Mensagenda columnist (and communications officer) Mat Rouch wrote an article for the September issue on a topic that fascinates lots of people, including him and me. He asked, “Why do mirrors reverse left-right but not up-down?” The article is available online in the members’-only section of the chapter website, http://www.mnmensa.org/.
I’d like to hear other members’ responses, so do read the whole thing (the article starts on page 18), and sound off in the comments. Mat’s conclusion:
And finally, when you look at your reflection in your bedroom mirror you do not perceive it as a flat image of the room you are in (which would be correct). You perceive it as a space behind the mirror. And the only rotational axis you can choose that (a) allows you to preserve the direction of gravity, (b) keeps the image of your bilaterally symmetric self still looking reasonable and (c) retains a sense of the reflection being a volume behind the mirror is the left-right axis. So that’s the one your brain chooses for you, automatically and beyond your control. That’s my story and I’m sticking to it.
It’s a fine story. But it’s not much like mine. I said:
If someone were standing next to you, walked forward past the plane of the mirror, turned around, and walked back to stand “next to” the apparent position of the mirror image, his right hand would be to your left. But the work here is being done by “turned around” — that is, he performed a 180-degree rotation around a vertical axis, and thus reversed both front-to-back and right-to-left. Your reflection in the mirror did not turn around, so it reversed only front-to-back. (If you have a ring on your left hand, and reach out and touch the mirror, the image-hand you touch also has a ring, and it is to the left in the mirror.) But it would be the ringless right hand of a person who turned around, and that is how your brain interprets it.
I think your analysis is precisely correct as a description of what a reflection is, but what I wanted to get across is why the human brain insists on interpreting it as a left-right reversal as opposed to any other axis, when others are perfectly valid. You want to interpret what you see as a space behind the mirror (which it isn’t) and the only sensible way you can do that, bilaterally symmetrical and stuck in a strong gravitational field as you are, is by swapping left-right. Flip up-down and not only is your head facing the wrong way, everything is stuck to the ceiling.
The four-armed starfish does not have that limitation. He lives more or less in zero-g and his head looks just like his feet. If he swapped up-down the result would be a perfectly reasonable space-behind-the-mirror, and the same would be true if he swapped left-right. So he could and probably would do either one, as appropriate.
There you go. Your turn!