On Friday 25 January 2008, Fred Lunnon wrote:
On 1/25/08, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
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.)
Replace "colour green" by vector normal to plane.
Replace "sticky plastic letters" by three points in general position on plane.
Now wriggle out of that! WFL
So now your configuration consists of a plane-with-normal-vector, and again it's obviously changed by reflection in that plane, and again I simply don't understand what's supposed to be difficult here. I think maybe we just have different intuitions about ... well, I don't know, but something. Maybe it would help if you'd say more explicitly what your argument is for why the answer to your original question might be, or at least might feel like it ought to be, "positive" (for either the sheet with letters or the plane with points and normal vector), because I'm just not seeing it. -- g