Volume 11, No. 1—February 2001  
Table of contents for this issue  
 
LETTERS TO THE EDITOR

IN HIS NOVEMBER HYPOTHESES COLUMN, Jim Holt explored a conundrum that has long confused philosophers, scientists, and others: Why do mirrors reverse left and right but not up and down? Below, Lingua Franca's readers offer their own reflections on the mirror problem.

The problem with the "mirror problem"--why does a mirror reverse left and right but not up and down?--is that mirrors don't reverse anything; we do. We reverse left and right owing to our prior (gravitationally motivated) commitment to preserving up and down. Imagine sharing a (gravitationally different) world with someone who walked on your ceiling. You might then try to preserve left and right by projecting yourself head over heels into your reflection; this--not the mirror--would in effect reverse up and down. What mirrors do to our reflections is in truth just a reflection of what we do when we look into them.

Taylor Carman
Assistant Professor of Philosophy
Barnard College

A mirror can reverse up and down: If you put a mirror on the floor and stand on it, your mirrored feet are up and your head is very much down. This was pointed out some years ago in a letter in the Dutch paper NRC.

Wim R. Van Dam
Leiden, Holland

Like Jim Holt, I have often been puzzled by the fact that mirrors reverse left and right but not up and down. Then the answer came to me: Nothing is reversed at all. A mirror just reflects what is in front of it at every point. Our perception that left and right are reversed happens only because we are bilaterally symmetrical but not up-down symmetrical.

Think about it. If mirrors really reversed left and right, then you could lie on your side in front of a mirror and your head and feet would be reversed. The fact that they are not is proof that there is nothing inherent in a mirror that creates the left-right reversal.

The reason why left and right, and not up and down, appear to be reversed is the same reason why, when another live human being stands facing you, her right hand matches up with your left hand and vice versa, while her head does not match up with your feet. A person who stands in front of you is merely turned 180 degrees around, thus reversing left and right but not top and bottom. A mirror image of yourself produces the same effect--it is as if you had rotated 180 degrees. There's no mystery about it, any more than there is mystery about why a human being standing in front of you isn't automatically standing on his head.

Stuart Buck
Fort Thomas, KY

Jim Holt suggests there's nothing very strange about "the fact that ordinary mirrors reverse left and right." There is: They don't.

Want proof? Write a word on something transparent. Standing before a mirror, hold the word in front of you and look through it. The image of the word reflected in the mirror isn't reversed. Turn the word around, and both the word and its reflection still match.

Some will be quick to argue that the reflection of the transparent word is indeed inverted, since the mirror is really reflecting the word's obverse. This, however, is to confuse two separate and distinct perspectives. And it is in this confusion, perhaps, that our perception of mirror reversal originates.

If a mirror truly reversed the images of the things it reflects, then we would see ourselves as others see us. Our left hand would appear to the right in the reflection, and our right to the left. Instead, our reflected symmetry remains parallel to our actual symmetry. Why, then, do we insist on seeing an inversion?

Perhaps, seeing our reflected self, we strive to relate it to what we imagine a person standing within the mirror would see looking out--that is, we compare what we see in the mirror to what we imagine the mirror sees of us standing before it. This imaginative act involves a transposition of our own front and back--and, consequently, our left and right--as we mentally enter the mirror to reposition ourselves. It is therefore not in reference to the perceptual map of our body but to the imagined one of our reflection that the notion of mirror reversal originates. This explains why it is that objects to our left as we stand before the mirror seem to appear to the "right" of our reflected selves.

Thus the phenomenon vexing Holt (and others) has nothing to do with the metaphysics of optics at all. It is instead merely a transposition of self resulting from our attempt to understand objects reflected by the mirror by imagining ourselves within the mirror. Assuming this to be so, a curious question remains: Are the reversals that reflection inspires a product of empathy or anthropomorphism?

Matthew Justin Kelly
New York, NY

Why do mirrors reflect backward but not upside down? It's basically the same reason why you can travel east or west forever, but if you go north long enough you'll start heading south, and vice versa. The human being assumes rotation to be on a vertical axis, because the human being himself rotates that way. The easiest way to experience this phenomenon is to stand in front of a mirror looking at a picture you hold in your hand. Looking in the mirror, you see the back of the picture. Now show the picture to the mirror so you can see the picture in the reflection but not directly. At that moment, take note of how you turned the picture to face the mirror. Did you turn it on a horizontal axis? No! That's the reason left and right switched, because you chose to switch sides along a vertical axis. Now do it again, but turn the picture over, instead of around to face the mirror. The image has then swapped top and bottom, but not left and right. To face something the other way, you have to switch one of the two dimensions, but not both. It's the assumptions of mankind that make left and right relative but up and down absolute. That's why children easily learn up and down--those directions never change. If I'm facing you, my left is your right, but our up and down are shared. I tried doing that the other way too, but my arms got tired.

Cormac Shea
Raleigh, NC

Mirrors indeed merely do a front-to-back translation. What we do to an object to see its reflection in the mirror affects our perspective about what a mirror does.

Try this: Stand in front of a mirror with a book's text facing you. Look in the mirror, and you see the cover of the book. Wonderful! The mirror is doing its front-to-back translation, letting you see the cover and text of the book at the same time. Now turn it toward the mirror so you can see the text in the mirror. You've chosen a way to flip the book--most likely you've flipped the book about the vertical axis, so the top of the book is still facing up. If you now try to read the book in the mirror, you'll have to read right to left (flipping characters, too, of course). You might say "the mirror flips it left to right." If instead you flip the book toward the mirror on a horizontal axis (end over end), you can read it left to right, but you have to read it bottom to top (inverting characters, too). You might just as well say "the mirror flips it top to bottom."

So, the fallacy is to say that the mirror flips text--or anything--in either direction. It's what you do to see the object in the mirror that defines the translation.

It's when bodies (especially our own) are involved that we become anthropomorphic about the reflection. We note that our "reflection's right hand" is opposite our left hand, but of course the situation is no different than with the book.

Steve Yost
Lexington, MA

An image in a mirror seems to be reversed about its vertical axis (that is, what we take to be its left hand appears directly opposite the right hand of the subject it reflects, and its right opposite the subject's left) while remaining unchanged around the horizontal axis (that is, the top of the reflected image is just opposite the top of the reflected subject).

The source of our feeling that the mirror has reversed the reflected object is due to something between an illusion and a delusion that most of us suffer from, and of which a thorough understanding is illuminating beyond the context of the original paradox. When we see in a mirror an image of a "handed" object--the human figure is the classical example--we find it almost irresistible to imagine that we are looking into a world to which the mirror is the portal.

What we seem to see when we look into a mirror is a person who is hauntingly familiar, but whom we cannot quite place. This person--"X," let us say--even reminds us in a strange way of ourselves, though perhaps not quite as good looking. But what some have found hair-raisingly strange is that X, although quite familiar in almost every way, has been subtly modified by stepping through the mirror portal; the watch we wear on our left wrist, X wears on his right. This has caused hyperventilation among some observers: Are we looking into the fourth dimension? The world of anti-matter? A parallel universe? Alice's dream? A Cocteau film?

I suggest we are looking into the world of hasty assumptions. When we face another three-dimensional human, we know that his right hand will be directly opposite our left; if we want to shake hands, we have to extend our right hand toward the left if we are to grasp his right. If the mirror really were a doorway through which we saw a room much like the one we stood in, and in which stood a three-dimensional person X who faced us from within that room, then the apparent isomeric reversal would be a reality; such an X would have his right hand where we would expect his left, and vice versa.

But this is not the case. The person X, with his left and right hands, is an artifact of our visual system and the assumptions that it has successfully relied on since its creation. The mirror is not a portal; there is no world on its "other side," and there is not a three-dimensional person X within that world who has turned to face us. X is simply the projection of our image onto the plane of the mirror, and back again directly to our eyes. The image of our right hand is where it belongs, directly opposite its subject, just as the image of our head is where it belongs, at the top of the mirror. What troubles us, in fact, is that the mirror, in its innocence, presents us with an image that does not reverse right and left, as is done by any human facing us. The image's right, if images had a right, would indeed be "on the wrong side"--but the "if clause" here is a counterfactual; mirror images have no rights, lefts, or anything else.

Think of a mirror image as being an anti-shadow. Just as our body's shadow is the area on some surface--whether that surface is a plane, or something more complex--from which our body occludes light, so our mirror image is the area of the mirror's surface onto which our body projects light. And just as we find nothing strange about the fact that the shadow of our right hand is directly opposite that hand itself, so there is nothing wonderful about the fact that the mirror image of our right hand is directly opposite that hand itself.

Mark Halpern

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