Theorem 9 (latent figures) is a video installation that combines computer science and cinematic art. Every frame in a digitized version of the film Alphaville (Jean-Luc Godard, 1965) is reconstructed using four distinct sets of prototypical frames (“visual archetypes”) extracted from that same film. Every set of prototypical images can be understood as a visual dictionary. By appropriately weighing (darkening or brightening) and summing the component images in each dictionary, it is possible to generate an approximate reconstruction of any other frame in the movie.

The project uses Simplex Volume Maximization, a machine learning method of matrix factorization where every image is represented as a convex combination of a set of prototypical images. These visual archetypes are selected to maximize the volume of the simplex whose vertices are the vectorized archetypes.    

Visual archetypes often carry thematic associations, which are obvious to anyone acquainted with Godard’s film. These associations generate visual metaphors. For instance, a flickering artificial light is associated with the supercomputer Alpha 60 and so with the cybernetic society denounced by the film. Agent Lemmy Caution is associated with certain hardboiled or noir heroes, and also with concepts of freedom, love, and rebelliousness. These associations imply thematic contrasts (cybernetics and control vs. freedom and love). In Theorem 9, the reconstruction algorithm juxtaposes various thematically charged dictionary images into a single reconstruction. Each individual dictionary image remains recognizable even in combination with other images.

These various connections (“visual figures”) sometimes foreground and potentially confound the thematic contrasts made in the original film. For instance, images of Lemmy Caution (associated with existential freedom) and Natasha (associated with love) blend together with the computer light (associated with authoritarian control and technocratic rationality), thus undermining thematic oppositions established in the film and suggesting the need to reframe our understanding of societies of control. The juxtapositions also foreground and undercut gender structures. The male protagonist is reconstructed using female faces.

The analogies are visually compelling because the elements juxtaposed in any reconstruction tend to mimic the graphical structure of the original image. This connection is accomplished automatically, by the algorithm employed to select and combine dictionary elements. The mathematical techniques employed are directly responsible for the conceptual and perceptual properties of this work