Mirror, Mirror

[stoutfellow]

In Martin Gardner's wonderful book The Ambidextrous Universe, the following question (one of many) is raised. It is a commonplace that mirrors reverse left and right. Question: how does the mirror "know" what left and right are? More precisely, what is there in the structure of the mirror that treats the left-right axis differently from other axes? The left-right axis is parallel to the surface of the mirror, but so are many others; how can the mirror pick out that one, in preference to all the others?

The problem becomes a little more apparent when we take the mirror off the wall. Imagine a mirror lying flat on a square table, only slightly bigger than the mirror. Now let Fred approach the table from the south, and let Ethel come up from the west. Fred says that the mirror exchanges left and right; so does Ethel; but Fred's left-and-right is Ethel's up-and-down, and vice versa. What on Earth?

The answer, as Gardner explains, is that the mirror does not, in fact, reverse left and right. What it reverses is front and back - and that axis is special relative to the mirror, since it is the one and only axis perpendicular to its surface. We see it as reversing left and right because we picture ourselves walking around to the other side of the mirror and turning around, and we compare what we see in the mirror with our rotated selves.

I read the above many years ago (and have used it from time to time in my classes). It came to mind this morning as I was showering, and suddenly cross-linked to something I read more recently, Stephen Levinson's Space in Language and Cognition (which I reviewed here). Levinson shows that languages can be analyzed according to the type of directional system speakers typically use. English, like most familiar European languages, uses a self-based system, resting on such oppositions as left/right and (personal) front/back. But there are other languages which rely more on an absolute system, using North/South and East/West, or other similar oppositions.

So here's my question. Speakers of English are easily led astray, in thinking about how mirrors behave. Would speakers of languages using absolute systems be so easy to mislead?

I'm tempted to try to find Levinson's e-mail address and ask him.

Comments

[joyeuse13.livejournal.com]

I remember a related discussion in John Holt's "Teach Your Own," about why children sometimes have a hard time learning right and left. He noted that left and right are often defined differently depending on what you might do with the object you're describing. "The coat's left pocket" means the pocket that would be on the left if you were wearing the coat, and "the desk's left-hand drawer" literally means the drawer I'd put my hand in if I were sitting at the desk. This requires the child to imagine a hypothetical situation. But "the monitor's left side" means the side closest to my left hand, because I'm facing it, and never anticipate getting behind it to face the world from its point of view. No wonder kids find this confusing!