clifford_a-_pickover_surfing_through_hyperspacebookfi-org

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less universes could be very different. Some might collapse into nothingness quickly
after their creation. Stephen Hawking has suggested that subatomic particles are constantly
traveling through wormholes from one universe to another.
The universe is its own mother: Physicists Li-Xin Li and J. Richard Gott III of Princeton
University suggest the possibility of "closed timelike curves"—where there is nothing
in the laws of physics that prevents the universe from creating itself] In a 1998
Science News article, Gott suggests, "The universe wasn't made out of nothing. It arose
out of something, and that something was itself. To do that, the trick is time travel." Li
and Gott suggest that a universe undergoing the rapid early expansion known as inflation
could give rise to baby universes, one of which (by means of a closed time-like
curve) would turn out to be the original universe. "The laws of physics may allow the
universe to be its own mother."
The multiverse: In 1998, Max Tegmark, a physicist at the Institute for Advanced
Study at Princeton, New Jersey, used a mathematical argument to bolster his own theory
of the existence of multiple universes that "dance to the tune of entirely different
sets of equations of physics." The idea that there is a vast "ensemble" of universes (a
multiverse) is not new—the idea occurs in the many-worlds interpretation of quantum
mechanics and the branch of inflation theory suggesting that our universe is just a tiny
bubble in a tremendously bigger universe. In Marcus Chown's "Anything Goes," in the
June 1998 issue of New Scientist, Tegmark suggests that there is actually greater simplicity
(e.g., less information) in the notion of a multiverse than in an individual universe.
To illustrate this argument, Tegmark gives the example of the numbers between
0 and 1. A useful definition of something's complexity is the length of a computer program
needed to generate it. Consider how difficult it could be to generate an arbitrarily
chosen number between 0 and 1 specified by an infinite number of digits.
Expressing the number would require an infinitely long computer program. On the
other hand, if you were told to write a program that produced all numbers between 0
and 1, the instructions would be easy. Start at 0, step through 0.1, 0.2, 0.3, and so on,
then 0.01, 0.11, 0.21, 0.31. . . . This program would be simple to write, which means
that creating all possibilities is much easier than creating one very specific one. Tegmar
extrapolates this idea to suggest that the existence of infinitely many universes is simpler,
less wasteful, and more likely than just a single universe.
2. Hinton coined the word "tesseract" for the unfolded hypercube in Figure 4.7.
Others have used it to mean the central projection in Figure 4.5, while still others use
it interchangeably with the word "hypercube." One of the earlier published hypercube
drawings (as in Fig. 4.5) was drawn by architect Claude Bragdon in 1913 who incorporated
the design in his architecture.
3. Could you really see all thirty-two vertices at once or would you see up to sixteen
at a time as the 5-D cube rotated?
4. Now that your mind has been stretched to its limit, I give some interesting
graphical exercises.