The Mirror Puzzle
The mirror puzzle refers to the way a reflective surface seems to reverse our left and right sides without ever reversing our top and bottom. Think about this for a second. Why is it that in a mirror your watch wearing left wrist magically appears on your mirror image’s right, but your head never switches place with your feet?
You may scoff at this so-called puzzle but after a little reflection I think you will find it a litle more... well, puzzling. At first, the very notion seems ridiculous. My feet in the air and my head on the ground!? But then why should my watch jump to my right wrist and my wedding ring jump to my right ring finger?
Not only this but should you lie on your side before a mirror you will still find that it is still your left and right sides that are reversed, not your head and feet, which you might expect after observing the left/right switch effected from a standing position. What gives reflective surfaces this strange preference for reversing our left and right (and only our left and right)?
The only solution I have heard for this involves the uniqueness of the human perspective on the situation. It is all in our minds. This explanation turns on the notion that we perceive the reflected image as if we had rotated around a vertical axis, thereby reversing left and right. The explanation given for why we do not instead see the image as if we had rotated about a horizontal axis (thereby reversing top and bottom) is that we are not in the habit of turning somersaults in real life while we do frequently and easily rotate about a vertical axis. The idea is that we perceive our reflection as a result of conditioning and habit. We are not in the habit of performing somersaults and so when we look in a mirror we don’t mentally project ourselves rotated about a horizontal axis.
This solution is essentially correct but there is a little more to it which I hope to supply with this essay.
Firstly, it is a misleading initial insight to consider the mirror puzzle as turning on a ‘reversal’ of left and right. After slipping into that mode of thinking it is difficult to climb out of the hole you have started to dig. No mirror has ever reversed any image before it. So what does happen when you look in a mirror? This is the all important first question.
When you look in a mirror, all that happens is the object directly in front of it appears reflected in exactly the same place in its surface. Talk about reversals only confuses the issue. So in front of your left hand a mirror image appears in the mirror of your left hand. In front of your head appears a mirror image of your head. And so on.
Now it is true that it appears as though everything has been reversed left to right, or rotated around a vertical axis, but this is a mentally created illusion caused by two facts:
1. We are symmetrical about a vertical line through the centre of our bodies.
2. Gravity combined with the fact that we have walking apparatus at only one end of our bodies ensures that that end (the feet) is always directed downwards. (In other words, a rotation about a vertical axis is easy while a rotation about a horizontal axis tends to involve some effort)
Both of these facts contribute to the way we perceive the image of ourselves standing directly in front of us. If we were not symmetrical about a vertical axis and we couldn’t so easily transpose ourselves in our imagination to the position of our mirror image through a rotation about a vertical axis, we wouldn’t experience the delusion that our left and right sides had been mysteriously reversed.
Imagine a gravity free room floating in space with only five objects floating in it. There is a round mirror and four shapes; a triangle, a square, a rectangle and a circle. Next imagine a central point about which we can say the circle is above, the square is below, the rectangle is to the left of and the triangle is to the right of. These objects are all reflected in the mirror.
Now if we were to see this situation as an outsider looking in, there is nothing in it that would cause us to imagine the mirror image had reversed either the left/rectangle and right/triangle or the top/circle and bottom/square.
If we had to say anything about this situation we would only comment that the mirror image of the rectangle is in front of the real rectangle, the mirror image of the triangle is in front of the real triangle and so on.
This can easily be confirmed by imagining someone arguing that they can still easily visualise the rectangle and triangle (left and right) as having switched places while it makes no sense to visualise the circle and square (top and bottom) having done so. This person has failed to fully separate himself from his natural, left/right symmetrical, human way of thinking. If everything in the room stays the same we would just take our non-believer and rotate him 90 degrees to the right without him knowing. We are in the middle of space so this is easy to do.
If we asked him to then describe the mirror image to us, he would confidently announce that it is still easier to imagine the left and right being reversed in the mirror. Only now, it would be the circle which has changed places with the rectangle (now left and right, formerly top and bottom).
Removing gravity and the natural left/right symmetry of the human body from the equation also removes the illusion of a left/right reversed mirror image.
Another (simpler) thought experiment involves considering what happens when we lie on our side in front of a mirror. Earlier I used this situation as a ‘proof’ that the mirror mysteriously reverses our left and right and never our top and bottom but there is a subtle flaw in that argument not immediately visible due to our unique human perspective contingent on the two facts I mentioned.
It is clear that if we are standing, it is the left and right which appear reversed. What happens when we lie on our right arm though? When we look in the mirror is it the left and right which appear reversed again? At first glance you might think that is exactly what has happened, after all, our watch now seems to be on our right wrist and our mirror image is lying on its left side… isn’t it?
Actually when we look in the mirror now, it is not the left and right which appear reversed. It is your left and right. We want to distance ourselves from the biases of the human mode of perception influenced by gravity and symmetry.
When you lie on your right side it is your left arm that becomes the top while your right arm is now on the bottom. Your head is to the right and your feet are to the left. So what has been reversed? It is no longer the right and left but the top and bottom. The mysterious reversal has now taken place about the horizontal axis not the vertical axis.
This tells us that there is nothing intrinsic about left/right reversals in mirror images. It is our left and right which are reversed, not the left and right, which means that the reversal is only in our mind, i.e. the way we perceive our reflected selves.
It is apparently absurd to claim that our head and feet have been reversed in a mirror image but what is not so obvious is that it is equally absurd to claim that our left and right sides have been reversed. Reversing our left and right only seems less absurd because we possess left/right symmetry, not top/bottom symmetry. The apparent reversal occurs solely due to this vagary of human perception and hinges on us imagining ourselves in our mirror image’s place through a 180 degree rotation about a vertical axis.
As I have attempted to show the mirror puzzle is explainable by reference to our symmetry about a vertical line through our centres and the fact that gravity keeps us feet-down almost 100% of our conscious lives. Both of these make the vertical-axis rotation in our minds an almost unconscious one when we see our mirror image. As hard as it may be to accept, the mirror puzzle is, literally, all in our minds. Perhaps this conclusion hints at the way our thoughts are so heavily influenced and biased by our (sometimes limited) perception and cognitive faculties. This of course begs the question central to the philosophy of mind; are things the way they seem to be because that is the way they are or are they the way they are because that is the way they seem to be?