We raised this question for discussons among many small groups of people in our "Geometry and the Imagination" class. At one time I thought the 'correct' answer is that a mirror doesn't actually swap left-to-right, but rather, front-to-back. This is certainly true if one is only thinking about the geometric-optics transformation. Then for another while I thought the even more correct answer is that we're bilaterally symmetric. We have special-purpose brain circuits wired to identify people, and put ourselves in their place. Up to this identification, it's certainly true that mirrors reverse the left and right (of a person). We have the brains we have: it's a fallacy to think that we can think abstracted from all the special- purpose non-mathematical-seeming tricks our brains use, of which this is one. 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. It's just confusing to find a good way to **talk about it**, and there is no best way---it depends on what you're trying to communicate to whom. Bill On Nov 25, 2007, at 8:28 PM, Gareth McCaughan wrote:
On Sunday 25 November 2007, Fred lunnon wrote:
Would you believe that I must have asked that dozens of times over the years --- and as far as I can recall, that's the first time it's ever received a correct answer, from people with a technical background included?
How depressing. I'd assumed your reason for describing it as "a claim I fear I may have made previously" was that you took it as obvious that everyone here would have no trouble with it. (My answer would differ from Gene's only in that I'd have added that we think of what a mirror does as exchanging left with right because the things we look at in mirrors -- most notably ourselves, but plenty else besides -- are much nearer to being left-right symmetrical than to being top-bottom symmetrical.)
It's an excellent example of how a badly-formulated linguistic trope may confuse its users so badly that they become incapable of disentangling its distinct meanings, even after those are explicitly pointed out. WFL
Yes. Though it's not only the linguistic trope that's at fault. (There's a *reason* why people commonly think that mirrors swap left and right, which is logically prior to that trope.)