FROM DIAGRAM TO DISORDER

‍ ‍From Diagram to Disorder

An Unfolding of a Brief Moment in the Braiding of a 3-Sphere

This gentle, coloured-pencil drawing came out of ten months of deconstruction, study and many long zoom meetings with knot theorist Professor Scott Carter. I will take you through my process starting with images of the professor’s diagrams.

I wanted to lift the diagram out of its page and give it a 3 dimensional quality. Here I separated the braided surfaces of the spheres and created view as if looking along them, between them. At this point I was still maintaining the sphere sections as rectangles.

You can see a bit of my drawing in this poster for the 2026 Art-Math exhibition

at the Institute Henri Poincare, Sorbonne University, Paris

My next step was to envisage the spheres having form and movement. This is one of many, many attempts to show the undulations of the surfaces of the spheres, seen here as separate sheets.

These were my starting point. Diagrams of The 3-fold branched cover of the 3-sphere branched along the trefoil knot. Scott calls these his radiators. Each yellow rectangular radiator has 3 layers which correspond to 3 sections cut out of 3 spheres that are nested one inside the other. These sections are flattened to become easy to read as a diagram. In order to understand what was happening I had to deconstruct them. You can see that I didn’t hesitate to write and draw all over the pages. There are 14 pages of diagrams all together, I concentrated on

Page 12

My first task was to draw the braids. Each set of three lines represents the contour of the three spheres. The left line is the sphere in the centre. The middle line is the sphere in middle and the right line is the outer sphere.

I began to formulate an idea that would express my interpretation of the graceful undulating character of the spheres. Here you can see the nested spheres and the braids that indicate the entangled surfaces of the three spheres.

The 3-sphere is a complex topological creature that I was trying to understand rather like a blind person tries to discover what the elephant is by walking around it, reaching out and feeling its legs, trunk and belly. Too be continued………………