Topologies - 2011

Topologies, is a series of three pencil drawings based on topological shapes and theorems. In this project I’ve used the surfaces of the klein bottle, torus, cross-cap, borromean knot and moebius strip to explore abstract notions of the possible shape of space and to visualize multidimensional spaces using two dimensional images. The first two pieces in Topologies represent a proposition with an unfortunate name - the Hairy Ball Theorem. This states that it is impossible to comb the hair on a sphere flat - you will always have either a cowlick and a hole, or two vortices, at the poles. It is, however, possible on the continuos surface of a torus. In the first diagram, thousands of hatch marks convey the direction of the hair on a large sphere which looms above a smaller schematic depicting the vortex point at the pole below. The second drawing follows the same composition, but depicts a torus with the direction of the marks perpetually circling the surface. The topology of a torus is finite, but without boundaries, making it a popular choice for the shape of the universe. The final piece in this series applies the Hairy Ball Theorem to a variety of topological shapes and knots which levitate in a loose orbit on the paper.