On Film Editing and the Math Proof
Written by Tashrika Sharma
Filmmaking and science have a long documented history, going as far back as early amateur filmmaker like Eadweard Muybridge who invented devices in the late 19th century to record movement. However, filmmaking and theoretical mathematics have little conversational history. One method of creating a conversation between the two fields could be by connecting them through their unique characteristics. While editing exists in all artistic mediums, editing in film is a technique that distinguishes film from other art forms. Whereas in mathematics, the math proof remains a mysterious combination of prose and symbols used to verify abstract statements unlike the hard sciences. These distinguishing characteristics of film and math reveal their ephemeral natures and thus provide one basis in which they can be related to each other.
“It may sound almost circular to say that what mathematicians are accomplishing is to advance human understanding of mathematics,” William Thurston wrote in On Proof and Progress In Mathematics, focusing on the psychological and sociological aspects of how math is practiced and not upon how to define it. The key aspect is that practicing mathematics involves advancing how human beings think and understand various aspects of the field. This can range from being part of a team that discovers a new result, or a team that rediscovers an old one. Thurston enumerates that aspects of math thinking involves: human language, visual, spatial, and kinesthetic sense, logic and deduction, intuition, association, and metaphor, as well as stimulus-response,and processing of time. Combinations of such thinking practices can lead to understandings that are harder to explain since they are often intangible, difficult to communicate, individual, and often the subtext of the conversation.
Photo credit: 8 1/2 (Dir. Federico Fellini, 1963), the audience is often between what the film director, Guido (center, played by Marcello Mastroianni), is fantasizing and experiencing as he embarks on making his film. He imagines Claudia Cardinale (left) gliding to give him a glass of water only to snap back into reality by the woman offering him the water (right).
The subtext is the unconscious aspect of communication that creates a more profound experience of the storytelling. “To me, the perfect film is as though it were unwinding behind your eyes, and your eyes were projecting it themselves so that you were seeing what you wished to see. Film is like thought. It’s the closest to the thought process of any art,” John Huston said in an interview published in Christian Science Monitor in 1973. The film 8 ½, which follows the creative process of the film director at the center of it, famously makes seamless transitions between the past, the present and the conditional future representing the thoughts of the director. While film is an immediate manifestation we experience, there are also internal understandings that arise in filmgoers. They arise from the thoughts guiding the films colliding with the personal associations each individual makes while watching.
Photo Credit: Meshes of the Afternoon (Dir. Maya Deren, 1943), “the woman (Maya Deren) later on in the film watches herself from a window experiencing an incident that occurred earlier in the film.” via Flicker Alley
Mathematics distinguishes itself from other fields in that ideas are communicated through proofs. A proof in the most general sense is defined as a clear flow of convincing mathematical ideas. While proofs are read linearly, readers often engage and process them non-linearly. Non-linearity in storytelling is often associated with surrealism or dynamic storytelling, one can see non-linearity in many of the sequences of the experimental film Meshes of the Afternoon which unfolds in a dream-like form. Proofs are not primary information but are a way to organize mathematical understandings and are extremely useful. These proofs are what subsequent generations encounter in terms of past work. The language they’re written in inadequately captures the way each generation thinks about the same ideas and communicates them.
Photo Credit: Meshes of the Afternoon (Dir. Maya Deren, 1943), “knife sequence is immediately proceeded by a key in the same spot” via Flicker Alley
While every field of art involves editing, filmmaking separates itself through the function of “separation” (or referred to in other cultures as “assembly”) of footage. This editing process produces a rhythm defined as the unseen but strongly felt guiding force behind an audience’s experience of watching. For these reasons, filmmaking is described as “sculpting in time” by the director Andrei Tarkovsky in his book Sculpting in Time. The editing process in this sculpting works similarly to how we blink, as remarked by Walter Murch in In The Blink of An Eye: A Perspective on Film Editing. Murch wrote.
“the blink is either something that helps an internal separation of thought to take place, or it is an involuntary reflex accompanying the mental separation that is taking place anyway.”
The choices in visual discontinuity by the blink (the edit) create a path for the film to convey the language intrinsic to itself, quite like a dream, to an audience ready to be convinced. In mathematics, it’s hard to talk about anything without explaining it. The proof or the explanation is a way of making the invisible visible - of building a path to get everyone on the same page. The communal language of the mathematical proof presupposes that the reader is prepared to be convinced. In both fields, one is telling a story making an audience familiar with something that at first feels unfamiliar, but with inexplicable revelations in each part of the proof or film, one is also at the same time becoming unfamiliar with the familiar. The latter sensation occurs when we shift our experience in reaction to something, whether a mathematical object becomes deeper in our mental image of it or watching a film expands our understanding of ourselves or others. In both cases, the math proof and the film are both temporally dynamic and exist in ways that paintings, sculptures, and other biological, chemical or physical objects are not.
If the film edit works to make films feel like a waking dream, then math progress and the mysterious way proofs work are like that of a sleepwalker. In that sense, there could be a relationship between the waking dream and sleepwalking to create work that enriches math communication and filmgoing experiences.
