Humke began by telling the audience that he had taught at seven different institutions, and that he was honored and pleased to work with his colleagues at St. Olaf. He also praised St. Olaf students.
"St. Olaf students are a hard working lot and it's been a pleasure working with them," Humke said.
Humke's lecture focused on an introduction into the properties and geometric characteristics of four-dimensional space, an exploration he conducted with an applied linear algebra class he taught 20 years ago.
Humke and his class calculated that a cube in the fourth-dimension would look like a three-dimensional cube with a smaller three-dimensional cube inside of it, connected to the outside cube by the eight corners.
The overall image appears to be a jumble of lines, which Humke said a person must learn to see.
"The mind ignores certain aspects of drawn figures to construct a 3-D figure," Humke said. "We don't see with our eyes but with our brains."
The next part of the project explored how the figure would move in the fourth-dimension, a main distinguishing factor between it and figures in the third dimension.
"Objects twist in a higher dimension as they move vertically through our space, which manifests itself as rotation in our space," Humke said. This "rotation" appears in the fourth dimension as an image repeatedly pulling itself inside out.
After his explanation of these properties, Humke showed a brief video of cubes in one, two, three and four dimensions exhibiting such movement.