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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?)

Qmechanic
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Chill dude on Earth
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  • An n-dimensional object doesn't have any physical meaning in an n+1 dimensional space. It's a pure abstract. – FlatterMann Jan 21 '24 at 10:21
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    How do you propose placing two 3-dimensional objects in parallel? – DanDan0101 Jan 21 '24 at 10:28
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    @FlatterMann You can certainly have an $n$-dimensional object embedded in $n+1$ dimensions. For example, the plane in 3 spatial dimensions, as said by OP. Could you please clarify the point you're trying to make? – DanDan0101 Jan 21 '24 at 10:30
  • @DanDan0101 A plane is an abstract. It's not a physical object. The nearest approximation of a plane in three dimensions is a sheet, i.e. a flat object with a thickness that is small compared to its other dimensions. It's still a three dimensional object. – FlatterMann Jan 21 '24 at 10:32
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    @FlatterMann Sure, I agree with you, but I think this misses the point of the question. – DanDan0101 Jan 21 '24 at 10:33
  • The problem with the question is the last sentence. Can 3-dimensional objects be placed in parallel in 4 dimensions? A three dimensional object is not an object in 4 dimensions. It does not have physicality in any operationally conceivable way. If the OP is talking about geometry, then the answer is trivial, but the question does not make sense in a physical context. – FlatterMann Jan 21 '24 at 10:40
  • Let us continue this discussion in chat. – FlatterMann Jan 21 '24 at 10:40
  • Possible duplicate: https://physics.stackexchange.com/q/4079/2451 – Qmechanic Jan 21 '24 at 11:16
  • We are not infinitely extended (like a plane is). Instead of thinking about two 2-dimensional planes, consider instead 2 rectangles (or maybe two identical drawings of a person), which are 2-dimensional objects of limited extent. You can place them in parallel in the way you describe (by sliding them on a 2-dimensional plane) without needing 3-dimensional space. They are just placed next to each other in the plane. So, no, us being able to do the same thing does not imply that space is 4-dimensional. – Filip Milovanović Jan 21 '24 at 11:51
  • I don't think this is a duplicate. The answer appears to be very different from the one linked. The concept of "parallel" you are thinking of here is actually a 1 dimensional concept used to map 3d objects. Parallel objects means we can draw 2 parallel lines (1 dimensional) and define a relationship between points of one object and the first line and the corresponding points of the second object and the second line. We only needed 1d lines, so a 3d space is more than sufficient. Parallel 3d spaces (requiring 4 dimensions) are hard to intuit because you and I live in 3d. – Cort Ammon Jan 21 '24 at 16:51

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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.

DanDan0101
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