clifford_a-_pickover_surfing_through_hyperspacebookfi-org

HYPERSPHERES AND TESSERACTS 87
running down the middle. But you're right, topologically speaking, a
hyperbeing could do weird things to us."
Outside your window, you see the man in the Santa Glaus outfit.
"Who is that?"
Sally looks out. "No one special, I'm sure."
You try desperately to glimpse his face, but there is not enough light.
All you can see is a figure dressed in a red suit. Even though you can't
observe the man's face, you recognize something familiar. On his left
hand is a tattoo in the shape of a tesseract projected into two dimensions.
Could he be an agent of the Omegamorphs? Worse, you sense that the
man is looking for you.
You are paralyzed; you are certain the Santa Glaus man knows you are
there. Your body tenses, waiting—but for what? Outside on the street,
the sounds blend in a cacophonous hiss. You hear voices, but can never
identify sentences. There is some laughter.
You blink and the man is gone. Just as many people are walking by on
the sidewalk, but the sounds are softer, less tense.
Sally taps you on your back. "It was no one. It's that time of year."
You nod and withdraw a wooden cube from your cabinet. "Follow me
to the blackboard. I want to talk about tesseracts, the 4-D analogs of a
cube. You can get an idea about what they're like by starting in lower
dimensions. For example, if you move a point from left to right you trace
out a 1-D line segment." You place the tip of your chalk on the blackboard
and move the tip to the right so that it produces a line. "If you take
this line segment and move it up (perpendicularly) along the blackboard,
you produce a 2-D square. If you move the square out of the blackboard,
you produces a 3-D cube" (Fig. 4.3).
Sally comes closer. "How can we move the square out of the black
board?"
"We can't do that, but we can graphically represent the perpendicular
motion by moving the square—on the blackboard—in a direction diagonal
to the first two motions. In fact, if we use the other diagonal direction
to represent the fourth dimension, we can move the image of the cube in
this fourth dimension to draw a picture of a 4-D hypercube, also known
as a tesseract. Or we can rotate the cube and move it straight up in the
drawing" (Fig. 4.4).
"Beautiful. The tesseract is produced by the trail of a cube moving
into the fourth dimension."