2022 Joint Mathematics Meetings

Chris McCarthy

Artists

Chris McCarthy

Associate Professor of Mathematics

Mathematics Department, BMCC City University of New York

New York, New York

cmccarthy@bmcc.cuny.edu

Statement

This artwork came out of my dissertation which involved proving theorems related to the Hilbert Metric. The dissertation, “The Hilbert Projective Metric, Multi-type Branching Processes and Mathematical Biology: a Model of the Evolution of Resistance" is about the mathematics underlying some of the models that are helping us to understand the rate at which diseases become resistant to treatment. I applied the Hilbert metric to the 2 simplex (i.e., to a triangle) by writing a computer program to draw lines uniformly far apart w.r.t. the metric. The resulting grid tiled the simplex with Hilbert Metric congruent equilateral triangles and circles (the hexagons). I added colors and created the artwork collage.

Artworks

Image for entry 'A Variety of Perspectives: The Hilbert Metric on the 2 Simplex'

A Variety of Perspectives: The Hilbert Metric on the 2 Simplex

22 x 28 cm

Digital Print

2021

The Hilbert metric is a way to measure the distance between points. It results in a hyperbolic non-Euclidean geometry. With respect to this geometry lines originating from a triangle's vertex are parallel (non-intersecting). To our eyes, those lines do not look parallel, unless perhaps we see them as being parallel lines going off into the distance, drawn in perspective. We see patterns in the lines and colors. Our minds try to make sense of the complexity. Our perception shifts between seeing hexagons (which are circles with respect to the Hilbert metric), parallel lines, and an occasional parallelepiped. The collage evokes our various perspectives: combining, changing, conflicting, agreeing. The reality we see shifts with our perspective.