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MIRROR WORLDS 133
Rotate
Figure 5.6 The two triangles can be superimposed only if one is first rotated up out
of the page into a higher dimension.
whose right and left ears are identical, not enantiomorphic. Can you imagine
what they might look like?)
Mobius Worlds
If our entire universe were suddenly changed into its mirror image, would we
perceive a difference? To answer this question, consider a Lineland on which
reside only three slimy aliens: "Thing 1," "Thing 2," and "Thing 3," all facing
east—that is, they are all looking to the right.
_Thing 1 _ Thing 2 _ Thing 3. _Lineland
If we reverse Thing 2, the change will be apparent to Thing 1 and Thing 2. But
if we reverse the entire line of Lineland, the 1-D aliens would not perceive a
change. We higher-dimensional beings would notice that Lineland had
reversed, but that is because we can see Lineland in relation to a world outside
it. Only when a portion of their world has reversed can they become aware of a
change. The same would be true of our world. In a way, it would be meaningless
to say our entire universe was reversed because there would be no way we
could detect such a change. Why is our world a particular way? Philosopher
and mathematicians Gottfried Wilhelm Leibniz (1646—1716) believed that to
ask why God made the universe this way and not another is to ask "a quite
inadmissible question."