clifford_a-_pickover_surfing_through_hyperspacebookfi-org

MIRROR WORLDS 137
Figure 5.9 Computer graphic representation of a Klein bottle. (Computer rendition
by the author; see Appendix F for program code.)
point he could paint no further. If the paint were toxic, a mad Flatlander using
this approach could ensure that all life-forms were destroyed. Similarly, in Einstein's
model of the universe, if a human began to map the universe in everexpanding
spheres, he would eventually map himself into a tiny globular space
on the opposite side of the hypersphere.
Our universe could have other equally strange topologies like hyperMobius
strips and hyperdoughnuts, with additional interesting features that are beyond
the scope of this book. 2 For example, in 4-D space, various surfaces containing
Mobius bands can be built that have no boundary, just like the surface of a
sphere has no boundary. The boundary of a disc can be attached to the boundary
of a Mb'bius band to form a "real projective plane." Two Mobius bands can be
attached along their common boundary to form a nonorientable surface called a
Klein bottle, named after its discoverer Felix Klein (Fig. 5.9). The Mobius band
has boundaries—the band's edges that don't get taped together. On the other