clifford_a-_pickover_surfing_through_hyperspacebookfi-org

112 surfing through hyperspace
Using the equations for volume given here, you'll find that an 11-D sphere
of radius 2 feet is 333,763 feet. 11 Considering that the volume of a brontosaurus
(nowadays called an apatosaurus) is about 100,000 cubic feet, does
this mean that the brontosaurus could be crammed into this small 11-D
sphere? This amusing thought is just a prelude to the questions that follow.
Some Hypersphere Questions
She reappeared, looking back at him from her fat flat suspicious face,
and Kevin understood the reason why she had disappeared for a
moment. It was because the concept of "a side view" didn't exist in a
world where everything was perfectly flat. This is Polaroidsville, he
thought with a relief which was strangely mingled with horror.
—Stephen King, Four Past Midnight
Now the time has come for considering some really tough questions. If you are
a teacher, why not give these to your students to answer.
1. Examine the graph in Figure 4.21. Could a 24-D sphere of radius 2
inches contain the volume of a blue whale (Fig. 4.23)?
2. Could a 1000-D sphere of radius 2 inches contain the volume of a
whale, considering that the sphere's hypervolume is very, very close to 0
(Fig. 4.21)?
3. Could a Sea World animal trainer fit a whale into an 8-D sphere (of
radius 1 inch) as its aperture intersected with our 3-D world?
4. The number of atoms in a human's breath is about 10 21 . If each atom in
the breath were enlarged to the size of a marble, what percentage of a
human's breath could fit into a 16-D hypersphere of radius 1.1 inches?
5. Estimate the value of the 24-D hypervolume of a whale. To compute
this, assume that the length of a blue whale is about 100 feet.
6. What is the one-million-dimensional hypervolume of the earth? Assume
the earth to have a diameter of 4.18 X 10 7 feet. Also, can you approximate
the 4-D hypervolume of Albert Einstein's brain? (The brain of an
average adult male weighs 3 Ibs. 2.2 oz., decreasing gradually to 3 Ibs.
1.1 oz with advancing age.) Another problem: In 1853, the 350-foot-tall
Latting Observatory in New York City was the highest manmade structure
in North America (Fig. 4.24). Estimate its 4-D hypervolume.