Not Knot (3-d animation, 1991)

Animated at the Geometry Center, University of Minneapolis, Minnesota.

I have always been interested in making images that help people understand mathematics.

During a residency in the art department at Princeton University I met the charmingly wild mathematician John Conway and the visual topologist Bill Thurston, who now heads the Mathematical Science Research Institute in Berkeley, California. They were teaching an inspired mathematics course for undergraduates that taught cutting edge geometric and topological ideas through the sorts of hands-on experiences usually found only in grade schools. The course was wildly popular, with students who might otherwise shun mathematics clamoring to get in.

Bill was at the time also working on a movie called "Not Knot" at the Geometry Center at the University of Minnesota, Minneapolis. Later that year I talked my way into doing the title sequence for Not Knot. The title comes from the idea of visualizing the structure of the negative space around three interlocked loops, in other words, the space that is not the knot.

The alliterative title suggested that I make the first word be the shadow of the last three letters of the second word. Every letter here is a knotted closed loop. In fact they are all topologically the same basic overhand knot. I originally wanted the letters to morph into identical knots to make the similarity apparent, but found it was hard enough to get the letters to rotate rigidly into position.

The 15-minute movie visualizes some mind-bending recent ideas in the topology of knots. The movie ends with a positively trippy flight through a wildly fisheyed gridwork animted by mathematician Charlie Gunn, whose high animation standards had been shaped by time spent at Pixar. The movie is a treat to watch whether or not you follow the mathematics. While there are holes in the logic of the film, it is certainly a courageous first attempt to bring current mathematics to a wider audience.

I animated the sequence in SoftImage on a Silicon Graphics workstation, coached by veteran computer animator Delle Maxwell, who I had met years earlier when she had worked at Pacific Data Images in Sunnyvale, California. Under her guidance I learned just how much work goes into lighting and animating 3-d models. My experience with then new SoftImage would prove useful later that year when I produced images for the George Coates Performance Works theater piece "Invisible Site", and years later designing the intricately 3-dimensional opening space of the computer game Obsidian.