Hollis Frampton
Zorns Lemma 

Scott MacDonald

Like several of the films discussed in Part i, Hollis Frampton's films are radically different from conventional movies, not only because of their minimal content and the nature of their systematic structures, but in their "address" to the viewer. As is true of most critical films, Frampton's films provide experiences most conventional viewers would consider entirely non filmic, with no indication that anything out of the ordinary is occurring. Of course, like the films discussed in Part i, Frampton's films were not made with the idea of their being available to conventional moviegoers in conventional circumstances. I would guess Frampton made his films for himself (or, as Gertrude Stein, a Frampton favorite, might say, for himself and a few friends) in the hope that some larger part of the art world would discover them later. But even those who might see these films at a specialized screening room would be confronted by much the same "problem" more conventional viewers would face: Unlike conventional film directors whose ability to function within the industry requires that their films create at least the illusion of accessibility and clarity, the illusion that viewers know all they need to, Frampton did not hesitate to make use of types of information few moviegoers of any type would be conversant with, and he did so with no explanation whatsoever - apparently on the assumption that filmgoers can be expected to do research. 

Even a partial understanding of Frampton's films requires a rudimentary sense of the history of mathematics, science, and technology and of the literary and fine arts. Maxwell's Demon (1968), for example, is an homage to physicist James Clerk Maxwell, "father of thermodynamics and analytic color theory"; Prince Ruperts Drops (1969) gets its title from a demonstration done in physics classrooms; States (1967, 1970) is edited according to a system derived from what mathematics calls the Fibonacci series (in which each member is the sum of the previous two). The structure of Palindrome (1969) was a conscious application to film of musical principles explored by the composer Webern; and the content and structure of later Frampton films owe a good deal to James Joyce and Gertrude Stein. Nowhere is Frampton's assumption that his viewers can be expected to be informed, or to inform themselves, more obvious than in Zorns Lemma, the challenging film that established Frampton as a major contributor to alternative cinema. 

Zorns Lemma combines several areas of intellectual and esthetic interest Frampton had explored in his early photographic work and in his early films. His fascination with mathematics, and in particular with set theory - explicit in his generation of numerical sets as a way of determining the placement of imagery in States and Heterodyne (1967), and implicit in his use of a deck of playing cards as a system for the photographic series, The Secret World of Frank Stella (1958-6z)' - is the source of the title Zorns Lemma. Mathematician Max Zorn's "lemma," the eleventh axiom of set theory, proposes that, given a set of sets, there is a further set composed of a representative item from each set. Zorns Lemma doesn't exactly demonstrate Zorn's lemma, but Frampton's allusion to the "existential axiom" is appropriate, given his use of a set of sets to structure the film. Frampton's longtime interest in languages and literature is equally evident in Zorns Lemma. In the brief opening section of the film the viewer watches a dark screen as a woman reads verses from the Bay State Primer (Euro-America's first English grammar text) that highlight words beginning with the successive letters of the Roman alphabet: "In Adam's fall we sinned all"; "Thy life to mend, God's Book attend"; "The Cat doth play, and after slay" (italics added). And the film's long second section begins with set after set of alphabetically arranged environmental words. 

Once the voice has finished reading the verses from the Bay State Primer, Frampton begins the second section with a run-through of a twenty-fourletter version of the Roman alphabet (U and V. I and J are considered the same letters), against a black background, one second per letter - a temporal rhythm maintained throughout the remainder of the film. During the fortyseven minutes of the second section, the viewer at first sees (this section is silent) set after set of alphabetically arranged words recorded in locations all over lower Manhattan (each set is separated from the next by one second of darkness). The words are not arranged so that they make sense together (the rare conjunction of successive words - "limp" "member," in the thirtysecond set, for example - is the exception that proves that Frampton's rule was to avoid combining words). The overall experience is of a phantasmagoria of environmental language. Although the basic one-second rhythm of the section never changes, the experience of the sets of words is far from uniform and regular. The location of particular words within the frame and their material presentation (the nature of the words themselves, the specific movements of Frampton's hand-held camera, and the environment in which the words are seen) are continually changing so that the eye's exploration of successive shots functions as a counterpoint to the one-shot-per-second meter. As more and more repetitions of alphabetized words are presented, the formal properties of certain sets of words become motifs: For example, there is a set of superimposed words and a set of words seen in paper collages constructed by Frampton. 

Once viewers have begun to grow accustomed to the relentless alphabetic organization, Frampton institutes a second procedure that in the end transforms the section. One-second successive bits of ongoing phenomena or activities are gradually substituted for the one-second environmental words. The first four substitution images are a large bonfire at night (for the letter X), ocean waves breaking on a beach (for Z), a tracking shot of weeds (for Y), and steam escaping from a street vent (for Q) - a reference to the four classic elements: fire, water, earth, air. Most later substitutions involve people accomplishing various everyday tasks - a close-up of hands turning the pages of a book (A), hands grinding hamburger (I/J), three construction workers digging a hole (M), a man (Robert Huot) painting a wall (K), a man (Frampton) changing a tire (I) - and still others reveal animals and plants: two rhinoceri (S), a red ibis flapping its wings (C), a single tree in winter (F). In nearly all instances in which people are seen accomplishing particular tasks, the tasks are placed within Zorns Lemma so that they are completed precisely when the second section is complete. For some viewers, a good bit of suspense develops during the latter stages of the section about which letter will be replaced next, and, at the very end, at what point the final substitution will bring the entire set of developments to a close. 

If the second section of Zorns Lemma is Muybridgian - not only in its general use of the serial, but because the one-second bits of the replacement images "analyze" continuous activities or motions in a manner analogous to Muybridge's motion studies - the final section is Lumieresque. For eleven minutes we watch a man (Robert Huot), a woman (Marcia Steinbrecher), and a dog walk across a snowy field, beginning near the camera and moving directly away from the camera down across a small valley, then up toward and into a distant woods. The walk takes nearly four complete ioo-foot rolls of film spliced together so that, although the pauses between rolls are visible, the film creates the sense of a long continuous shot. After the couple has entered the woods, the final roll flares to white. On the soundtrack six female voices read a portion of On Light, or the Ingression of Forms, a metaphysical explanation of the structure of the world by Robert Grosseteste (Bishop of Lincoln during the eleventh century), alternating voices one word at a time, in synchronization with a metronome: The/first/bodily/f orm/I/judge/to/be/Light. The tripartite structure of Zorns Lemma can be understood in various ways, at least two of them roughly suggestive of early film history. The progression from darkness, to individual onesecond units of imagery, to long, continuous shots is reminiscent of what Frampton may have seen as the movement from no experiences of animated motion, to the brief bits of illusory motion created by nineteenth-century philosophical toys and by Muybridge's use of the Zoopraxiscope, to the Edison and Lumière cameras/ projectors that made extended moving images possible. When sound is taken into consideration, the progression may suggest the development from sound technology (the Edison labs had developed the phonograph before Edison conceived of motion pictures as a potentially marketable accompaniment to phonograph discs) to silent film (and the silent era's development of increasingly sophisticated editing strategies) to the coming of sound film (and Bazinian commitment to the continuous shot). 

The most fruitful approach to the progression, however, is to see it as a narrative mapping of human intellectual development. This approach accounts not only for the film's particular imagery and sound, but for the unusual experience the film creates for viewers. Essentially, the three sections of Zorns Lemma correspond to three phases of life - childhood, youth or young adulthood, and maturity - phases that are often characterized by different forms of intellectual process. Frampton places the viewer in relationships to imagery and sound that are analogous to the successive phases of development. 

In the opening passage, for example, viewers are in a dark room waiting for imagery to be projected, listening to a narrator read a series of verses - an experience Frampton sees as analogous to the intellectual experience of childhood. Frampton's view of his/our first years is the diametric opposite of Stan Brakhage's. Whereas Brakhage was for a time consumed by what he saw as the wonders of childhood vision (vision "under childhood," before verbal training has begun to limit what and how we see), Frampton sees childhood as a time of darkness, a period of near stasis during which nothing of importance is seen and almost nothing understood. The basic situation of a woman reading verses, and from The Bay State Primer in particular, recalls those early months when an adult reading to a child is a central form of interchange that has as much to do with passing on accepted moral and religious lessons as with transferring to the child the intellectual tools necessary for effectively exploring the world (in the Bay State Primer verses, the alphabet - the supposed pretext for the verses - is, for all practical purposes, buried within the religious references). The schoolmarmish voice of the woman suggests a period when the adults in charge of a child's education are primarily important as disciplinarians and the earliest lessons have mostly to do with what happens when rules are disobeyed. 

For Frampton, the development of verbal skills doesn't destroy visual innocence; it releases the child from the prison of ignorance and indoctrination. Immediately following the completion of The Bay State Primer verses, Zorns Lemma jumps into the energetic image-per-second rhythm it maintains until the final moments of the film. This sudden, dramatic change is Frampton's way of recreating for the audience some sense of the experience of moving from a time when children are intellectually cloistered into a period when the acquisition of basic verbal/linguistic skills enables them to codify and understand the world, and to enter new realms of experience. 

Frampton's decision to use a twenty-four-letter version of the Roman alphabet, rather than the twenty-six-letter modern alphabet, also makes sense in a context of the educational process. The choice seems an obvious allusion to the fact that each second of sound film is composed of twentyfour frames, and a way of emphasizing that each alphabetic set is composed of a set of sets of film frames. The film's continual reiteration of the alphabet is, on one level, a reminder of a process almost all of us experienced during our early years in school. On another level, the extended parallel between the alphabetic set and the individual second of the film suggest that Zorns Lemma is a new, cinematic schooling, where viewers are learning to understand the organization of this film and, by implication, discovering that there are many more ways of constructing a film experience than their conventional viewing experiences have prepared them for. 

During the second section of Zorns Lemma, Frampton explores a longer and more elaborate period of intellectual growth. Not surprisingly, the visual imagery is much more various and complex than the auditory imagery presented in the film's opening passage, and the audience's position with regard to this imagery is correspondingly challenging. At first, the experience of seeing the sets of environmental words is a rush, particularly since there's a tendency not only to see the words and recognize their position in the alphabetic order, but to try to explore the environment within which each word is filmed. Frampton makes this process intriguing by filming the words in a wide variety of circumstances. Often, he films words printed on or exhibited inside of the windows of businesses so that other imagery is seen with the word or so that the imagery reflected by the window surfaces is superimposed over the verbal "content" of particular shots. Although the repeated alphabetic sets provide a regular, simple structure for hundreds of brief shots, the varied spaces that surround the words render the audience's experience roughly akin to the Odessa Steps section of Eisenstein's Potemkin (a passage Frampton had burlesqued in an earlier film). 

As set after set of alphabetized words and their environments is experienced, it is difficult not to develop a sense of Frampton's experience making the film. The film's collection of hundreds of environmental words suggests that the film was a labor of love, and an index of the filmmaker's extended travels around lower Manhattan, looking for, finding, and recording the words. In fact, the film's serial organization forms a grid against which we can measure Frampton's motions as filmmaker collecting the units that form the grid. 

Once viewers notice that Frampton has begun to replace the environmental words with the onesecond bits of continuing activities, the experience of the second section becomes very different. When I have taught Zorns Lemma, I have often asked students if they can remember which replacement image was substituted for each letter, and I have discovered that a good many viewers consciously memorize the correspondences. For most viewers the experience of "learning" the correspondences is fatiguing - especially since the process of watching sixty shots a minute for more than forty-seven minutes is grueling by itself - but the laborious process has been willingly (if somewhat grudgingly) accepted. The experience of learning the correspondences is the central analogy of the second section. It replicates the experience of learning that set of terms and rules necessary for the exploration of any intellectual field. It is particularly reminiscent of the process of learning a foreign language - we must memorize what particular vocabulary words mean and how they fit into meaningful sequences - but it applies equally to mathematics and the sciences and to other areas of the arts and humanities. The overall change from thrilling rush to exhaustion and finally relief and sense of completion (once the final substitution is made and the section ends) is analogous to the experiences we have as we move into any new intellectual discipline and explore it in depth. 

The overall change in the second section of Zorns Lemma from the focus on the alphabet to the focus on continuous activities suggests among other things the way in which we develop both intellectual facility and an ability to accomplish practical tasks. The fact that the environmental words are seen first, and the substitution imagery later, makes sense, since in most instances our ability to function practically in the world requires that we've learned to read and, in a more general sense, to be able to organize and internalize bits of information codified by words. Further, the segmenting of continuous activities into one-second bits replicates the one-step-atatime procedure we need to learn in order to complete practical or intellectual tasks: Frampton once said, "There are no complex ideas, only long series of simple ideas."' 

A further dimension of the process of maturation is suggested by the fact that while many of the replacement activities are of finite duration, Frampton's arrangement of the individual segments of these activities toys with viewers' time sense. In real time, it takes the man who walks a city block - the replacement image for H - fifty-eight seconds to round the corner and disappear (or, really, fifty-six seconds, since in the final set of images he peeks back around the corner, surprising those viewers who have assumed his walk is candidly recorded, and revealing that he has walked for Frampton as Muybridge's subjects walked for him - acting out the appearance of candidness), but his walk takes more than twenty minutes in film time. On the other hand, Frampton begins to change a tire (T) during the eightysecond alphabetic set, and seems to complete the job in twenty-eight seconds, spread over approximately eleven minutes of film time. Other replacement images document portions of ongoing activities, and still others record cyclical natural phenomena that have no conclusion: ocean waves breaking (Z), a tree in winter (F). One of the challenges of the world that language delivers us into is coming to understand and learning to prioritize the network of patterns within patterns that creates the context for human experience. Our lives are inevitably part of different patterns simultaneously, and the best we can hope for is to maintain a healthy balance of these patterns as long as possible: Ideally our attempts to build a meaningful career on the basis of what we learn will be successful before we complete the inevitable physical process of birth, aging, and death. 

Some years after completing Zorns Lemma, Frampton himself provided a reading of the film's second section: 

Cortically speaking, we are of distinct and separate minds .... Generally, it would appear that, in right-handed persons, the left hemisphere is concerned with language and with linear and analytic language-like deductive activities. The right hemisphere is concerned generally with synthesizing nonlinear inductive activities .... My own reading of the forty-five-minute central section of Zorns Lemma, in which the image that is statistically before one passes gradually from a language-dominated one to a continuous non-language-dominated one, is a kind of allegory, an acting out of a transference of power from one hemisphere of the brain to the other. Of course, that was nowhere within my thinking of the film when I was making it.' 

Whereas the second section of Zorns Lemma tends to create a sense of overload and exhaustion in the viewer, the final section comes as a relief. Even though the one-shot-per-second rhythm is maintained on the soundtrack, the overall mood of the section is one of calm. Once again, the experience Frampton has created for the viewer is analogous to the stage of intellectual development the section focuses on: the achievement of philosophical/spiritual awareness and serenity. It is clear, well before the man, woman, and dog reach the distant woods, that this section will not end until they have traversed the fields between the camera and the woods (the fact that so many of the activities in Section z are structured into the grid so as to become "clocks" for measuring our temporal position within the section has prepared us to make this deduction). There is nothing for the viewer's eye to do during the interim except explore the lovely winter scene and to notice how the sun's going behind intermittent clouds affects the look of the landscape. If the second section is extended climax, this section is an extended denouement during which we get to see at least the illusion of the world as whole. The section's meditation on landscape is reminiscent of the belief, so prevalent during the nineteenth century, that contact with the spiritual dimension of existence or with God is available in nature. The subtle transformation of the scene by the intermittent sunlight is particularly suggestive of Luminist landscape painting, especially since the spiritual implications of light are directly spelled out in the text we are hearing as we watch the scene.' 

Although on one level the soundtrack may seem rather out of sync with the visuals - the awkwardness in the reading created by having successive words spoken by different speakers is emphasized by the metronome sound - it is both philosophically and literally appropriate. In a philosophic sense, Grosseteste's treatise is an attempt to understand the entirety of the perceivable world as an emblem of the spiritual. And, on the literal level, what Grosseteste describes in the eleventh century is demonstrated by the twentieth-century film image: For a filmmaker, after all, light is the "first bodily form," which, literally, draws out "matter along with itself into a mass as great as the fabric of the world." When the six readers review the numbers from i to io (io being "the full number of the universe"), it is difficult to ignore that the fence over which the walkers step halfway to the woods defines ten intervals from the left side of the film frame to the right. The film image thus becomes a metaphor for the universe; the filmmaker analogous to God; and the walkers analogous to the viewers whose trek from one end of the film to another is a cinematic emblem of our real lives. 

The final moments of Zorns Lemma confirm this set of analogies. After the reading of the passage from Grosseteste is complete, the film continues for a minute or so more: The man, woman, and dog reach the distant woods and enter, and after a moment the screen flares to white. Given its position within the structure of Zorns Lemma, the moment when the walkers enter the woods is certainly suggestive of death - one is reminded of Robert Frost's "Stopping by Woods on a Snowy Evening." And the flare-out to white not only signals the end of the roll and the film, it is suggestive of the widespread observation by those who have had near-death experiences that, at the moment of death, we see a powerful light. Finally, since Frampton may have assumed that the coming of the light at the end of Zorns Lemma would be followed by the lights coming on in the theater and the audience filing out, the exit of the man, woman, and dog from the field is not only echoed by the viewers' exit from the cinematic incarnation, but is prescient of our ultimate exits from life, and the concluding moment of our intellectual growth. 

In the years following the completion of Zorns Lemma, Frampton worked on two major film projects: Hapax Legomena, a seven-part film completed in 1972; and Magellan, a thirty-sixhour film meant to be seen calendrically over the course of 371 days, which was nearly complete when Frampton died in 1984. Magellan occupied Frampton for more than ten years. In fact, the idea for the epic was already germinating when he was shooting Zorns Lemma: In the replacement image for A, the book the hands are turning the pages of is Antonio Pigafetta's diary of his voyage with Magellan.' While Zorns Lemma uses the alphabet as an organizational grid, Magellan uses the calendar. Frampton made a film for each day of the year, and special films for special days: the solstices, the equinoxes. While I have seen most of Magellan (since titles of individual sections changed during the years when they were being shot, and individual films were periodically revised, it's difficult to be positive about how complete my viewing of the epic has been), I have not seen it presented as a yearly cycle. In fact, current institutions for film exhibition and distribution are ill-equipped for showing the film as Frampton presumably meant it to be seen. In this sense, Magellan offers a challenge to the current state of film accessibility, a challenge based on Frampton's admiration of epic literature, and particularly for Joyce's Ulysses and Finnegans Wake: For Frampton the challenge was to extend cinematic horizons so that the pleasures and revelations of cinematic thought could be as flexible, in terms of accessibility, as the experience of reading serious literature.' 

As interesting as Frampton's concept for Magellan is, I am not convinced that the concept is successfully fleshed out in the films that make it up, though there are remarkable moments, including Gloria! (i7), the film in which Frampton dedicates Magellan to his maternal grandmother. A set of poignant, witty computer-generated texts about his Irish grandmother is combined with two early commercial narratives about Irish wakes, and with a passage of lovely green film leader accompanied by a tune played on an Irish folk instrument described in one of the computer-generated texts. Gloria! is a film about death, about the spatial/temporal margins of experience and of cinema. In the final section of Zorns Lemma, Frampton looked at "death" from a distance, as a metaphor. By the time he made Gloria!, he had experienced the deaths of his grandmother and father, and he knew he had cancer: His voyage "around the world" in Magellan (and around the two hemispheres of the brain) had brought him across that snowy field to the edge of the woods themselves! 


1. Bruce Jenkins and Susan Krane's Hollis Frampton, Recollections/Recreations (Buffalo, NY and Cambridge, MA: Albright-Knox Art Gallery and MIT Press, 1984), a catalogue for a traveling exhibition of Frampton's nonfllm work that toured the United States in 1984-5, includes extensive information about, and illustration of, Frampton's photographic series, several of which refer to or are reminiscent of Muybridge. Frampton was to remain interested in making photographs and in writing about the history of photography throughout his career. His writings, including his interesting essay on Muybridge, "Eadweard Muybridge: Fragments of a Tesseract," are collected in Circles of Confusion (Rochester, NY: Visual Studies Workshop Press, 1983) 

2. Frampton describes the burlesque in his comments on the now lost A Running Man (1963) in Scott MacDonald, A Critical Cinema (Berkeley, CA: University of California Press, 1988), pp. 26-7. 

3. Frampton made this remarkable observation to me during informal conversation. 

4. A Critical Cinema, pp. 58-9. 

5. For a discussion of the Luminists, see Barbara Novak, Nature and Culture (New York: Oxford, 1980), pp. 28-33. 

6. This is not evident in Zorns Lemma. Frampton indicates that it was Pigafetta's diary in A Critical Cinema, p. 1. 

7. I have always had a suspicion that Frampton used Joyce's literary career as a model for his own career as filmmaker. Joyce began with short stories; Frampton, with short films. Zorns Lemma is Frampton's Portrait of an Artist as a Young Man; Hapax Legomena, his Ulysses; Magellan, his Finnegan's Wake. There is no point in trying to elaborate this parallel in a note, but I am confident that it is not only generally suggestive, but can be developed in some detail, work by work. 

8. The two most useful sources of information about Frampton's life are Susan Krane's "Chronology" in Hollis Frampton, Recollections/Recreations, and Barry Goldensohn's "Memoir of Hollis Frampton" in the special Frampton issue of October, no. 32. (Spring 1985), pp. 716. 


Zorns Lemma

Hollis Frampton