Through the Looking Glass

I’m back, I’m married, we had a fabulous time, and now I’m setting up new machines and figuring out what the heck I’m doing on the C# team. Today, we’ll get back into it with some non-tech fun.

A regular flat mirror seems like it ought to be perfectly symmetrical in its operations. So why is it that mirrors produce an image which reverse left and right, but not, say, top and bottom?  (A concave mirror, like the inside of a spoon, reverses top and bottom, but let’s worry about only flat mirrors for the duration of this article.) How does a flat mirror know which way is left-right?

Think about that for a while before you read on. See if you can figure it out for yourself.

Stuck?  Try this.

  1. Get a mirror. 
  2. Stand in the place where you live.
  3. Now face north.
  4. Think about direction.  Wonder why you haven’t before.
  5. Hold the mirror out in front of you with your left hand.
  6. Point east with your right hand.
  7. The “person in the mirror” is still pointing east, and towards the right side of the mirror (from your perspective), but doing so with their left hand while facing south.

Wait a minute.  The mirror not only produces an image which reverses left and right but not up and down; apparently it also reverses north and south but not east and west!

It’s more productive to think of a mirror as actually producing an image which reverses front and back. If you’re facing north then “front and back” is the same as “north and south”. If the mirror is on the floor then “front and back” is the same as “up and down”. Note that if you took a movie of someone and flipped the movie film front-back when you showed it, you’d get the same effect.

But why then do we all think of mirrors as reversing left and right, if in fact they reverse front-back?  Psychologically, humans see a front-back-reversed human as a left-right reversed human.  That image of a south-facing person smiling back at you is not an image of a human being at all. Their DNA spirals the wrong way. All their body fat is made out of indigestible Olestra.  Their heart is on the wrong side of the body. If we could somehow create a real being who produced exactly that image, down to the front-back-reversed internal structure, there’s no way that they could produce viable offspring with a non-reversed human.

But none of these is apparent at a glance. Since humans have almost perfect left-right symmetry it is extremely easy to interpret an image of a back-front-reversed human as a left-right reversed human. After all, if you were trying to act to look like the person in the mirror, that’s what you’d do – simply reverse your left and right behaviour. You decide what is “slippable” and what isn’t.  If you are trying to look like the image in the mirror looks, you’d ignore all that stuff about your DNA and internal organs and reverse left and right, because that happens to produce the image that looks most similar. If humans had different symmetries then mirrors would not appear to reverse left-right at all, because our psychology would be different.

Imagine a race of super-intelligent fishes that look like eels with a perfectly circular cross-section.  Our fishes have a blue fin on one side, a red fin on the other side, one eye in the very front of their face. These eely fishes can swim with their fins rotated in any direction they choose.  That’s a weird looking fish, but bear with me. Such a fish looking in a mirror would probably see the back-front reversed image as being not left-right reversed – because, what’s left-right to a symmetrical fish? – but rather as rotated 180 degrees.  That’s what a fish would have to do in order to imitate the fish in the mirror.  The super-intelligent fish version of this blog entry would be “why do mirrors rotate images?”

Similarly we could come up with bizarre creatures whose various lines of symmetry would cause them to see mirror images as top-bottom reversals. Even more bizarre, suppose human males and females were more or less exactly the same in their outward physical characteristics, except that men had both arms on the right side of their body, and women had both arms on the left side of their body.  We’d then be asking why mirrors change sex! And who knows what inhabitants of the planet Cheron would think?


Comments (17)

  1. Chump says:

    That was like a shotgun to my mind.

    The cleaners will find my brain dripping down the wall behind my desk.

    Thanks Eric.

  2. There’s more to it. The symmetrical fish would have to put the mirror on the floor, because the room would have to be rotational symmetrical too.

    Also there’s no way to do a front and back reversing tranformation in the real world. (Halfway everything is flat). But a left and right reversing transformation is a real world rotation around a vertical line.

    And gravity must have something to do with this.

  3. Miki Watts says:

    I’m first to call reference to Stand by REM :)

  4. Arun Philip says:

    Weird. Just two days back I was using the very same explanation of symmetry, and a spherical creature to explain this to my brother and his wife.

  5. mike says:

    Speaking of super-intelligent creatures:

    One day, making tracks

    In the prairie of Prax,

    Came a North-Going Zax

    And a South-Going Zax

    And it happened that both of them came to a place

    Where they bumped. There they stood.

    Foot to foot. Face to face.


    "The Zax" — Dr. Seuss

    PS If you’re confused, check with the sun.

  6. EricLippert says:

    Fish have rooms?

  7. Congratulations for you and Leah! and welcome back. We’re waiting for the pictures.

  8. barrkel says:

    Of course, people with situs inversus totalis do live in the world behind the looking glass:

  9. Am I the only one who finds it vaguely unsettling that one of Eric’s tests for whether he considers you to be human is whether he’d be able to digest your body tissue?

  10. Steve says:

    You were gone to long Eric. ;)

  11. Lance Fisher says:

    Hi Eric, congratulations on everything! I’m a long time reader, and infrequent commenter. Recently I’ve weeded the list of technical blogs I read, and yours is one of the few I kept.

    I’m looking forward to reading about new fabulous adventures, and enjoying the other stuff. I posted a link to this article on my completely non-technical blog, <a href="">here</a&gt;.

  12. atthecrux says:

    Just dropping in…

    Though you may have addressed it, I’m having some trouble figuring out how the "front-back" reversal applies if one holds up a two-dimensional printed sheet to a mirror? This certainly looks as though it’s flipped left-right, but doesn’t your explanation of left-rightness rely on three dimension?

  13. EricLippert says:

    Look at it this way — a front-back, left-right or top-bottom reversal are all the same thing. They’re all flips around one axis. If you took a piece of paper with some writing on it and constructed three molecule-by-molecule replicas, one flipped ONLY back-front, one flipped ONLY left-right and one flipped ONLY top-bottom, you’d end up with three identical pieces of paper, right?

    But the left-right reversed and top-bottom reversed pages would be oriented "flipped over" compared to the back-front reversed page. Similarly, the left-right and back-front pages are oriented "upside down" compared to the orientation of the top-bottom reversed page.

    The fact that we psychologically choose to see a mirror-reversed sheet of paper as "left-right reversed and flipped over" rather than, say, "top-bottom reversed and upside down" or most sensibly, "back-front reversed, period" is a fact about human brains, not about mirrors.

    Does that make more sense?

  14. Phil Jollans says:

    I figured out long ago, that the answer to the question, why to mirrors reverse things left-right but not top-bottom was quite simply, that they don’t. Just imagine how it would be to drive a car where the rear view mirror really did swap left and right.

    In fact, on the rear window of my car is a transparent sticker from the car dealer. I can read this when I stand behind the car. I can read it when I sit in the car and look in the mirror. I am still facing in the same direction and nothing has been reversed.

    The psychological aspect may have something to do with the way we turn round to look behind us. I usually turn around a vertical axis, and it is this action of turning which reverses left and right. However, I can look behind me, by bending forwards and looking between my legs. That way, left and right stay the same, but top and bottom are reversed. If I then looked in a mirror, I could say that the mirror had reversed top and bottom, but only if I was really stupid.

  15. Antimail says:

    In a recent post that I’ve missed until now, Eric Lippert describes a simple mental experiment: why a…

  16. John C. Lilly says:

    Your super-intelligent fish looks like a dolphin.