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