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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208 appendix I<br />
this lattice, how big a piece of paper would you need? Provide answers to<br />
this question for 2-D and 3-D dimensional figures.<br />
2. If each cage region contained a single grain of sand, what size lattice would<br />
you need to hold the number of sand grains contained on the Coney Island<br />
beach, which has been estimated to be 10 20 grains? If you were to draw this<br />
lattice, how big a piece of paper would you need? Also provide answers to<br />
this question for a hyperlattice in the fourth dimension.<br />
3. Akhlesh Lakhtakia has noted that the lattice numbers L(n) can be computed<br />
from triangular numbers (T n ) m . Why should the number of cage assemblies<br />
be related to triangular numbers? (The numbers 1, 3, 6, 10, ... are called<br />
triangular numbers because they are the number of dots employed in making<br />
successive triangular arrays of dots. The process is started with one dot;<br />
successive rows of dots are placed beneath the first dot. Each row has one<br />
more dot than the preceding one.)<br />
Optical Aid for "Seeing" Higher Universes<br />
Have you ever wondered what it would really be like to gaze at the fleshy, hairy blobs<br />
that this book suggests as models for 4-D beings intersecting our world? Luckily, it is<br />
quite easy for students, teachers, and science-fiction fans to gaze at such odd apparitions.<br />
Visionary engineer William Beaty gives exact construction details for an optical<br />
device that, when pointed at a person's skin (or other body parts), gives a realistic<br />
impression of a 4-D being's cross section—namely, as he puts it, "fleshy, pulsating balls<br />
of skin, covered with sweaty hair!" At his Internet web page (http://www.eskimo.com/<br />
-billb/amateur/dscope.html), Beaty describes the visual effect in detail:<br />
While looking <strong>through</strong> the device, I moved my arm up and down. The<br />
ball of flesh pulsed. I put the palm of my hand on the end of the mirror<br />
device, and made a nice clean smooth sphere of skin. I cupped my<br />
hand to fold the skin, and this produced an obscenely throbbing wrinkled<br />
flesh-ball. I shoved some fingers into the end, and saw a spiny<br />
sphere of waving fleshy pseudopods. I placed it against the side of my<br />
fist, clenched and unclenched it, and created throbbing <strong>org</strong>anic orifices.<br />
I grabbed coworkers, placed my mouth against the end, made<br />
biting and tongue movements, and said, "Look into this thing." They<br />
recoiled in revulsion and/or hilarity.<br />
To create the "4-D viewer," he uses three trapezoidal-shaped mirrors, each with<br />
dimensions of 12" X 5" X 2" (In other words, the two small edges are 12 inches