner


Neil Bates said...

Heh, this is a good one. Basically (as I worked out myself and found various mostly agreeing commentary, e.g. Gardner gets it): the mirror doesn't *really* reverse left and right! The apparent image ("AI") is reversed "front to back" through the mirror. (Coordinate shift, if x, y is the mirror plane: z <----> -z.) Here is an embarrassing trick to play on yourself (if a revelation) or others: Take a piece of clear glass or plastic you can write on with e.g. grease pencil. Write your name, whatever that looks different reversed. But instead of *turning the sheet around* to face the mirror, just hold it up: the letters are not reversed! Everything is just where you write it, all matching up perfectly. See - hope it's not too embarrassing - all those times you wrote on something and "looked at it in the mirror", *you* reversed left and right by turning the paper around. You had to do that, not because of some logical or geometric ray issue, but merely becasue the paper is opaque and cannot be seen through. Same issue for in the rear view mirror: you turn around and switch your own L and R when you face away from things and then look at them behind you. (BTW you can get folded mirrors that literally reverse your L and R sides of presentation. They show you as others see you, hair part on the other side etc. as if you really turned around.)

I embarrassed some folks at my 20th college reunion with that. I told them not to feel bad (hey, just consider those who can accept MWI!)

But wait, there's more! We could consider that the "standard" of left and right for the AI is reversed, and then even though your right hand is seen "on the right", it really counts as "a left hand" if the mirror person was imagined real and making the judgments from their own perspective! Oh woe ...

Behold the penetrating insights of the great Lord QuaQua!

Ulla said...

There is a very simple answer. There is no top-bottom symmetry, usually. Maybe, if we were spheres :)

Neil Bates said...

Ulla: No, it's not about the symmetry of the things we're viewing in the mirror. It wouldn't matter what we had there. Because a mirror does not really reverse left and right, it does not reverse top and bottom, either. Like I said, it reverses "in and out", and most of the illusion of L-R reversal comes from *you* turning papers etc. around. People's hands reverse left and right to look at opaque objects, not the mirrors.

Jérôme CHAUVET said...

Why does a mirror reverse only left and right sides of things, not up and down?

Because flat mirrors do planar symmetry.

On the contrary, concave mirrors (like silver spoons) do central symmetry, and as such reverse up and down too.

In any event, rotation and reflexion are two transformations of the same kind (orthogonal automorphism) simply differing from one minus sign in the matrix and the brain may find it hard to distinguish them sometimes.

Ulla said...

Ye, this was about how we experience the mirror. Remember, we already reverse the picture once in our brain, and we have no problems with real 'mirror-pictures'.

It would be very odd to see the feets at the heads place, and try to walk :)