In a sense, it is true to say that an x-plane can be knotted in x + 2 dimensions, though another interpretation gives it as 2x + 1 dimensions.
My choice of words is very bad here
but I don't know how else to explain.
If x = 1, then x + 2 = 2x + 1 = 3, so it does not reveal much.
It just shows that a latrix can be knotted in realmspace.
Wendy has explained how a knotted hedrix in tetraspace would be unstable, and how it can be made stable in pentaspace. We can actually visualise it as a long cylinder in the VWX realm knotted in the VWXYZ pentaspace. The hedrix in question is the curved surface of the cylinder. The process of knotting involves almost forming a duocylinder in the VWXY tetraspace and then, before completing it, moving one of the end points (end circles?!
) through the z-direction. Here if we consider the cylinder as the object being knotted, x = 3 and 5 = x + 2 and if we consider the curved surface of the cylinder as the object being knotted, x = 2 and 5 = 2x + 1.
But in this case, it is not possible to knot a hedrix in tetraspace with x = 2 and x + 2 = 4. One might get the wrong notion that if a cylinder could be knotted in pentaspace, a circle could be knotted in tetraspace. But an attempt to knot a circle in tetraspace is as meaningful as an attempt to knot a point in planespace.
Let me now consider the possibilities of knots in hexaspace. Certainly, a prism of the knotted hedrix/cylinder would fail by the same logic as applied in the case of the knotted hedrix in tetraspace. But how about a spherinder being knotted in hexaspace? The surcell of a spherinder is like a prism of the surface of a sphere, giving x = 3, and 6 = x + 3 or 2x. The process for the knot formation is as follows:
A spherinder in the UVWX tetraspace is curved through the UVWXY pentaspace and the formation of a 32 (Number series notation for the Cartesian product of a sphere and a circle) is almost completed when suddenly one of the end spheres is moved through the z-direction and the spherinder is knotted. I have an intuition that this is no more stable than the knotted hedrix in tetraspace but I don't understand why. Can somebody explain?
PS
I hope my terminology is acceptable