On 11/26/07, Steve Witham <sw@tiac.net> wrote:

... Mirrored pairs are called "right-handed" and "left-handed"-- is that the "badly-formulated linguistic trope" you mean, Fred?

Yes indeed. That's what I had in mind when I queried to association of left-handed writing with left-handed coordinates.

Or is it the whole treatment of "swap" as a verb, or...?

This could be queried as well, I suppose --- there's an implicit "modulo proper isometries", as several people pointed out. Of course, with a little surgery, the mirror could be implanted along the observer's plan of (approximate) bilateral symmetry, when it really does "swap left with right" ... WFL

...

From: Bill Thurston <wpt4@cornell.edu>

Ultimately, I mellowed. I realized that people were unconvinced by each other's explanations because they weren't actually confused about what a mirror does. There's not an actual question here without words.

Sure --- but understanding takes place at several levels. If you are caught out by the question --- as most people are, unless they've made a specific study of the Euclidean group --- then I claim you have something to gain by grasping exactly why. WFL