“[T]he English language likes to collapse left and right: beside and next to denote side-by-side without specifying who’s on the left, but there’s no word like bebove or aneath that denotes up-and-down without specifying who’s on top.”
On the other hand, if you face someone that’s a true mirror image of you (and not a copy of you turned around), he will claim he raised his right hand, even if it looks like his left hand to you. His brain and everything else is wired in reverse and he’ll be utterly convinced that you’re the backwards one.
Only some very complicated experiments involving a particle accelerator could ever prove him wrong.
But then mirror-image me will say that I appeared to raise my left hand, and we’re back where we started.
I think you guys are overthinking this.
A mirror is just a dumb object that reflects light. The way it reflects light causes humans to label what it is doing in terms of left-right, up-down, etc. It appears that things are reversed, but they’re not. The mirror is simply reflecting light as best it can, and our eyes and minds are interpreting it in way we can understand it.
And yes, up and down can be reversed. Imagine a building with a lake in front of it. In the lake reflection, the building is “reversed” up and down (the top of the building is closer to you than the bottom) but that’s all just in your mind.
Another example of how your mind does stupid things to help you understand the world is a picture of the same lake/building. Which one is closer to you? Whatever is lower in the picture (the lake) is considered closer to you, when technically, neither are closer or farther from you when it is in a 2d picture.
Stand in front of a mirror. Turn around so your back faces the mirror. Turn your head so you can see the image. Raise your right hand. Magically, the image in the mirror will also raise it’s right hand.
Call Ghost Hunters, I think I have magic mirror.
Of course. It just demonstrates that “left” and “right” are inherently ambiguous–most of the time. You can resolve the ambiguity any number of ways, like saying “I raised the hand with which I’m better at writing”.
That said, there is a physical way to resolve the ambiguity. You say: “Put cobalt-60 in a magnetic field and allow it to decay. More electrons will travel along one axis than the other. Arrange a hand such that the fingers curl with the current in the magnetic field, and your thumb points in the direction of more electrons. Which hand did you use?”
One of you will say “left” and the other “right”. You’ll each point to a hand with the same basic shape, but not with the same (reversed) scars/birthmarks/etc. The mirror copy will disagree with the published literature and so know he’s a fraud.
Interesting bit of OT, since the wide-open title “Mirrors” just seemed to beg for an OT hijack… 
… which concerns the equivalencies of mirror rotation. If you could literally step into the mirror world, would anything be really different except that you were now left- vs. right-handed or vice versa, your hair is parted on the wrong side, etc.?
Arthur C. Clarke wrote a sci-fi story about that in which he got it right – such a person would not be able to survive long because levo-rotary and dextro-rotary isomers of essential proteins and nutrients don’t have the same chemical properties (they do amongst each other, but we happen to be comprised of a particular mixture of isomers that wouldn’t play well in the mirror world).
There is also asymmetry at the subatomic level for some particles – for instance, the decay of pions always produces left-handed spin muons and never the right-handed kind, an amazing parity violation first reported by Lederman et al. in 1957.
But not always, as per above!
But L-glucose and L-fructose would make for fantastic diet sodas!
Though that still depends on the two of you agreeing on which is matter, and which is antimatter. To resolve that, you’ll need to bring in the decay of long-lived neutral kaons.
And even that doesn’t help if one of you is traveling backwards in time :).
I just want to mildly disagree with this. There is an interesting geometric notion involved here, which is that of orientation. There are two ways of orienting three-dimensional space, and reversing any one axis takes one orientation to the other. Rotating space doesn’t change its orientation. (The left-hand rule and right-hand rule are ways of specifying an orientation.)
So, the mirror reversing only front-to-back changes the image’s orientation. What we do when we see our mirror image is mentally rotate it to decide which is its right hand and which its left, correcting the front-to-back reversal but producing what we then interpret as a left-to-right reversal – some axis must be reversed.
Who do you think you are, a… a… well, huh. Never mind.
I can’t find it on-line, either. But I did find it on my bookshelf (Ha! score one for paper!). It is in Chapter 5 (“Deep Questions”) of “More of the Straight Dope,” 1988.
Cecil’s answer was basically, “Mirrors *don’t *reverse right/left and not up/down, you just *think *they do.” And then he goes on to explain basically what **Isilder **described. Only with more snark, of course.