ORIGINAL POST: September 7, 2005

As a professional illustrator I have specialized for many years in Celtic design. One of my favorite aspects of this intricate style is the interwoven bands of knotwork. Knot TheoryIt took lots of practice before I became comfortable with the underlying pattern for constructing the more complicated knots, but eventually I became familiar enough (through much repetition) with the geometric principles that aid in creating good designs. These knotwork patterns all begin with a system of grids, so Moleskinei notebooks with gridded pages have always been a favorite place of mine to work out the details of a knotwork design. Below is the frontispiece to my Knot Theory notebook, a large size Moleskine Volant with squared pages.

It was only quite recently that I discovered this special branch of mathematics devoted to the study of knots, called, surprisingly enough, Knot Theory. It is a subsection of mathematical discipline of Topology which brings us such novelties as the Klein Bottle. In Topology mathematicians study the properties that do not change through deformations like stretching and twisting, but cutting and tearing are strictly not allowed. To a Topologist a doughnut is the same as a coffee cup, a cube equal to a sphere. This would make for an interesting parallel universe if the laws of matter adhered to these topological principles, and additionally a great plot structure for a possible episode of Farscape (also in a parallel universe, one where this series wasn't canned!).