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From any point in space, you are free to move in any direction you choose. No matter how you orient yourself, you can travel forwards-or-backwards, up-and-down, or side-to-side: you have three independent dimensions that you can navigate. There is a fourth dimension: time; we move through that just as inevitably as we move through space, and via the rules of Einstein’s relativity, our motion through space and time are inextricable from one another. But could additional motions be possible? Could there be additional spatial dimensions beyond the three that we know?

This has been a question that physicists have entertained for about than a century, and that many mathematicians and philosophers have wondered about for significantly longer. There are numerous compelling reasons to consider the possibility, but there’s also the evidence we have from our Universe: both from a mathematical point of view and from a purely physical point of view. Although the physical consequences that would arise from extra spatial dimensions have tight constraints on them, the mathematical possibilities are just as mind-expanding as ever.

Perhaps the best starting point is to consider what life would be like if you, a three-dimensional being, were to encounter someone who lived in a two-dimensional Universe, as though they were confined to living on the surface of a sheet of paper. They would be able to move forwards-or-backwards as well as side-to-side, but they would have no concept of up-and-down. To them, it would be like asking “what’s north of the north pole?” here on Earth; it’s a question that just doesn’t make sense.

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