clifford_a-_pickover_surfing_through_hyperspacebookfi-org

26 surfing through hyperspace
Sally nods. "I can think of another way Flatlanders can distinguish
objects. They can tell when one object is front of another, and this also
provides a visual depth cue." Sally places one of her hands in front of the
other. "The same is true in our world. I see one hand in front of my other
hand. I don't assume that one hand is magically passing through the
other hand. I recognize that there is a third dimension of space, and that
one hand is closer than the other in this dimension."
"Right. Just as we build up a mental image of our 3-D world, the Flatlanders
have many ways to understand and survive in their 2-D world."
You pause. "But Abbott's book doesn't only discuss 2-D worlds. It also discusses
the square's visions of a 1-D world called Lineland. The square says":
I saw before me a vast multitude of small Straight Lines (which I
naturally assumed to be Women) interspersed with other Beings
still smaller and of the nature of lustrous points—all moving to and
fro in one and the same Straight Line, and as nearly as I could
judge, with the same velocity.
A noise of confused multitudinous chirping or twittering issued
from them at intervals as long as they were moving, but sometimes
they ceased from motion, and then all was silence.
Approaching one of the largest of what I thought to be Women,
I accosted her, but received no answer. A second and a third appeal
on my part were equally ineffectual. Losing patience at what
appeared to me intolerable rudeness, I brought my mouth into a
position full in front of her mouth so as to intercept her motion,
and loudly repeated my question, "Woman, what signifies this concourse,
and this strange and confused chirping, and this monotonous
motion to and fro in one and the same Straight Line?"
"I am no Woman," replied the small Line. "I am the Monarch of
the world."
You hand Abbott's drawing of Lineland to Sally. The drawing shows
women as mere dots and the rest of the inhabitants as lines (Fig. 2.2).
Sally studies the diagram. "It seems to me that the only parts the
Linelanders can see of one another are single points."
"Right."
"How do the Linelanders tell where other inhabitants are located in
their world?"