2024 Honorable Mention – Josey Kathleen Hanish

n-sphere

Medium

Letterpress print

Abstract

This piece shows how the concept of the sphere, a set of points equidistant from the origin, generalizes to different dimensionalities. It also refutes the common misconception that the term “n-sphere” refers to an object embedded in n dimensions and teaches the difference between the topological concepts of the sphere, a surface, and the ball, a solid. Understanding how mathematics generalizes to different dimensionalities is essential for general relativity and for string and membrane theory.

“n-sphere” shows how the concept of the sphere generalizes to different dimensionalities, from one to four dimensions. Although we live in three-dimensional space and commonly use the term to refer to the shape of a basketball, the sphere is mathematically defined as the set of points equidistant from the origin – for any number of dimensions! Understanding how mathematics generalizes to higher dimensionalities is essential for general relativity and for string and membrane theory. Furthermore, the sphere in n+1 dimensions can be constructed from spheres in n dimensions. For example, the globe, a 3D sphere, can be constructed from lines of longitude, which are circles. Likewise, a 4D sphere is like a set of 3D spheres, which is shown on the right-hand side of this print. This piece also refutes the common misconception that the term “n-sphere” refers to an object embedded in n dimensions and teaches the difference between the topological concepts of the sphere, a surface, and the ball, a solid.

I printed this piece using the letterpress equipment at the Book Arts Studio in the Duderstadt center. By manually setting antique lead type – lining up each punctuation mark and piece of spacing with a pair of tweezers – I have created an analog facsimile of a 3D rendering. This tri-color print was made with three different formes – one for each color – and three different passes through the press.

Additional photos below show the three formes of lead type and the process of inking the type. After inking the type, paper is laid over the forme, and the press is rolled over the paper (not pictured).