**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 if we'll still have time, we'll prove that these knots
are really knotted.

**Handout:** K34.pdf

**Slides:** K34-Slides.pdf

**Annotated Slides:** K34-Slides@.pdf

**Talk Video**. (Also @YouTube).

**URL:** http://drorbn.net/syr21.