Saturday, May 18, 2013

Reflections On Reflection

Note: A shorter version of this post will appear at A Moment Of Science very soon. If you're interested in my extra sciencey stuff, that's where to watch.
Alice peers through the looking glass.

When I was a little baby freshman philosopher, one of my very first professors asked me this question: Why do mirrors flip images left and right, but not up and down? 

At first, I didn't understand what this had to do with philosophy (not that I knew what philosophy was--which was exactly his point!). It sounded like physics to me, and answering surely required knowledge of optics that I didn't possess.

Today, I consider the process of working out the answer to this question one of the very best illustrations of philosophical methodology I've ever seen. This an ode to figuring things out.

Understanding the Question

First, let's make sure we know what the problem is.

Imagine that you're you. (This is either very easy or very difficult, but I'm not sure which.) Or go find an actual glove and just be you. Either way. Now put a glove on your left hand, leave your right hand bare, and stand in front of a mirror. What do you see? You see an image that looks just like you, except she’s wearing a glove on her right hand while her left hand is bare.

This is what we mean when we say that mirrors seem to flip images left and right. But if they flip left and right, why don’t they reverse up and down as well? Why isn't your mirror image standing on her head? How does the mirror know which way is “up”?


Let's try making a few guesses. Guessing give us something to work with.

  1. Maybe it has to do with binocular vision. You can draw an imaginary line from one eye to the other, and that line is horizontal. Could that be responsible for the strange asymmetry?
  2. Or maybe the molecules in the mirror somehow constantly re-orient themselves according to the nearest large source of gravity. If your last chemistry or physics class was in high school, this is a perfectly reasonable hypothesis. Maybe some feature of the molecular orientation causes the asymmetry. Mirrors would have to do it really quickly so that if you flip a mirror 180 degrees, the molecules will have already adjusted before you could see an upside-down image.
  3. Or perhaps mirrors are made of thousands of long thin tiles laid side by side. Each one reflects light both up-down and left-right, but they’re so thin in the up-down flipping direction that the big combined reflection is only flipped left-right.


We've got some guesses above, and we want to know if any of them is correct. Let's see how far we can get with just thinking before we have to turn the problem over to professional scientists.

  1. Suppose it's true that mirrors do what they do because of binocular vision. What does that mean exactly? It means mirrors seem to know which way is "up" because our eyes are two points defining a line. A line can be an axis, and we think of this particular one as horizontal. If you have one axis, you can imagine another that's perpendicular to the first, and in this case we'd think of that one as vertical. Now we've got a reference frame for what is "left" vs. what is "up". The guess is that this reference frame determines our perception of our reflection in the mirror.

    What could we predict if we knew that were true? Well, we'd expect to be able to change what the mirror seems to count as "up" by changing the orientation of that horizontal axis defined by our eyes. So let's check.

    While standing in front of the mirror with the glove on your left hand, spread your arms and lean over so that your left hand is up in the air, your right hand is reaching toward the floor, and your head is tilted 90 degrees from to its usual position. What do you see?

    The mirror hasn’t fallen for your trick, has it? Your reflection is still wearing a glove on her right hand, which is reaching up--but her feet are exactly where they were before despite being to the “right” from the perspective of your head rather than “down”. So binocular vision can't be the answer.
  2. Our second guess was that the molecules re-orient according to the location of the nearest large gravity well. This one's harder. To test this, it seems you’d either need a gravity well more massive than Earth (which I really hope you don’t have handy), or you’d need a rocket ship headed for the moon with a camera mounted on it filming a mirror as the Moon’s gravity took over. That’s not an impossible test, but it’s not a cheap one either. And it just doesn't quite feel right, does it? But that's not enough to dismiss the hypothesis.

    We've mostly escaped the realm of thought experiments at this point. But that doesn't mean it's time to stop thinking. Let’s assume, just for now, that this won’t give us the answer and try some other things first.
  3. The third guess is that mirrors are made of zillions of long thin tiles. Each strip flips the image up/down as well as left/right, but they're so thin you don't see the up/down part. I'm pretty fuzzy on how zillions of thin tiles would end up making a single, cohesive, life-sized image. Perhaps that's a problem for another day. But let's take that for granted and see what happens.

    This is much easier to test. If the tile hypothesis is correct, you should be able to make an up-down flipping mirror by turning a left-right flipping mirror sideways. But that's not actually what happens, is it? So this can't be the answer either.

Time For a Closer Look

It’s looking even more now like the mirror somehow knows which way is “up”. As a general rule of problem solving, when you end up more sure that household items are conscious than you were when you began, it’s time to re-check your assumptions.

We assume two key things when we ask, “Why do mirrors flip images left and right, but not up and down?” First, we assume that mirrors flip images left and right. Second, we assume that mirrors don’t flip images up and down.

Let’s start with the second. What would it mean if you, out in the real world and not in mirror land, flipped yourself in the up/down direction? It would mean you were standing on your head. You’d have rotated yourself 180 degrees around the (horizontal) x axis. Mirror images don’t stand on their heads when we stand on our feet, so assumption two is correct. Mirrors really don’t flip images up and down.

But what would it mean if you flipped yourself left/right? If flipping up and down means rotating 180 degrees around the x axis, then flipping left and right must mean rotating 180 degrees around the (vertical) y axis. 

Rotating around the y axis is what we usually call “turning around”. Is that actually what mirrors do? Do they make turned-around pictures of us?

Imagine that you make a perfect, flesh-and-blood copy of yourself. She, too, is wearing a glove on her left hand. Place her in front of you so that you’re looking at her back. Now, while you stay perfectly still, rotate her 180 degrees around the y axis--that is, turn her around to face you.

Where is her glove? Why, it’s still on her left hand! To shake gloved hands, you’d have to reach across your body. If she were a mirror image, it would be on her right hand, not her left. So the first assumption must be wrong. Mirrors do not, in fact, flip images left-and-right.

So what’s really going on?

Mirrors don’t flip up and down, and it turns out that they don’t flip left and right either. But there’s some sort of flipping or reversing happening. Otherwise ambulances would just have “AMBULANCE” written on them instead of the odd backward version you can read normally in your rear-view mirror.

There’s only one obvious dimension left for flipping. If it’s not up and down, and it’s not left and right, then it must be back to front. But what would that mean?

Take off your glove, and hold it so the thumb is on your left and the palm is facing up. If you turn it upside down, the palm is facing down. If you turn it around from the starting position, the thumb is on your right.

Now, again from the starting position, turn the glove inside out without turning it in any other direction. The wrist part of the glove, which used to be closest to you, is now farthest away, while the the fingers are pointing toward you. It has not flipped upside down. It has not turned left or right. The glove has flipped front-to-back, and it now fits on your right hand instead of your left. 

If that’s what mirrors were doing, then what would you expect to see?

Suppose you’re looking at a mirror while facing North. The part of you that’s farthest South in reality, namely your bottom, would seem farthest North in the image--and, indeed, it does. The part that’s farthest North in reality, namely your nose, would seem farthest South in the image--and, indeed, it does.

You wouldn’t expect, however, to have to reach across your body to shake gloved hands, and you wouldn’t expect your image to do a headstand without your help.

That’s it, then! Mirrors don’t know which way is up after all. They just flip images front-to-back.

The Beauty Of Confusion

To review: 
  • We asked a question. 
  • We took some time to understand what was being asked. 
  • We made a few guesses. 
  • We tested them in our heads when we could, and pinned down how to go about testing them outside our heads when we couldn't. 
  • When none of that gave us the answer, we doubled back to check our assumptions. 
  • In the end, we solved the problem by dispelling a simple misunderstanding hidden in the question. 
Misunderstandings hide in questions all the time. If you're impatient and epistemically reckless, that's horribly frustrating, and it probably causes you to waste a lot of time trying to answer questions that don't make sense. This is much of why a healthy helping of philosophy is a tasty and nutritious side-dish even when science is your main course. If you're patient and rigorous, if you enjoy taking the time to simply think, you can learn all kinds of new things just by reflecting on them. 

Nifty, huh?

"Hang on a minute here, you're thinking. "At first we wanted to know why mirrors flip images left/right but not up/down. Turns out we were confused about that. But now I don't know why mirrors flip images front/back but not left/right or up/down!"

Impressive. Most impressive. But you are not a Jedi yet.

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