**Handout:**
Vis4D.html,
Vis4D.pdf,
Vis4D.png.
**Sources:** pensieve.

**Abstract.** Much as we can understand 3-dimensional objects by staring
at their pictures and x-ray images and slices in 2-dimensions, so can we
understand 4-dimensional objects by staring at their pictures and x-ray images
and slices in 3-dimensions, capitalizing on the fact that we understand
3-dimensions pretty well. So we will spend some time staring at and
understanding various 2-dimensional views of a 3-dimensional elephant, and
then even more simply, various 2-dimensional views of some 3-dimensional
knots. This achieved, we'll take the leap and visualize some 4-dimensional
knots by their various traces in 3-dimensional space, and this achieved, I
will tell you about the simplest problem in 4-dimensional knot theory whose
solution I don't know.