clifford_a-_pickover_surfing_through_hyperspacebookfi-org

98 surfing through hyperspace
In Hinton's book, Astrians have only one eye, just as Abbott's Flatland creatures.
(In principle, both authors could have given their creatures two eyes,
each with 1-D retinas, to provide binocular vision.) To pass each other as they
travel on the surface of Astria, the inhabitants must go under or over each other,
like acrobats. All female Astrians are born facing west; all males are born facing
east. Astrians keep their orientation until they die because there is no way to
"flip over" without being rotated in the third dimension. To kiss his son, an
Astrian dad must hold the boy upside down! (It's too bad that Astrians didn't
have long necks that would permit them to tilt their heads backwards and
upside down to see behind them.)
What would it be like to live on Astria, a fully developed 2-D world with
gravity and all the laws of physics? For one thing, it would be difficult to build
houses that have several windows open at the same time. For example, when
the front window is open, the window in the back must be kept closed to keep
the house from collapsing. Perfectly hollow tubes and pipes would be difficult
to construct. How would you keep both sides of the pipes together without
sealing the tube? It might be possible to have tubes with a series of interlocking
valves, like the self-gripping gut discussed in Chapter 2. You could make a tunnel
with a series of doors that closed behind you as you walked. But you could
never have all doors open at once or the tunnel could collapse. Ropes could not
be knotted since line segments don't knot in two-space. Hooks and levers
would work just fine. Birds could still fly by flapping their wings.
In Hinton's book, one of the Astrians comes to realize that there is a third
dimension and that all Astrian objects have a slight 3-D thickness. He believes
that the Astrians slide about over the smooth surface of what he calls an "alongside
being." In a moving speech to his fellow Astrians, he proclaims:
Existence itself stretches illimitable, profound, on both sides of that
alongside being. . . . Realize this . . . and never again will you gaze into
the blue arch of the sky without added sense of mystery. However far
in those never-ending depths you cast your vision, it does but glide
alongside an existence stretching profound in a direction you know
not of.
And knowing this, something of the old sense of the wonder of the
heavens comes to us, for no longer do constellations fill all space with an
endless repetition of sameness, but here is the possibility of a sudden and
wonderful apprehension of beings, such as those of old time dreamed of,
could we but. . . know that which lies each side of all the visible.