THEOREM 8.1 explores the intersection of art and mathematics. It investigates the artistic possibilities of the mathematical concept of orthogonal projection. Given a set of digital images from the Jean Luc Godard film Alphaville (1965), the projection decomposes any source image of those dictionary images. The elements of the film are brightened or darkened so that their mixture approximates as closely as possible the source image. The aim of this project is to open up this technological black box, to foreground the computational process involved, and to experiment with its artistic possibilities.