clifford_a-_pickover_surfing_through_hyperspacebookfi-org

86 surfing through hyperspace
"That's a good question. 1 I have no answer, but now it seems that the
Omegamorphs are changing all that."
Sally tosses the tennis ball to you. "If we lived on a hyperspherical universe
and you traveled to a point in the universe that was furthest from
me, I would still be able to see you with a telescope in no matter what
direction I looked."
"That's true if the sphere were not too large."
"If I could see you no matter where I looked, would you seern infinitely
big to me?"
You place the tennis balls back in the cabinet. "Yes. Even stranger, I
would be 'inside out.' In other words, instead of my skin and hair forming
a surface around my guts, it would seem that my guts were on the
outside, and my hair and skin would be surrounding you! Of course, I
wouldn't notice anything strange. I wouldn't be about to die. To me, you
would look infinitely large arid inside out" (Fig. 4.2c).
You toss a basketball to Sally. "Next lesson. If you cut this sphere with
a plane, you'd produce a circle. If you cut a hypersphere with a 3-D
hyperplane, the cross section is a sphere."
Sally looks at the basketball. "What happens if you try to cut a hypersphere
with an ordinary 2-D plane?"
"Sally, you can't slice a hypersphere into two pieces with a 2-D plane.
A hyperbasketball, sliced down the middle by a plane, remains in one
piece, just like a sphere pierced with a line does not fall apart into two
separate pieces. This means that a guillotine for a hyperbeing would be a
3-D object like a cube, not a plane."
You take the basketball from Sally's hands and deflate it with a pin. "If
I asked you to turn this basketball inside out, could you?"
Sally studies it for a moment. "I don't think so, not without cutting
it."
You nod. "Correct. However, a flexible sphere of any dimension can
be turned inside out through the next-highest dimension. For example,
we 3-D beings can turn a rubber ring inside out so that its outer surface
becomes the inner, and the inner becomes the outer. Try it with a rubber
band. Similarly, a hyperbeing could grab this basketball and turn it inside
out through his space."
"Does this mean that a hyperbeing could turn a human inside out?"
"From a practical standpoint, we're not quite as flexible as a rubber
ball. We're also not spheres. We're more like a sphere with a digestive tube