Mirror, Mirror

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.

G'bye, Joan

Well, it's official: Joan of Arcadia has been cancelled. I can't say that I'm broken up about it. The first dozen episodes - up through "Jump" (the Science Fair episode) - were brilliant, but the show seemed to stumble after that. There were a number of good episodes in the second half of season one and in season two, but there were also a number of real clunkers. Characterizations went awry, themes grew heavy-handed where they weren't disjointed, and several plotlines began promisingly but dwindled into inconsequence. (The lawsuit comes to mind, in particular.) The last two episodes seemed to herald a new direction, but it would, I think, have been difficult to execute without deteriorating into sentimentality.

But the show still leaves me with plenty of good memories. "Just Say No", "Bringeth It On", "Death Be Not Whatever", "The Devil Made Me Do It", "The Uncertainty Principle", "Jump" - these were outstanding episodes, and TDMMDI and "Jump" were stellar even in that company. Had the writers, crew, and actors maintained that level of excellence, Joan would have gone down, at the very least, as one of the great cult classics. That they did not... is frustrating.

raises glass

Padre Power

I've been putting off the second installment on knot theory, mainly because I'm having a hard time seeing how to say what needs saying without pictures. But I will get to it in the next day or two.

Meanwhile, I'd like to gloat a little. My hometown team, the Padres, had an absolutely miserable April. Now, though, they've won six consecutive series, sixteen out of nineteen games, and climbed into first place in the National League West. Among their victims have been Arizona (formerly first in the West, two out of three), St. Louis (first place in the Central Division, three out of four at St. Louis), Florida (second place in the East, three straight), and Atlanta (first place in the East, three straight). Khalil Greene has come back from his finger injury; after a small slump, he's caught fire - two three-run home runs in today's victory over the Braves. Brian Giles and Ryan Klesko have also come alive in the past couple of weeks. Jake Peavy is as brilliant as ever; Tim Stauffer, 22 years old, is showing remarkable poise and may be the fifth starter they've been looking for; and the bullpen has been fortified by the addition of some reliable middlemen.

It's going to be a long, tough fight; Arizona and LA are powerful, and the Giants won't stay down forever. But right now the Friars are on top, and that makes me happy.