> "However, in four-dimensional space we can knot spheres. To get a sense of what this means, imagine slicing an ordinary sphere at regular intervals. Doing so yields circles, like lines of latitude. However, if we had an extra dimension, we could knot the sphere so the slices, now three-dimensional rather than two, could be knots."
After a little searching, here's an animated video on how to construct a 3D representation of a 4D knot... very cool and strange stuff:
> "However, in four-dimensional space we can knot spheres. To get a sense of what this means, imagine slicing an ordinary sphere at regular intervals. Doing so yields circles, like lines of latitude. However, if we had an extra dimension, we could knot the sphere so the slices, now three-dimensional rather than two, could be knots."
After a little searching, here's an animated video on how to construct a 3D representation of a 4D knot... very cool and strange stuff:
https://www.youtube.com/watch?v=h68AxRiGxBw&t=0s