clifford_a-_pickover_surfing_through_hyperspacebookfi-org

120 surfing through hyperspace
Figure 5.1
Rotating a 2-D person about a central axis.
"Not at all. Imagine a 2-D man living in Flatland. Pretend his right
eye is brown and his left eye is blue. He wakes up one day and his wife
screams, because his eyes have switched places. What actually happened
is that a 3-D being rotated him about the center of his body into the
third dimension" (Fig. 5.1).
You hand Sally a card with the words:
IN A SPACE OF H DIMENSIONS
THE MIRROR IS A SURFACE OF N- 1 DIMENSIONS
"Sally, in one dimension, objects are mirrored (reflected) by a point.
In two dimensions, figures are mirrored by a line. In our world, mirrors
are planes. In four dimensions, mirrors are solid!" You pause. "If a Flatlander
could be rotated about a line in his plane, he would be turned into
his mirror image. In general, if an object could be rotated around a mirror
by moving into the higher dimension, the object would become its
mirror image."
"What have you got in your hand?"
You hold up your left hand. "Nothing."
"Silly, your other hand."