clifford_a-_pickover_surfing_through_hyperspacebookfi-org

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