clifford_a-_pickover_surfing_through_hyperspacebookfi-org
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notes 223<br />
less universes could be very different. Some might collapse into nothingness quickly<br />
after their creation. Stephen Hawking has suggested that subatomic particles are constantly<br />
traveling <strong>through</strong> wormholes from one universe to another.<br />
The universe is its own mother: Physicists Li-Xin Li and J. Richard Gott III of Princeton<br />
University suggest the possibility of "closed timelike curves"—where there is nothing<br />
in the laws of physics that prevents the universe from creating itself] In a 1998<br />
Science News article, Gott suggests, "The universe wasn't made out of nothing. It arose<br />
out of something, and that something was itself. To do that, the trick is time travel." Li<br />
and Gott suggest that a universe undergoing the rapid early expansion known as inflation<br />
could give rise to baby universes, one of which (by means of a closed time-like<br />
curve) would turn out to be the original universe. "The laws of physics may allow the<br />
universe to be its own mother."<br />
The multiverse: In 1998, Max Tegmark, a physicist at the Institute for Advanced<br />
Study at Princeton, New Jersey, used a mathematical argument to bolster his own theory<br />
of the existence of multiple universes that "dance to the tune of entirely different<br />
sets of equations of physics." The idea that there is a vast "ensemble" of universes (a<br />
multiverse) is not new—the idea occurs in the many-worlds interpretation of quantum<br />
mechanics and the branch of inflation theory suggesting that our universe is just a tiny<br />
bubble in a tremendously bigger universe. In Marcus Chown's "Anything Goes," in the<br />
June 1998 issue of New Scientist, Tegmark suggests that there is actually greater simplicity<br />
(e.g., less information) in the notion of a multiverse than in an individual universe.<br />
To illustrate this argument, Tegmark gives the example of the numbers between<br />
0 and 1. A useful definition of something's complexity is the length of a computer program<br />
needed to generate it. Consider how difficult it could be to generate an arbitrarily<br />
chosen number between 0 and 1 specified by an infinite number of digits.<br />
Expressing the number would require an infinitely long computer program. On the<br />
other hand, if you were told to write a program that produced all numbers between 0<br />
and 1, the instructions would be easy. Start at 0, step <strong>through</strong> 0.1, 0.2, 0.3, and so on,<br />
then 0.01, 0.11, 0.21, 0.31. . . . This program would be simple to write, which means<br />
that creating all possibilities is much easier than creating one very specific one. Tegmar<br />
extrapolates this idea to suggest that the existence of infinitely many universes is simpler,<br />
less wasteful, and more likely than just a single universe.<br />
2. Hinton coined the word "tesseract" for the unfolded hypercube in Figure 4.7.<br />
Others have used it to mean the central projection in Figure 4.5, while still others use<br />
it interchangeably with the word "hypercube." One of the earlier published hypercube<br />
drawings (as in Fig. 4.5) was drawn by architect Claude Bragdon in 1913 who incorporated<br />
the design in his architecture.<br />
3. Could you really see all thirty-two vertices at once or would you see up to sixteen<br />
at a time as the 5-D cube rotated?<br />
4. Now that your mind has been stretched to its limit, I give some interesting<br />
graphical exercises.