Through the Looking Glass

Through the Looking Glass

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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?


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