T. G. Vanini

Statement

In the course of my research in mathematical logic (under my real name of Laurence Kirby) I made visualizations of the construction of hereditarily finite sets. Pleased with the organic feeling and sometimes surprising forms of these diagrams, I started to explore their aesthetic possibilities and this grew into an artistic obsession. Each element in my images is grown from a mathematical seed which I control, with the aid of experiment and imagination and Mathematica software, to obtain a visually satisfying form. In my creative life as a songwriter, poet and violinist I’ve long been concerned with exploring the boundaries between art, science and mathematics – between form and emotion. My digital prints continue this exploration.

Artworks

In set theory, each set is built up from the empty set using set-theoretic operations and ordinal arithmetic, and the construction can be represented as a digraph using the membership relation. This is a visualization of one such representation of a finite set, designed to bring out its structure and beauty. The Axiom of Extensionality, which ensures the digraph is rigid, helps to give this picture its organic feel.

This image, part of a series titled Finite Set Theory, combines contrasting visualizations of three hereditarily finite sets. Each set is represented by the graph of the membership relation on its transitive closure.