Topological knots act as lures for my imagination. Even after hours of detailed instruction in rudimentary knot theory they retain their sinuous attraction. Tying the creative process to mathematical accuracy brings up engaging and often seemingly insoluble problems. On the one hand there are the specific constraints of the knots, and on the other there is finding a visual solution that satisfies the untamed creative impulse. Sitting in judgement of the synthesis is my visual gatekeeper, who is annoyingly strict. I make hundreds of corrections before a drawing gets the OK. An eraser is essential! As always, my thanks to Scott Carter, emeritus professor, University South Alabama, for his patient guidance.
I am playing with topological knots 6_1, 7_6 and 8_1. The section in the centre is a braid diagram of the three knots conjoined. Braid diagrams show the crossing order of a knot and whether the strand crosses over or under itself. Imagine the loose ends of the braid are joined making a single strand, a closed knotted loop. The braid can be unravelled to discover its knot. The drawing on the left depicts the braid gently opening out. Drifting, the strand frees itself of its linear, diagrammatical constraints. Unfolding it will become the knot which is the union of the three . On the bottom right are the three knots taken directly from the Knotinfo table. On the top right are the same three knots in 3D, made from black mesh tubing.