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XIV
preface
problems—from a four-dimensional version of Rubik's cube and the evolution of
four-dimensional biologies, to four-dimensional fractal quaternions with infinitely
complex structures. However, the emphasis will be on the powers and
appearances of four-dimensional beings. I want to know if humankind's Gods
could exist in the fourth dimension. 2
If a fourth dimension did exist, God could be so close we could hear His
breath, only inches away, but impossible to see because our perception is seemingly
confined to three dimensions.
What if you could visit a four-dimensional world filled with intelligent lifeforms?
Would the aliens have heads, arms, and legs, or even be vaguely
humanoid? What capabilities would they possess if they were to visit our
world? The challenging task of imagining beings from other dimensions is useful
for any species that dreams of understanding its place in a vast universe
with infinite possibilities.
Is there really a fourth dimension we can explore and understand? This question
is an old one posed by philosophers and scientists and has profound implications
for our worldview. There seems to be no reason why a four-dimensional
world of material four-dimensional objects could not exist. The simple mathematical
methods in this book reveal properties of shapes in these higher spaces,
and, with special training, our dimensionally impoverished minds may be able to
grasp the "look and feel" of these shapes. As we speculate, we touch on the realm
of mysticism and religion—because in the fourth dimension the line between
science and mysticism grows thin.
Hyperbeings living in a four-dimensional space can demonstrate the kinds of
phenomena that occur in hyperspace. For example, a hyperbeing can effortlessly
remove things before our very eyes, giving us the impression that the
objects simply disappeared. This is analogous to a three-dimensional creature's
ability to remove a piece of dirt inside a circle drawn on a page without cutting
the circle. We simply lift the dirt into the third dimension. To two-dimensional
beings confined to the piece of paper, this action would appear miraculous as
the dirt disappeared in front of their eyes. The hyperbeing can also see inside
any three-dimensional object or life-form, and, if necessary, remove anything
from inside. As we will see later, the being can look into our intestines, examine
our nervous system, or remove a tumor from our brain without ever cutting
through the skin. A pair of gloves can be easily transformed into two left
or two right gloves, and three-dimensional knots fall apart in the hands of a
hyperbeing who can lift a piece of the knot up into the fourth dimension. In
his correspondence and verse, the eminent physicist James Clerk Maxwell
referred to the fourth dimension as the place where knots could be untied: