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