Knots are 1-dimensional objects embedded in 3-dimensional space. So generalizing in an n-dimensional space, a knot would be an embedded (n-2)-dimensional object. Therefore in a 4-dimensional space we would embed a (4-2)-dimensional object, or a 2-dimensional object. Now when trying to visualize a 2-dimensional knot we need to come up with a fourth dimension. This …
MathSantaCruz 