Knotted Spheres

I think I have figured out from first principles, how to tie a sphere into a simple knot. I spent about 20 minutes this morning just thinking about it. As far as I can tell, it requires 5 spatial dimensions. First stretch the sphere into a long sausage shape. Then bend the sausage into a C shape. Now twist the one end of the sausage into the 4th dimension, and the other end into the 5th dimension. Now all that remains in the original 3space of the ends are two sections of a loop. Interlink these (i.e. remove a point from one of the loops (i.e. cut it), pass the other loop through the gap, and replace the point (i.e. re-connect it). Viola.

Actually, later in the day, I read up a bit, and tried to explain it to a work colleague, Ben. While explaining it, I realised that that was not a knot, but would become untangled, so here is how to knot it.

Start with a normal sphere. Rotate by 90 degrees around a plane through its centre. You now have a series of circles, one in each 3-space. Create a knot with each circle simultaneously.

Now you have a knotted sphere in 4-space.