On Friday 25 January 2008, Fred Lunnon wrote:
On 1/25/08, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
I don't understand what the problem is. It's negative; the sheet is a three-dimensional object, even though one dimension is rather small, and you've reflected it across that small dimension. What's conundral about this? I'm obviously missing a subtlety...
Idealised, the sheet (together with its inscription) is a plane --- and so is the mirror. In real life, of course, an experimenter would have to separate them slightly to observe what's happening, if his imagination is unequal to the task of mental recreation.
You stipulated that the letters are different colours on the two sides. Therefore the sheet-plus-inscription is *not* a two-dimensional object in any relevant sense. (You might get away with "2+epsilon- -dimensional", but that's not enough for your argument.) -- g