clifford_a-_pickover_surfing_through_hyperspacebookfi-org

90 surfing through hyperspace
Figure 4.5
A wire-frame model of a cube viewed head-on and a tesseract.
square. The smaller square is further away from your eye and is drawn
smaller because the drawing is a perspective drawing. If you looked at a
hypercube in the same manner, you would see a cube within a cube. The
closest part of the hypercube appears as a large cube, and the part farthest
away appears as a smaller cube inside the larger one. This is called a 'central
projection' of the hypercube. More accurately, it is a plane projection
of a 3-D model that is in turn a projection of a hypercube (Fig. 4.5). This
is a shadow you might see if a hypercube is illuminated from a point
upsilon above ordinary space in the fourth dimension."
Sally studies the figure. "A cube is bounded by square faces and a
hypercube by cubical faces?"
"Right."
"A hypercube contains eight cubes on its hypersurface?"
"Correct."
"But I don't see them in your central-projection drawing" (Fig. 4.5).
"Sally, six of the eight cubes are distorted by projection just as four of
the cube's square faces are distorted when drawn on a plane. For a tesseract,
the eight cubes are: the large cube, the small interior cube, and six
hexahedrons (distorted cubes) surrounding the small interior cube."
You smile as you look into Sally's upturned face and study the paleness of
her skin, the smoothness of her lips, the soft wetness of her eyes. She has the
eyes of a doe. For an instant you imagine yourself and Sally in front of a
roaring fireplace with slender glasses of champagne. Ah, but such a fantasy is
ridiculous. You are professionals.