Radiometric dating simplified
Afterwards you just “lower” the segment of the string back so that it all sits in 3D and now you’ve just got a loop of unknotted string (very creatively, this is called an “unknot”).So, you’ve managed to untied your knot without worrying about self-intersections and all it took was an extra dimension.The image here is only a cross-section of such a knot.
The generalization of a loop (a 1-sphere) to higher dimensions is first the surface of a regular sphere (a 2-sphere), then the surface of a hyper-sphere (a 3-sphere) and so on.
And yes: you can keep going into higher and higher dimensions using the same idea.
While you can’t directly picture a four dimensional knot, you can create cross-sections (the same way a 2-dimensional being might picture 3-dimensional objects using cross-sections).
In part because once you’ve connected the ends of your string the knot you’ve got is the knot you’ve got, and that invariance is very attractive to math folk.
Left: In two dimensions, no matter how complicated and convoluted your string is it can never be tied in a knot.