As far as we know: If two one-dimensional lines are placed parallel, they need to be on a two-dimensional plane. If two 2-dimensional planes are placed parallel, they need to be in a 3-dimensional space. So is our space a 4-dimensional space because we (3-dimensional objects) can be placed parallel? (or am I misunderstanding?)
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Unless you're a string theorist, we typically consider ourselves to live in 3 spatial dimensions and 1 time dimension. So, you'll often hear people refer to the 4-dimensional spacetime.
DanDané˘
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