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John asked:
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How can any intelligent individual entertain the possibility of finite space (I know, Einstein, Hawking,
etc)? Everywhere there must be either something or nothing. One is occupied space, the other is
unoccupied space. Space therefore is infinite.
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============
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It is probably true that everywhere there must be something or nothing. But this is just a tautology,
and says nothing. "Everywhere" means the sum total of "somewhere's", (or something similar). Space
is finite, because there is only a limited amount of 'somewheres'. (And don't ask what is outside of
these limited "somewhere's": It only makes sense to talk about an outside if there is somewhere
outside.)
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Will Greenwood
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Here is a thought experiment. You wake up in the middle of the night to discover that the universe
has shrunk to the size of your house.
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You open the front door, and as you step across the threshold, you find that you are walking in
through the back door. As you climb out of the kitchen window, you find yourself climbing in through
the window of your study. And so on.
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I have just described a possible world in which space is finite. Whether space is in fact finite or infinite
is an empirical question.
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Geoffrey Klempner
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