Posted by on Apr 5, 2007 in mirror puzzle | 14 comments

# Mirror puzzle

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?

1. This is, of course, a trick question, with a relatively simple answer.

2. 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.This is a scary statement, especially coming from a professional. There is a simple answer… but only if you look at the problem from a particular perspective. On the other hand, there are good, albeit quite complicated answers, from other perspectives.I think one of the differences between philosophers and scientists/engineers is that when we (I’m an engineer by profession) find a way of looking at a problem which yields a simple answer, we call it the “true” perspective and move on.Philosophers, on the other hand, don’t seem (in my albeit limited experience) to do so: They seem to try and find the perspective which yields the most complicated answer(s) and chew on the problem for a thousand years or so.

3. Ok show me your solution. Then I’ll show you mine…!

4. Oh, ok. I didn’t want to spoil the trick.The answer is that mirrors do not reverse left and right just as they do not reverse top and bottom. They don’t reverse anything.It is our minds which want to reverse left and right, because we interpret the image in the mirror as a rotation, not a reflection. When the mirror does not do so, we attribute the discrepancy to a mysterious property of the mirror, not our own ontological naïveté.

5. An interesting corollary to this phenomenon is that the word “CHOICE” (in all capitals) is apparently not reverse by a mirror, counter-intuitively because of each letter’s symmetry around the horizontal axis. Turning the word upside down puts in the rotation we expect from the mirror.

7. Additionally, our minds don’t expect to see a rotation around the horizontal axis because people are not symmetric around the horizontal axis and we have—unlike left and right—an absolute frame of reference for up and down. We are thus unsurprised when the mirror does not supply a rotation we don’t expect.

8. Well I found the explanation (our brains interpreting the reflection as a rotation) absolutely fascinating! It occurs to me that comparing the phenomenon with the image of our shadows is potentially instructive. As with the mirror, our right hand could be interpreted as being the shadow’s left hand, etc. However, since the image is obviously “tied” to us, and is a very poor facsimile, we have no trouble with it. Standing facing an image in the mirror that appears independent and very life-like causes the brain to interpret it as another figure, looking at us. Apparently we are capable of understanding that it is actually ourselves, but we persist in seeing it as a rotated version of our own image. Hence the confusion of left and right. We never have this confusion with our shadows, because they don’t resemble an acutal human enough. The illusion is absolutely permanent, no matter how hard you try to outdo it – in a similar way that the hollow mask phenomenon is(http://www.youramazingbrain.org/supersenses/hollow.htm#).Fascinating.

9. That last address was cut off:www.youramazingbrain.org/supersenses/hollow.htm#

10. When I read this article, I must admit to checking the date for an April Fool. I must now confess to worrying that I may have missed the crux of the problem.The reason for the illusion is quite easy to visualise. Imagine looking down upon a person facing a mirror. Light hitting their left shoulder travels to the mirror and is reflected back towards their eyes (one eye, two eyes, doesn’t matter). What does matter is that the light enters the eye at an oblique angle from the left, relative to the eye. Our brain is used to seeing light travelling from the right shoulder of people standing in front of us (as the reflection appears to do) entering our eyes from the left, and therefore imagines a bilateral switch of features from left to right, where there is none (the comment above which mentions turning into position explains this well).Of course, light from the top of the head, when refelected in the mirror, still reaches us from above – exactly where we expect it – whilst that from our feet reaches us from below. So no vertical reflection.

11. The mirror has only reversed depth.When you see yourself in the mirror, you see an image of someone staring back at you. In order to get into that position, you imagine yourself rotated a half turn.If a person were lying sideways, you imagine the image reversed vertically, because this would fall along the axis of symmetry.You will then quickly rotate the image in your mind to a vertically posed person and claim there is left-right reversal.Keep in mind the image in the mirror is chiral. It does not represent the same image as the model creating it.

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