Thursday, January 3, 2019

Topology for artists - workshop sketch 11

Topology for artists, walkers and other non-mathematicians
One of my little dreams is to make and give a workshop about topology for artists, walkers and outher outsiders. It might be called: The topological toolkit. What you didn't know about spaces. Or maybe: Topology as philosophy of space. These are preliminary notes: YouTube topology, Styles of topology, Spaces and maps, Translation, Words in linguistic space, Workshop contents sketch, Workshop content sketch 2. I try to post small updates often, to keep myself working on this.

I found this original book in the Rotterdam library. It's called 'Topologie door zien' that translates into 'Topology through seeing' or 'Intuitive understanding of topology'. It is a hand illustrated book. The author took drawing lessons to make the pictures. It's an excellent illustration of the weirdness of topological objects. Many of the illustrations are eerie. I don't think it was done on purpose, but the illustrations are just as uncanny as the Codex Seraphinianus. If I make a workshop, I would like to make that the central point.

The Antoine wild sphere - mapping a sphere to the Cantor dis-continuum. This has something to do with the Antoine necklace, another wild object.
Continuity - as an introduction to homeomorphism.
The Alexander wild sphere - as an example of a pathological object.
A proof of the hairy ball theorem.
The Warsaw circle and the Knaster bucket handle.
The Sierpinsky carpet, containing both the Knaster bucket handle and the Warsaw circle.
Compactness - contrasted with closed-ness.

Also found this: - antoine necklace is a cantor set - geometric toplogy - geometric topology - metric spaces - metric space and toplogy