Take a look at yourself in a mirror. Now imagine yourself actually standing where the mirror-version of you appears to be standing. Of course, your mirror-self’s head is still at the top and their feet are at the bottom. But notice that their left and right sides are switched round. Raise your left hand and wiggle your fingers. It is the right hand of your mirror-self that wiggles their fingers. Mirrors reverse left-to-right. But not top-to-bottom.
But why do mirrors reverse the left-to-right, but not top-to-bottom? What accounts for this peculiar asymmetry? Some of the world’s greatest minds – including that of the Ancient Greek philosopher Plato – have struggled with and been defeated by this infernal mystery.
Notice that this left-right switch still happens no matter which way up you happen to be. Lie on your side in front of a mirror and see the result. It Is still your left and right sides that are switched round, not your head and feet. Nor does it matter which way round the mirror is. Turn it upside down. The effect is exactly the same.
Sometimes people suppose the effect must be due to our having a left and a right eye, rather than a top and bottom eye (as perhaps some aliens do). But that is not the explanation. Cover one eye, leaving yourself with just the other, and the asymmetric reversal remains.
Can science solve the mirror puzzle?
Might science solve the mirror puzzle? In particular, is the explanation that light is reflected differently left-to-right than it is top-to-bottom?
It seems not. Draw a clock face held up in front of a mirror and draw arrows linking each number on the clock face with the same number reflected in the mirror.
The arrows show that the way the mirror reflects is entirely symmetrical in every direction. The arrows do not cross over top to bottom. But neither do they cross over left to right. It is not as if a mirror reflects rays of light differently depending on whether they are coming from your left and right sides rather than your top and bottom. The light is reflected in the same way no matter where it happens to land on the mirror.
So the puzzle has absolutely nothing to do with how light is reflected off the surface of the mirror. Indeed, the puzzle is not a scientific puzzle at all. Even when we know all the scientific facts about how mirrors and light behave, that still leaves the mystery of why mirrors reverse one way and not the other.
The more we grapple with this mystery, the deeper it seems to become, and the more they seem to take on an almost magical quality. Just why do mirrors do what they do? The profound sense of bafflement raised by this question is typical of that raised by philosophical problems more generally.
What’s the solution?