This question was first framed as a logic puzzle in Martin Gardner’s book The Ambidextrous Universe (Basic Books, 1964). It is also featured in William Poundstone’s How Would You Move Mount Fuji? (Little, Brown, 2003).
Does a mirror reverse left and right? It is more accurate to say that a mirror reverses the relative positions of points along a line perpendicular to, not parallel to, the mirror. For example, if you stand on a mirror that is lying flat on the floor, the mirror reverses the relative positions of your feet and head, which are nearer and farther from the mirror. Why then do we say that a mirror reverses left and right? We say this because our bodies are bilaterally symmetrical. When you stand in front of a wall mirror and hold up your right hand, your reflection seems to hold up its left hand, so we say a mirror reverses left and right. But you could say it reverses front and back: Imagine walking straight forward into your reflection, matching head to head, feet to feet, hands to hands, and heart to heart. Everything fits, but your front and back are reversed. So you could say, although it’s less intuitive, that a mirror reverses top and bottom, or front and back.
1. Balls fall down because “down” is defined by the direction of gravity, which exerts a downward pull on objects.
2. Clock hands turn clockwise because “clockwise” is defined by the direction in which the hands of a clock move.
3. The letters of the alphabet are in alphabetical order because “alphabetical order” is defined by the order of the letters in the alphabet.
4. A concave curved mirror, such as a bent piece of shiny metal, or two mirrors that meet at a right angle, such as at the corner of a room.
5. A horizontal mirror on the floor or ceiling.
6. A vertical mirror hanging on the wall.