clifford_a-_pickover_surfing_through_hyperspacebookfi-org

164 surfing through hyperspoce
away from a new world, but forever confined, isolated by a seemingly impenetrable
boundary: the pond's 2-D surface. If higher spatial dimensions exist,
humanity may still have to wait a few hundred years before developing the capacity
to explore them, but such a capacity may evolve for our survival—much like
fish learned to leave the confines of their pools through evolution. It is possible
that humans will some day have proof of higher spatial dimensions, such as those
suggested by Kaluza-Klein theories. As discussed in Chapter 4, many cosmological
models have been devised in which our universe curves through four-space in
a way that could, in theory, be tested. For example, Einstein suggested a universe
model in which a spaceship could set out in any direction and return to the starting
point. In this model, our 3-D universe is treated as the hypersurface of a huge
hypersphere. Going around it would be comparable to an ant's walking around
the surface of a sphere. In other universe models, our universe is a hypersurface
that twists through four-space like a Klein bottle. These are closed, one-sided,
edgeless surfaces that twist on themselves like a Mobius strip. Using various satellites,
astronomers now actively search for evidence of the universe's shape by
studying temperature fluctuations in deep space. 1
Can we learn to see the fourth dimension? Our inability to clearly visualize
hyperspheres and hypercubes may result solely from our lack of training since
birth. Our memories are of 3-D worlds, but who knows what might be accomplished
with proper early training? This question has been discussed seriously by
a number of mathematicians. Also, to say the fourth dimension is beyond imagination
may be an exaggeration if we consider how far humans have stretched
their imaginations since prehistoric time. From electrons to black holes, the history
of science is the history of accepting concepts beyond our imagination. As
Edward Kasner and James Newman note in Mathematics and the Imagination,
"For primitive man to imagine the wheel, or a pane of glass, must have required
even higher powers than for us to conceive of a fourth dimension." Whatever our
limitations may be, even today the geometry of four dimensions is an indispensable
part of mathematics and physics.
Worldview
The definitive discovery of 4-D beings would drastically alter our worldview
and change our society as profoundly as the Copernican, Darwinian, and Einsteinian
revolutions. It would impact religions and spur interest in science as
never before.