Imagine, for a moment, what it would be like to peer through the world’s first telescope, observing in detail the chasms on the surface of the moon. The light from the sun, striking the moon at an angle, produces crescents around every crater and jagged lines around every facet of the topography. Focusing on any one particular area of the moon only reveals more and more details of its landscape, of its history.
This was the experience of Galileo Galilei during the fall of 1609, and it must have been a revelation. Every person to have ever lived looked at that moon from a distance of roughly 238,900 miles. Galileo saw it as if it were twenty times closer. Up until then, scores of philosophers assumed the moon, as they assumed of all heavenly bodies, to be perfectly spherical, like polished marble. But Galileo’s observations revealed to us that the moon is not, after all, composed of fundamentally different stuff than the earth.
Galileo published Sidereus Nuncius, the book in which he reveals his findings, in 1610. I first read the book a year and a half ago as part of a class, Classical Quadrivium, taught by Dr. Lehman in the Education department.
Before I signed up for the class, the quadrivium had never once crossed my mind. I took the class for the sole reason that my minor required it. At registration, I did a quick Google search and found that the quadrivium was the middle portion of education in the medieval era, and within its range of study was geometry, arithmetic, astronomy, and music. Today, it is not talked about often, even in such a place as Hillsdale. Much more commonly known is the first half, the trivium—grammar, logic, and rhetoric. But after a few weeks in the class, I saw that the arts of the quadrivium offer an especially beautiful lens through which to look at the world. And that word, beautiful, is apt; the quadrivium’s main points of focus are beauty, perfection, order, rhythm.
When studying the quadrivium in class, we did not burden ourselves with mastering the technical particulars of geometry, arithmetic, astronomy, and music. Doing so would take far more time than a semester can offer. Instead, we used the particulars to unlock the meaning of each of those disciplines. Why do we find symmetry mesmerizing? What is truly so sublime about the motion of the stars? Why have all our greatest painters spent so much effort creating images with balance and proportion? Why is every building made up of triangles? And how is it that three notes played simultaneously can make us feel something in our souls? These are the sorts of questions that underlie the quadrivium, questions that unite visible and auditory sense directly to philosophical inquiry. By studying order and perfection in the material world, we begin to see how our lives might become more ordered and perfect. The quadrivium is a curriculum that calls us to contemplate the relationships between lines, spaces, bodies, and sounds, and in answering that call, we become more aware that beauty really does exist.
For me, the class came out of nowhere, yet answered so many questions salient to my interests in art. After writing for several years, I had been growing more enraptured by a relatively new medium, film, and my love of the craft was accumulating to a critical mass. I was beginning to consider making movies as a way of life. But out of all the wonderful books I was reading in classes, few spoke to me directly about film. After all, the medium has only been around for 120 years, and I felt a tangible lack of a tradition. There was a gnawing uneasiness that my Hillsdale studies might have little to do this new art. Film was rootless, flimsy, a fledgeling medium without connection to a meaningful heritage. Thus began my search to find thinkers, artists, and philosophers from the past who could ground my films in something I could trust, allowing me to grow beyond that past and create something for my own time. And this man, Galileo, this mythical figure of Western thought, had taken a lens, looked through it, and with an keen eye made the universe seem suddenly new. I felt an urge to do the same with a camera.
Now imagine that you are standing on a bustling train platform in 1896, one eye squinting through the viewfinder of a cinematographe, one of the first motion picture cameras. There is a growing dot on the horizon, and soon a train engine rushes toward you. The people on the platform bristle and shuffle toward the tracks, and the engine barrels past, just a few feet from the camera. Later, when you show the footage in a theater, some of the audience members scream and dash out of the room for fear that the train will run them down. This was the experience of Auguste and Louis Lumiere. They were engineers, and they had invented their own camera.
The same semester I took Classical Quadrivium, I also took one of Hillsdale’s rare film classes, Dr. Angell’s Movies as Medium, where we watched all of the Lumiere films.
The first footage the Lumieres captured displayed workers streaming out of the Lumiere factory and beginning the walk home. Thirty-foot tall wood doors heave open, and over the fifty-second, unbroken shot, it is mostly women who emerge, women wearing white aprons tied over sturdy dresses that brush the cobblestone. At one point, a tall, lean dog materializes from the crowd, its tail hooking upward and curling back in almost a full circle, and it runs to the opposite corner. A covered wagon leaves, and two men mount bicycles.
The Lumieres filmed that scene on three separate occasions. Why? Film was incredibly expensive, so what fascinated them about pedestrians? The second and third shots have all the same elements, just in different orders. The women with hats and dresses and white aprons emerge from the same exit, and soon the dog leaps in from the left, barking and chasing one of the bicycle men. The camera startled the Lumieres into a deep fascination with the daily things. Like Galileo with the telescope, for the Lumiere brothers, the camera made a sight they had seen hundreds of times before seem utterly spellbinding.
Their curiosity didn’t stop at the factory. They captured a baby eating, a boy pulling a prank on a gardener, three men playing cards while drinking and puffing cigars. In a curious shot, construction workers obliterate the remains of a house, dust clouding the air, but then the clip plays in reverse, and the dust sucks back into the pores of the cinder blocks and the wall rights itself like a man sitting up after a nightmare. Already, they were experimenting with strange techniques.
We think of these scenes as mundane, but at the time, entire neighborhoods came to see them projected on the silver screen. The camera made everything into magnificent spectacle. There had never been anything else like it.
Like a bolt of lighting connecting ground to sky, watching the Lumiere films while reading Galileo fused my love of the canon to my love of the medium. Galileo, and the quadrivium at large, imparted to me a new way of looking at film. Or rather, the quadrivium taught me an old way of looking at the world, and using it to look at film made the medium seem whole.
When explaining the connection between quadrivium and film to friends and family, convincing them of the connection between astronomy and film has always been the trickiest of the four. An easy analogy is to say that cinematography is the astronomy of film. Both use light as their primary source of data, and both use optics to manipulate that light to produce better results. But more importantly, the astronomer looks through a telescope to explore outer-space; the filmmaker looks through the camera to explore the human person—oftentimes, just as strange a subject.
Music is typically the easiest to connect to film. Just about every film has music. Naturally, studying music should enliven my film-going and filmmaking experiences. And music in film is deeper than just the score. Music is rhythm, and editing is nothing but rhythm. Acting is different rhythms complementing and competing with each other. Which actor is melody, and which is harmony? Directing is the management of the melody and harmony.
But exploring music under the umbrella of the quadrivium doesn’t necessarily entail the study of any particular instrument, and not even of music theory per se. We were considering music in the old sense, as the auditory manifestation of the movement of the planets—the music of the spheres, as it used to be called. We were studying the beauty of melody and harmony and rhythm and the way they are analogous to the beauty of symmetry and proportion. It is telling that Plato argues in the Republic that music is a force powerful enough to stir the soul to either frenzy or bliss. And in the Timaeus, he claims that just as the planets in motion create a song, so too do the motions of the soul create a kind of internal music, audible only if we philosophize and listen. More telling still is the ever-presence of music in Scripture. It was the sound of the trumpets that brought down the walls of Jericho, the melody of David’s lyre that calmed King Saul’s rage, the angels’ lyrics that announced the savior of the world. From all this we can know and in fact even feel that song is an expression of spirit.
Geometry and arithmetic, I think, are tangibly connected to film as well. All our great painters were masters of these disciplines. DaVinci’s Vitruvian Man is nothing but geometry and arithmetic, and you can see the painter’s mastery of ratio and proportion forever emblazoned on the ceiling of the Sistine Chapel or in the repetition of rectangles throughout The Last Supper. DaVinci was a pioneer of linear perspective, one of the artistic techniques that allows a painter to create the realistic illusion of depth. Linear perspective mimics the depth cues that a single stationary viewer would see when staring in a single direction. What else has linear perspective? A camera.
Geometry and arithmetic are the bedrock of all visual art, the foundational principles upon which art derives its foundational principles. The concepts of line, shape, balance, contrast, and perspective are based on geometrical and arithmetical relationships. We spent about one third of the quadrivium class learning and memorizing Euclid, the old master of geometry and arithmetic, and Euclid shouts at us even in something as disorienting as Marcel Duchamp’s cubist work Nude Descending a Staircase (No. 2).
The Lumieres brothers, too, like all the visual artists before them, have a mathematical awareness visible in their framing. In the factory shots, the wood doors fill the right half of the frame, but there is a smaller door on the left side, lending balance to the composition. The position of the camera allows us to see multiple planes at different depths. The black-and-white exposure creates sharp lines and contrast. While I would hesitate to call them masters of cinematography, the Lumiere brothers knew how to create pleasing images. With the first motion-picture cameras, they had better eyes for composition than most of us do with the infinitely more sophisticated cameras in our cell-phones.
After we finished watching the early film experiments in Dr. Angell’s Movies as Medium, we moved on to experience the brief heritage of cinema. We saw the silent comedies of Buster Keaton and Charlie Chaplin, the silver-screen legends of Orson Welles and Humphrey Bogart, the oft-forgotten masterpieces of continental cinema from Sergei Eisenstein and Jean Renoir, the classics of Hitchcock, and even a number of moving contemporary foreign films. But one film so sublimely distilled all of my connections between the quadrivium and film, rendering me utterly transfixed and forever changed.
That film was 2001: A Space Odyssey, directed by Stanley Kubrick.
I saw it with one of my classmates in a dark screening room projected on a huge screen with surround sound. There is no better way to watch 2001, and perhaps no better way to watch any film. The quadrivium was alive; music thundered at me through the speakers; astronomy leaped off the screen; geometry and arithmetic suffused every frame that passed before my eyes. This was what I had been searching for: a work that would show me how the ancient, modern, and contemporary worlds could live in the same film.
2001 gestures wildly toward the perpetual philosophical questions—the creation and nature of man, primarily—but in all of my viewings, it has yet to yield many answers. My suspicion is that Kubrick primarily wants us to be arrested by sight and sound. Answers are secondary.
Though there are many scenes that demonstrate the quadrivium’s presence in the film, my favorite is a five-minute sequence about half an hour in where a shuttle docks with a circular space station while “The Blue Danube Waltz” plays. While the melody gently introduces itself and crescendos, satellites move in perfect, regular motion across the screen, orbiting the earth. The music suddenly speeds up and crescendos further as the space-station comes into view, a circular vessel composed of two parallel rings connected by a bridge in the middle. The space-station remains on-screen for thirty seconds, slowly rotating and moving closer to the camera, the music eventually settling down again into the calming melody. The shuttle inches into the frame, and then we are inside the shuttle as the music erupts again, and there is a man asleep in the shuttle, his pen floating in front of him. A flight-attendant emerges from a door, walking carefully with shoes that grip the floor, and puts the pen back into his chest pocket. The shuttle nears the space-station, using its thrusters to match the perfect circular rotation of the space-station, and it enters, docking in a hangar.
It is a simple sequence, and magnificent in its simplicity. Watching it, I could tell that Kubrick was enamored of the perfect motion of objects in outer space. Seeing his obvious delight in the rhythm and synchronization, I, too, was enamored. The sequence reminded me of the music of the spheres. Not only are the actual planets visible in many of the shots, but the docking ship has a music of its own. And the ships themselves are eminently geometrical, made up of clean circles, lines, rectangles, and triangles. To me, that sequence is the quadrivium on camera.
When I was about eleven, my father bought me a telescope, about two feet long, resting on a short plastic tripod. At the time, I wanted to be an astronaut, and I loved reading in my space encyclopedia about the craters and chasms on the surface of the moon, about the way a planet’s gravity can bend the path of light, about the annihilating grasp of black holes. I couldn’t understand the mysteries of outer space, but they fascinated me nonetheless.
About a year later, my mother showed my sister and me 2001 for the first time as part of an effort to educate us in important films. We saw it on a bright afternoon on a small tube television. I thought it was terribly boring, but something about its strange, bold vision disturbed me and remained with me for many years.
Now, a year and a half after those classes, I know from experience that every formal decision I make as a filmmaker will affect the tension between order and chaos in the finished edit. As a filmgoer, I analyze films according to geometry, arithmetic, astronomy (cinematography), and music. Through film, I can travel to other worlds, see something new, experience something transcendent. A quote from Plato’s Timaeus is now a guiding principle when I make or watch a film: “this is the cause and these the reasons for which god discovered vision and gave it to us as a gift: in order that, by observing the circuits of intellect in heaven…thus imitating the utterly unwandering circuits of the god, we might stabilize the wander-stricken circuits in ourselves.”
Chandler Ryd is a senior studying English.