PARALLEL UNIVERSES 231
object in the universe, from the tip of our noses to the most distant of
all galaxies.
A fourth spatial dimension seems to violate common sense. If
smoke, for example, is allowed to fill up a room, we do not see the
smoke disappearing into another dimension. Nowhere in our universe
do we see objects suddenly disappearing or drifting off into another
universe. This means that any higher dimensions, if they exist at all,
must be smaller than an atom.
Three spatial dimensions form the fundamental basis of Greek
geometry. Aristotle, for example, in his essay "On Heaven," wrote, "The
line has magnitude in one way, the plane in two ways, and the solid in
three ways, and beyond these there is no other magnitude because the
three are all." In AD 150 Ptolemy of Alexandria offered first "proof" that
higher dimensions were "impossible." In his essay "On Distance," he
reasoned as follows. Draw three lines that are mutually perpendicular
(like the lines forming the corner of a room). Clearly, he said, a fourth
line perpendicular to the other three cannot be drawn, hence a fourth
dimension must be impossible. (What he actually proved was that our
brains are incapable of visualizing the fourth dimension. The PC on
your desk calculates in hyperspace all the time.)
For two thousand years, any mathematician who dared to speak of
the fourth dimension potentially suffered ridicule. In 1685 mathematician John Wallis polemicized against the fourth dimension, calling it a
"Monster in Nature, less possible than a Chimera or Centaure." In
the nineteenth century Karl Gauss, the "prince of mathematicians,"
worked out much of the mathematics of the fourth dimension but was
afraid to publish because of the backlash it would cause. But privately
Gauss conducted experiments to test whether flat, three-dimensional
Greek geometry really described the universe. In one experiment he
placed his assistants on three mountaintops. Each one had a lantern,
thereby forming a huge triangle. Gauss then measured the angles of
each corner of the triangle. To his disappointment, he found that the
interior angles all summed up to 180 degrees. He concluded that if
there were deviations to standard Greek geometry, they must be so
small that they could not be detected with his lanterns.
object in the universe, from the tip of our noses to the most distant of
all galaxies.
A fourth spatial dimension seems to violate common sense. If
smoke, for example, is allowed to fill up a room, we do not see the
smoke disappearing into another dimension. Nowhere in our universe
do we see objects suddenly disappearing or drifting off into another
universe. This means that any higher dimensions, if they exist at all,
must be smaller than an atom.
Three spatial dimensions form the fundamental basis of Greek
geometry. Aristotle, for example, in his essay "On Heaven," wrote, "The
line has magnitude in one way, the plane in two ways, and the solid in
three ways, and beyond these there is no other magnitude because the
three are all." In AD 150 Ptolemy of Alexandria offered first "proof" that
higher dimensions were "impossible." In his essay "On Distance," he
reasoned as follows. Draw three lines that are mutually perpendicular
(like the lines forming the corner of a room). Clearly, he said, a fourth
line perpendicular to the other three cannot be drawn, hence a fourth
dimension must be impossible. (What he actually proved was that our
brains are incapable of visualizing the fourth dimension. The PC on
your desk calculates in hyperspace all the time.)
For two thousand years, any mathematician who dared to speak of
the fourth dimension potentially suffered ridicule. In 1685 mathematician John Wallis polemicized against the fourth dimension, calling it a
"Monster in Nature, less possible than a Chimera or Centaure." In
the nineteenth century Karl Gauss, the "prince of mathematicians,"
worked out much of the mathematics of the fourth dimension but was
afraid to publish because of the backlash it would cause. But privately
Gauss conducted experiments to test whether flat, three-dimensional
Greek geometry really described the universe. In one experiment he
placed his assistants on three mountaintops. Each one had a lantern,
thereby forming a huge triangle. Gauss then measured the angles of
each corner of the triangle. To his disappointment, he found that the
interior angles all summed up to 180 degrees. He concluded that if
there were deviations to standard Greek geometry, they must be so
small that they could not be detected with his lanterns.