clifford_a-_pickover_surfing_through_hyperspacebookfi-org

CHALLENGING QUESTIONS FOR FURTHER THOUGHT 207
To contain the approximately five billion people on earth today, you would
need a 59 X 59 X 59 cage zoo. You would only need a 40 X 40 X 40 (n = 40) zoo
to contain the 460 million humans on earth in the year 1500.
Here is a table listing the size of the cages needed to contain various large numbers,
assuming that each quadrilateral contains a single unit of whatever is listed
(e.g., pills, objects, stars, or colors):
1. Largest number of objects found in a person's stomach:
2,533 (5X5X5 cage)
(This number comes from a case involving an insane female who at the age
of forty-two swallowed 2,533 objects, including 947 bent pins.)
2. Number of different colors distinguishable by the human eye:
10 million (21 X 21 X 21 cage)
3. Number of stars in the Milky Way galaxy:
10 12 (141 X 141 X 141 cage)
Let's conclude by examining the cage assemblies for fleas in higher dimensions. I've
already given you the formula for doing this, and it stretches the mind to consider
just how many caged fleas a hypercage could contain, with one flea resident in
each hypercube or hypertangle.
The following are the sizes of hypercages needed to house the 1,830 flea varieties
I mentioned earlier in different dimensions:
Dimension (m)
2
3
4
5
6
7
Size of Lattice (»)
9
5
4
3
3
2
This means that a small n = 2, 7-D lattice (2 X 2 X 2 X 2 X 2 X 2 X 2) can
hold the 1,830 varieties of fleas! An n = 9 hyperlattice in the fiftieth dimension
can hold each electron, proton, and neutron in the universe (each particle in its
own cage).
Here are a few wild challenges.
1. If each cage region were to contain a single snow crystal, what size lattice
would you need to hold the number of snow crystals necessary to form the
ice age, which has been estimated to be 10 30 crystals? If you were to draw