Nancy Hocking
While dipping into knot theory online I came across a topological knot table called the First Seven Orders of Knottedness. (Only a topologist would come up with a title like that!) I was delighted by the hundreds of lovely turning and twisting knots. My partnership with topology now had fuel for at least ten more years!
Through my topologist father, the world of multiple spatial dimensions, knotted spheres and a bottle with no inside or outside fascinated me from childhood. There is mystery in these odd concepts that I need to explore. I have the help of topologist Professor Scott Carter, whose brain I pick regularly. While Scott walks through the center of the mystery too concentrated to notice it, like a tourist I marvel and am in awe.
This drawing depicts six topological knots. Knots,are classified by how many times the strand of the knot crosses itself. Top left is the unknot, which is, weirdly (topologists are a strange bunch), just a circle with zero crossings. The knots then proceed from 4 up to 8 crossings. I laid the knots out flat in copper wire. Copper wire is very malleable and therefore compatible with continuous deformation, which is a central concept in topology. I twisted and pulled the wire until each set of 3 knots balanced aesthetically. The drawings were then done from photographs I took. It is quite a challenge for even me to determine where the crossings are among the sensuous turns and twists. For those who are keen I offer them the same challenge.