clifford_a-_pickover_surfing_through_hyperspacebookfi-org

HYPERSPHERES AND TESSERACTS 83
simply 3-D space curved in 4-D space. As I once told you, some scientists
think that our universe is the hypersurface of a very large hypersphere.
However, even if this is true, people seem to be confined to three
degrees of freedom because they are confined to the 3-D surface. Similarly,
an ant walking on the surface of a sphere is confined to the 2-D surface
and has two degrees of freedom.
You go over to a handsome walnut cabinet in a dark corner of your
office. The cabinet door is locked, so you fumble in your pocket for a
key. Nearby, a stand holds sheet music and a guitar. On your coffee table
is an odd assortment of magazines, from Wired to Sushi News, Chess Life,
and Scientific American.
Around the table are three antique Chippendale chairs, covered in
tapestry. Sally takes a seat and stares at the paintings on the wall—various
French Postimpressionist works with lush colors, especially those by Paul
Gauguin. Your favorite is Spirit of the Dead Watching depicting a woman
lying on a bed with an owl flying above her and a man, dressed in black,
sitting nearby. The painting is an excellent reproduction—the original is
worth millions of dollars, hardly affordable on the meager salary the FBI
pays you.
You unlock the cabinet and withdraw a large bone. "Sally, take this
bone."
"Where did you get this thing?"
"It's the longest human bone on record—a 29.9-inch thigh bone of
the German giant Constantine, who died in Mons, Belgium, in 1902 at
age thirty."
Sally eyes you suspiciously.
"Suppose I put a pin through one end of this bone and rotated the
bone on a table. What shape would its free end trace out?"
"A circle."
"Now start swinging the bone all around, but keep your hand in one
point as much as possible."
Sally starts swinging the bone in all directions. "What are you getting
at? My arm is getting tired."
"Now the free end is tracing out a sphere. Assume now that space has a
fourth coordinate at right angles to the other three and that you could
swing the bone in four-space. The free end would generate a hypersphere.
"The surface of an /z-sphere has a dimensionality of n — 1. For example,
a circle's 'surface' is a line of one dimension. A sphere's surface is two-