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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.
Assistant Professor of Philosophy
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
Wim R. Van Dam
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.
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
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.
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.
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
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
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.
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