clifford_a-_pickover_surfing_through_hyperspacebookfi-org

DEGREES OF FREEDOM 13
angles and look for sums that are not 180 degrees. Mathematical physicist Carl
Friedrich Gauss (1777-1855)—one of the greatest mathematicians of all
time—actually attempted this experiment by shining lights along the tops of
mountains to form one big triangle. Unfortunately, his experiments were inconclusive
because the angle sums were 180 degrees up to the accuracy of the surveying
instruments. We still don't know for sure whether parallel lines intersect
in our universe, but we do know that light rays should not be used to test ideas
on the overall curvature of space because light rays are deflected as they pass
nearby massive objects. This means that light bends as it passes a star, thus altering
the angle sums for large triangles. However, this bending of starlight also
suggests that pockets of our space are curved in an unseen dimension beyond
our spatial comprehension. Spatial curvature is also suggested by the planet
Mercury's elliptical orbit around the sun that shifts in orientation, or precesses,
by a very small amount each year due to the small curvature of space around the
sun. Albert Einstein argued that the force of gravity between massive objects is a
consequence of the curved space nearby the mass, and that traveling objects
merely follow straight lines in this curved space like longitude lines on a globe. 1
In the 1980s and 1990s various astrophysicists have tried to experimentally
determine if our entire universe is curved. For example, some have wondered if
our 3-D universe might be curved back on itself in the same way a 2-D surface
on a sphere is curved back on itself. We can restate this in the language of the
fourth dimension. In the same way that the 2-D surface of the Earth is finite
but unbounded (because it is bent in three dimensions into a sphere), many
have imagined the 3-D space of our universe as being bent (in some 4-D space)
into a 4-D sphere called a hypersphere. Unfortunately, astrophysicists' experimental
results contain uncertainties that make it impossible to draw definitive
conclusions. The effort continues.
A Loom with Tiny Strings
In heterotic string theory . . . the right-handed bosons (carrier particles) go
counterclockwise around the loop, their vibrations penetrating 22 compacted
dimensions. The bosons live in a space of 26 dimensions (including
time) of which 6 are the compacted "real" dimensions, 4 are the dimensions
of ordinary space-time, and the other 16 are deemed "interior
spaces"—mathematical artifacts to make everything work out right.
—Martin Gardner, The Ambidextrous Universe