clifford_a-_pickover_surfing_through_hyperspacebookfi-org

34 surfing through hyperspace
cumbed by cannibalizing his own body, despite the occasional Burger
King scrap you threw into the tank and the infrequent dead rat the cleaning
staff left outside your door for food.
Now you keep the tank in your room to help visualize intersections of
3-D objects with 2-D worlds. You reach into the water and withdraw a
ball. "Here's what a sphere looks like to an inhabitant of Flatland. The
surface of the water is a metaphor for Flatland." You push the ball down
so that it just touches the water at a point. You push further and the
point turns into a circle. The circle enlarges until it reaches a maximum
size and then shrinks back down to a point as you push the sphere under
the water. The point disappears.
You turn to Sally. "Imagine how difficult it would be for an inhabitant
of Flatland to think of all these different circles as together forming a 3-D
object" (Fig. 2.9).
Sally walks over to the tub of water. "It's as if the square had blinders
on that didn't permit him to look up or down, just straight ahead. If an
ant floated on the surface of the water and could only see along the surface,
it would see the sphere as just a circle growing and shrinking in
size." She pauses. "Sir, could we have blinders on? Could our brains blind
us from looking 'up' and 'down' in the fourth dimension where God,
demons, angels, and all sorts of beings could be listening to every word,
watching our every action, just inches away from us in another direction?"
(Fig. 2.10).
"Ooh, Sally, I thought you were supposed to be the skeptic." You
begin to hum the eerie, repetitive theme of the Twilight Zone. "Sally, I'm
beginning to like you."
She smiles. "I'm just speculating out loud."
You slam your fists together and she gasps.
"Sally, what would you see right now if a 4-D hypersphere were to
pass through the space right in front of your eyes?" You wiggle your fingers
in front of her face and she backs up.
"Put your hand down," she says. "Reasoning from your analogy with a
sphere penetrating Flatland, we would first see a point, then a small
sphere, then a big sphere. Eventually the sphere would shrink down to
point and disappear from our world. It would be like inflating and deflating
a balloon."
"Correct, all balloons are beings from the fourth dimension."
"What!"