| | n-dimensional
space: Robert Heinlein "Just
what is n-space? Length, breadth, and thickness are all you see … how about
these other dimensions?" "By logic.
You see four dimensions … those three, and time. Oh, you can't see a year,
but you can measure it." "Yes, but
how can logic …" "Easy as can
be. What is a point? A location in space. But suppose there isn't any space, not
even the four ordinary dimensions. No space. Is a point conceivable?"
"Well, I'm thinking about one." "Not
without thinking about space. If you think about a point, you think about it somewhere.
If you have a line, you can imagine a point somewhere on it. But a point is justy
a location and if there isn't anywhere for it to be located, it's nothing. Follow
me?" … "Did you soak up that
about a point needing a line to hold it?" "Uh,
I think so. Take away its location and it isn't there at all." "Think
about a line. If it isn't in a surface, does it exist?" "Uh,
that's harder." "If you get past that,
you've got it. A line is an ordered sequence of points. But where does the order
come from? From being in a surface. If a line isn't held by a surface, then it
could collapse into itself. It hasn't any width. You wouldn't even know it had
collapsed… nothing to compare it with. But every point would be just as close
to every other point: no 'ordered sequence.' Chaos. Still with me?" "Maybe."
"A point needs a line. A line needs a surface.
A surface has to be part of a solid space, or its structure vanishes. And a solid
needs hyperspace to hold it… and so on up. Each dimension demands one higher,
or geometry ceases to exist. The universe ceases to exist." He slapped the
table. "But it's here, so we know that multi-space still functions…
even though we can't see it, any more than we can see a passing second."
"But where does it all stop?" "It
can't. Endless dimensions." Robert
Heinlein: Citizen of the Galaxy
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