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