clifford_a-_pickover_surfing_through_hyperspacebookfi-org

50 surfing through hyperspace
we could hide from the prying eyes of a 4-D being by hiding in the hyperholes
of a 4-D Swiss cheese or any 4-D object overlapping our world. Although we
could not directly know the locations of 4-D hiding spaces, we might be able to
infer their positions by noticing that there were spots where 4-D visitations
never took place.
A Day at the Beach
Let's take a brief stroll along a 4-D beach fdled with sunbathers. Our tour
guide is a 4-D friend I'll call Mr. Plex. To take this tour, you need to be peeled
out of our 3-D universe and placed into the fourth dimension. Look around.
Much of what you see is confusing. Blobs appear out of nowhere, constantly
changing in size, color, texture. Sometimes the blobs disappear and you can't
tell which blobs are part of Mr. Plex and which are pieces of bodies from other
bathers. Many of the blobs are flesh covered, so you let your imagination run
wild, assuming that the bathing suits are quite scanty and you are watching a
4-D version of Baywatch.
Mr. Plex introduces you to his wife, Pamela Sue. You see a fleshy ball and
another ball covered with blond hair. "Pleased to meet you," you say. Aside
from the occasional hairy ball, the only way you can differentiate Mr. Plex
from his wife is by observing how the blobs change shape. When Mr. Plex
brings you to the snack bar, there is no way you can tell all the creatures apart.
There are just too many changing blobs and colors.
Mr. Plex's artwork is strange and oddly disjointed both in space and in color
combinations. You understand why. When you look at a 2-D painting on a wall,
you step back in the third dimension and can see the boundary of the painting
(usually rectangularly shaped) as well as every point in the painting. This means
that you can see the entire painting from one viewpoint. If you wish to see a 3-D
artwork from one viewpoint, you need to step back in the fourth dimension.
Assuming that your eyes could grasp such a thing, you would theoretically see
every point on the 3-D artwork, and in the 3-D artwork, without moving your
viewpoint. This type of "omniscient" seeing and X-ray vision was known to
Cubist painters such as Duchamp and Picasso. For this reason, Cubists sometimes
showed multiple views of an object in the same painting. Present-day
sculptors, such as Arthur Silverman, often place six copies of the same 3-D
object, on separate bases, in six orientations. People viewing the six disjoint
sculptures often do not realize that they are all the same object. Mathematics professor
Nat Friedman (State University of New York at Albany) refers to this theo-