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Parallelism Application

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I get the basic idea of applying parallelism to scaling, but in specific cases I'm a little confused. I get the whole part about how you can't have two 2D planes extend infinitely without touching unless they're in 3D space, but what about something like a timeline or universe with a space-time? Would the space they're within be 5D because time is infinite and there's infinitely many snapshots of the universe? Does it matter whether or not the universe within the timeline is infinitely large? Even if they weren't, would a statement saying that the universes are parallel worlds qualify?
 
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