Thursday, April 5, 2007

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?

23 comments:

The Barefoot Bum said...

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

The Barefoot Bum said...

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.

Stephen Law said...

Ok show me your solution. Then I'll show you mine...!

The Barefoot Bum said...

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.

The Barefoot Bum said...

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.

Tom Freeman said...

I agree with the barefoot bum: mirrors do reverse top-to-bottom. Or rather, they reverse top-to-bottom every bit as much as they reverse left-to-right.

It’s a matter (perhaps unsurprisingly) of perspective. When you imagine yourself “actually standing where the mirror-version of you appears to be standing”, how is it that you imagine yourself getting there?

If, most naturally, you think of yourself as walking round – or horizontally rotating 180 degrees about a point at the centre of the mirror – then you’ve imagined altering your position horizontally. And, indeed, the imagined result is horizontally at odds with the reflection in that the parting of your hair, say, is located differently horizontally.

Now try it a different way. It requires some energetic acrobatics, but thankfully only in the imagination. Leap, up and head first, over the mirror and into the reflection zone. Or, more specifically, imagine rotating 180 degrees vertically about a point at the centre of the mirror. The result is that your feet are where your reflection’s head is and vice versa, but you get to keep your parting on the same side.

So if you compare your reflection with an imagined you having had your position altered by a vertical rotation, the reflection’s reversal is construed as top-to-bottom; if you imagine a comparison with your position altered by a horizontal rotation, the reflection’s reversal is construed as left-to-right.

The Barefoot Bum said...

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.

Jeremy said...

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.

Jeremy said...

That last address was cut off:

www.youramazingbrain.org/supersenses/hollow.htm#

John said...

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.

student said...

possibly this?

http://www.d7s.com/mirror.htm

Anonymous said...

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.

geert.arys said...
This comment has been removed by the author.
geert.arys said...

I hope this is a simple answer to the question:

Put on a white t-shirt and position yourself facing north. Write in front of your t-shirt north, and on the back south. On your left side, write west, on your right side write east. On top of the t-shirt write up, at the bottom write down.

Place a mirror in front of you. You'll see that your mirror image (m.i.) still has a correct east, west, up and down marker. However, your m.i. faces south but m.i.'s t-shirt says north.

Place the mirror left or right of you. You'll see that m.i.'s t-shirt has a correct north, south, up and down marker. However, your m.i. t-shirt's west is in the east.

Place the mirror above or below yourself. You'll see that m.i.'s t-shirt has a correct north, south, west and east marker. Only you're seeing yourself upside down.

In all cases, the mirror only mirrors one axis. And, in all cases, when you lift your right hand, your m.i.'s left hand will be risen.

How is THAT possible? simple: we defined left and right relative to ourselves: standing upright, facing north we defined 'left' as the arm in the west. But turn yourself over any axis by 180° and your left arm will point to the east. What a mirror does is actually not TURN, but INVERT one axis (and it can be upside down, so the philosophical puzzle was flawed to start with), which has the same effect.

So, the answer is: up and down are relative to gravity, so up and down are only inverted for horizontal mirrors. Left and right are relative to our position, so are inverted always by a mirror. Any letters on our t-shirt were always written in mirror writ for the same
reason.

What does it learn me? That we, humans, have it hard to see beyond our own definitions once we consider them 'natural'.

Anonymous said...

Try looking through the clock from the centre where the hands originate from.....you find your answer here

MikeO said...

Hello Stephen,

Please allow me to offer some assistance to this mirror question. I do believe you have the correct solution, so my contribution will merely be in cleaning up some semantics.

The mirror reversal puzzle is not a matter of the science of light rays, optics, and the Physics behind reflection. It’s a people thing. I’d say it can best be solved by a science of human activities, a science that deals with how people interact with complicated or subtle things. The idea of “reversedness” in perceived images is far more subtle than the reversal of a photon trajectory.

When people want to compare two nearly identical objects for some subtle difference there are two common strategies they can use. These two strategies are often useful, but they are oddly contradictory.


***


In one strategy, the two objects are lined up to face in the same direction before they are compared. For instance, if two nearly identical pens are to be compared, no one I know of would ever hold one pen horizontally, the other vertically, and then proceed to compare them. People commonly hold them facing in the same direction for such a task.

When a person uses this strategy in the mirror situation, as you noted, they like to imagine themselves rotating about a vertical axis for a comparison with their image, while facing in the same direction as their previous image was pointing. This also requires them to mentally freeze their image as it was when they faced the mirror. When all this is done, the Left/Right reversal is obvious.


***


The second common human strategy for dealing with complicated situations, is to freeze EVERYTHING, and look at the situation “as is” in order to perform an analysis of the subtle differences between two objects.

In the mirror setup, performing this “as is” strategy means NOT rotating anything at all before doing the comparison, and the Left/Right reversal fails to show up. Instead, a Front/Back reversal is apparent in this “as is” comparison.


***


Of the two strategies, the second is the simpler. The first is almost too complicated when done mentally, and it’s often too much to document in any way. Yet, it can happen in a flash of mental imagery, only to fade as soon as words are brought in to capture it.

Often a person, deep in the throws of the mirror riddle, will drift from one strategy to the other subconsciously. This is often described as “magical” by those who delight in that sort of thing, while others will literally complain of the headache it causes them.

When each strategy is clearly thought through, one at a time, clarity results.

And yes, if some gymnast were to apply the first strategy by performing a hand stand in order to face in the same direction as the earlier image, then Up and Down are seen to be reversed. But who is prone to do this difficult action? And not only difficult, but risking injury and even seven years of bad luck if the mirror is broken?

So, it’s not the mirror that does any reversing of perceived images, it’s people who do that by their selection of strategies. Mirrors reverse the direction of light rays, but people decide how they are going to compare image to object.

I have a discussion forum website set up devoted to this mirror puzzle for those who want to see more of the details. Pleas come and visit: http://mirror-reversal.proboards.com

Thanks,

MikeO

Anonymous said...

The Barefoot Bum is in principle right.
He erred in the example he gave.
The word "CHOICE" will be reversed by a mirror, but if turned upside down it will be read normally.

Lenoxus said...

"CHOICE" will also "not-reverse" if it's held flat, like we normally read a paper on a desk. I imagine that's what the Barefoot Bum had in mind, rather than holding up the word "so that mirror-you can see it", though that's a natural assumption for the very same reason this "puzzle" works.

Of course, if we want to take that innate metaphor of ours more seriously… reality probably looks just as "reversed" from the mirror-person's vantage anyway, so she would actually find it easier to read CHOICE flat, or in general to read words that have been reversed.

Yet another way of thinking about it: if humans had next-to-no bilateral symmetry — or both horizontal and vertial symmetry — we would never have percieved this puzzle.

Lenoxus said...
This comment has been removed by the author.
Urlaub günstig said...

.. a morror puzzle is not the perfect solution for ever, so i think .. but i'm not sure

Blaise said...

Let's define some orthogonal coordinate axes. The x axis is left to right as you look at the screen. Y is up and down the screen and z is coming out of the screen towards the viewer.

The question is, why does a mirror flip the x axis but not the y axis?

The answer is, it doesn't flip the x axis. It flips the z axis. We tend to imagine ourselves behind the mirror and that leaves us thinking x has been flipped

Anonymous said...

mirrors don't flip left to right, they flip front to back.

Anonymous said...

I'm not sure if anyone has gave this answer, but, as Richard Feynman explained it, the mirror does not reverse left and right, but rather front and back. Your front in the reflection is facing a different direction than in actuality, left and right are maintained.