Stephen Law

This chapter never made it into the final version of my children's book The Outer Limits (vol 2 of The Philosophy Files, now part of The Complete Philosophy Files). For Whittermarsh Jr. 4. The Mirror Puzzle Sometimes it is the things that are most familiar to us that turn out to be the most deeply puzzling. Take mirrors, for example. How many times do you see yourself reflected in a mirror each day? 1.ILLUSTRATE: BOY LOOKING INTO A MIRROR At least ten or twenty times, I should think. Most of us never stop to think about what we see. But, as you are about to discover, mirrors are very strange and puzzling things. An adventure in the mirror Aisha and Kobir are visiting Kobir’s auntie. Auntie Anaximander lives in an enormous, fusty old house deep in the moors. 2. THE BIG SPOOKY HOUSE IN THE MOORS. LIGHTNING. It’s a wild and stormy night and the phone and power lines are down. Auntie Anaximander has gone off in her car to report the powercut leaving...

What follows is my own suggested solution to this puzzle - scroll down for the puzzle (I note several of you offer much the same solution) We noted before that, in a sense, mirrors don’t reverse anything. So why do we say they reverse left-to-right, but not top-to-bottom? Well, if the mirror before you was replaced by a sheet of glass, and you were to stand behind the glass in just the position your mirror-self seems to stand, then while your head would still be at the top and your feet at the bottom, your left hand would be over to the right, where your right hand appears in the mirror, and your left hand would be to the left, where your left hand appears. That is why we say the mirror reverses left-to-right, but not top-to-bottom. But notice that we have just taken something for granted: the axis about which we rotate you when we imagine you over there behind the mirror. When we turn something round, we rotate it about an axis. A spinning top, for example, rotates around a vertical a...

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 mirr...