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A three-dimensional analogue of Einstein’s four-dimensional Universe. To visualize the essence of this solution, we employ another analogy. Since no one has ever built a viewable model of anything in four dimensions, in this analogy we suppress one of those four dimensions. For sake of argument, imagine consolidating the three dimensions of space into only two dimensions. Then, with time as the remaining dimen- 20 P R O LO G U E sion, we can construct a three-dimensional analogue of Einstein’s fourdimensional Universe.

Regardless of which galaxy we inhabit, we would see all the other galaxies receding (though the galaxies themselves, held together by gravity, are also not expanding). The galaxies would appear to recede for any and all observers in the Universe. Nothing is special or peculiar about the fact that all the galaxies are receding from us. Such, again, is the cosmological principle: no observer anywhere in the Universe has a privileged position. And so it is in the real, four-dimensional Universe. Although the galaxies recede from us, this is not a peculiarity of our vantage point.

Such a Universe always was and always will be. The above models of the Universe stipulate evolutionary change as their guiding principle. Each is derivable from Einstein’s general theory of relativity, and together they are favored, in one form or another and with modifications, by the majority of today’s cosmologists. How- P R O LO G U E 33 ever, several other Universe models have been proposed over the years. Most of them do not follow directly from relativity; some don’t even call for change with time or embrace evolution as their central theme.

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