PRINT September 1971

“Zorns Lemma”

SINCE ITS BEGINNINGS IN THE 1940S, American experimental film has had, as a body of work, a fundamentally evocative intent. A primary concern was the recognition of how central the preconscious and irrational level of experience is to all human behavior. Like poetry, these films attempted to appeal directly, by means of potent imagery and rhythmic structure, to our emotions (i.e. our irrational and too often subconscious level of experience). The filmmakers were eager to explore how experience is constructed, how in fact the various levels of our minds interact in any given set of circumstances.

Their investigations fell more or less under the label of Surrealism, either lyrical (Deren, Broughton, early Brakhage) or epic (Anger, Markopoulos, later Brakhage). Labels notwithstanding, these films did share with Surrealism a fundamentally psychological concern. The nature of experience for these filmmakers was predicated upon an understanding of the conscious, rational, empirical mode as norm.

Evidence of a different and broader understanding of the nature of experience within the American art community began to emerge in the 1960s. There was a shift of emphasis from the things we experience (and thereby come to know) like objects, people, emotions, time, and space, to the actual process of experiencing, the ways in which we come to know anything. That shift may be described as a repudiation of psychology in favor of epistemology.

Since 1964 a development called structural cinema has taken place which appears to have initiated an epistemological stage in this exploration of the nature of experiencing. Rather than trying to evoke a complex, many-layered experience, these films try to isolate single aspects of that complexity for close examination by the viewer. The films within this definition are minimal both in terms of elaborate technique and symbolic content.

Typically a structural film confines itself to featuring one or two aspects of experience at a time; the way a single particular space functions in film time (Baillie’s All My Life), how light works on film (Conrad’s The Flicker), how color is perceived on film (Sharits’ N:O:T:H:I:N:G), how time functions within film “space” (Snow’s Wavelength). Obviously each such issue involves many of the others, and while these films are minimal in certain respects they are immensely complex in others.

P. Adams Sitney has described them as “audiovisual objects whose most striking characteristic is their over-all shape.”1 If there is no “content” in the conventional sense of action, narrative or characters, the structure of the film becomes its only content, and the film itself becomes an object. Like most objects that we encounter it must be examined from all sides, generally sniffed about, and finally fitted in somehow to some category of our experience (presumably the category of “film”). Most conventional narrative films (and, indeed, the film-poem forms previously mentioned) place their viewers within the complex web of their own feelings and responses. Structural films do just the opposite by refusing the viewer all such pleasures, thus producing rather a rude confrontation. What is this thing that calls itself a movie? That is the underlying question posed by structural cinema. Isolating the various parts of the experience of watching a film seems an efficient way to explore such complex phenomena as time and space and rhythm and human perception. After a time the evidence gleaned from such explorations may enlarge our understanding of each phenomenon and its interactions with the others.

HOLLIS FRAMPTON’S RECENT FILM, Zorns Lemma, seems to me unique with respect to previous structural film in that it attempts just such a synthesis of evidence gathered from various corners. The fiIm proposes a possible construct, a model in mathematical or scientific parlance, for the component parts and dynamics of the specific perceptual experience of film-viewing. (Presumably this particular situation will reveal itself to have implications for other life situations and experiences.) Zorn’s particular Lemma was a proposition within mathematical set theory—basically a theory to describe the “relative preponderance of shared qualities”2 for each element within a particular given situation, or set. As a title, Zoms Lemma is thus a succinct metaphor for the film’s subject and function.

The film is divided into three distinct sections. Section I (ca. 4 1/2 minutes) begins with no image, only a female voice reciting part of an 18th-century Bay State reading primer. Each couplet features an alphabet letter and is delivered in that morally instructional (and presumably elevating) tone peculiar to schoolmarms.

Section II (47 minutes, 9 seconds) begins with a silent run through a 24-letter Roman alphabet (no J or V) composed of large silver letters in relief on a black field. A word beginning with letter “A” (in this case the word is “a”) appears, is followed by a word beginning with “B,” and so on through the alphabet at a speed of one second per letter-word. The words all occur in the urban environment, on store fronts and other kinds of signs and notices. Each run through the alphabet preserves the same rhythm while the words and their contexts vary: On the 5th round the letter “X” is replaced by a shot of a bonfire at night. On the 7th round “Z” is replaced by an ocean wave advancing and receding down the beach, and on the 12th round a horizontally trucking shot of sea grasses blowing in the wind replaces the letter “Y.” The film proceeds with the gradual replacement of each alphabet-word by an image until at the end of the section the final run-through is composed entirely of these replacement images.

Section III is a static frame of a deep expanse of snowy field with woods at the far end. A man and woman, bundled in overcoats and accompanied by their dog, move slowly away from us into the depth of the screen. The sound track has six women’s voices reciting a text by cyclically alternating a different voice for each word. The effect of this is highly rhythmical while the sense of the sentences is indiscernible. Instead key words stand out by repetition and volume: Earth, Air, Fire, and Water; and Form, Matter, Composition, and Entirety. The latter portion of this section (ca. 1 minute of the 11 minutes of the section) has no sound track. When the couple finally disappear into the woods, we are left confronting only the silence of a snowy country field, and then that fades out to white.

Watching the film is a complex and cumulative experience. On first viewing one may not catch the alphabetical reference in the opening recitation. Certainly the black, dark screen seems mysterious. Once Section II begins we can relax—this is more familiar. Silent film is not so strange as unaccompanied sound track. The rhythm of the alphabet-words is even and pulsing. When the image-substitutions begin the game becomes apparent, and we enter into it, looking forward to what will happen next. After some time it becomes apparent that the game is going to proceed at its own leisurely pace and there is time to look around a bit. The individual images seem colorful and even amusing, but patternless. Towards the end of Section II tension builds up and the pace appears to quicken as we anticipate completion. That the film, in fact, goes on is a bit startling, but the six female voices of Section II take over and continue the pulsating rhythm of the alphabet images. Most of our attention, meanwhile, is taken up in trying to make sense of the “minimal” image (especially so in contrast to Section II) of the snowy field and walking couple. Eventually the sound track ends and we are left contemplating the empty field. Finally there is nothing, no sound and no picture, only a rectangle of white light shining through clear leader. The film is over.

A second viewing of Zorns Lemma is necessarily quite a different experience from the first. The suspense is gone and we can approach the film with confidence now that we know approximately what is going to happen. The opening recitation is no longer eclipsed by the mystery of that dark screen. We realize that it is an alphabet, and thus rather a neat and economic introduction to the film. Eventually we are sure something will appear on the screen to fulfill our expectations of this event as a movie (i.e at least partially visual). Accordingly, the first alphabet letter has considerable punch. It both ends the tension built up over the blank screen and, by means of its rhythmic repetitions, transforms that tension into a sense of “going somewhere” in time. (That knowledge seems to be a relief, and one might well ask why it is so disquieting for an audience to feel that it is “standing still” in time.)

Section II begins, on second viewing, to reveal the complexity of its rhythmic structure. The suspense surrounding the content of each new substitution is diminished and the relationships between images start to emerge. There are a number of progressive acts (an egg frying, a tangerine being peeled) which form a sort of counterpoint to the nonprogressive acts of their surrounding images. Frampton calls these convergent and nonconvergent actions. Additionally all the substitution images are divided into rhythmic or arrhythmic classes, so that there are four kinds of rhythms interwoven throughout this second section. All of that is, of course, playing against the 1-second pulse of the cuts from shot to shot. Since the effect of this is so absorbing, coming to the end of the section is a bit of a shock. By transferring the underlying pulse to the sound track (i.e. the six women’s voices alternating single words) and presenting the relatively “restful” image of a snowy field, we are eased out of Section II rather than traumatized. Finally we are left the silent snowy screen, a last resting place before being thrust out once more into the unsettling glare of “reality” which lies in wait outside all movie theaters. We begin in the dark and end in light, a suggestive metaphor for the experience proposed by this film.

THE IMMEDIATE SENSUAL IMPACT of Zorns Lemma bears a musical analogy. It functions similarly to a medieval canon, building up to a dense and highly controlled texture. In fact, the rhythmic structure of the film makes clear that film, like music, consists fundamentally of the rhythmic articulation of time by means of a basic unit of measure, one cut, one note, or groups thereof.

Having established itself as belonging to the generic category of “film,” Zorns Lemma proceeds to totally ignore normal movie conventions. Not only does the structure lie bare, unclothed by any vestige of “content,” but that structure is self-constructed. The filmmaker has provided a set of conditions and allowed them simply to take their course as if programmed by a calculating machine. A 24-letter alphabet at 24 f.p.s. provides the entire structural frame of the movie. The implication here, of course, is that the artist is less “responsible” than usual for his work. Rather than an inventor or “maker” he is a kind of “engineer,” a director of forces which already exist in his world. The 24-letter alphabet is man-made, while the 24-f.p.s. film speed is a requirement of film machinery. Philosophically this suggests a considerably less egocentric concept of the artist than has prevailed even in the earlier decades of our own century. And if the artist is not permitted full control of his creation, neither is the audience. Room is left for real interaction, for real discourse, in “real time” between the spectator and the thing observed. A work like Zorns Lemma is incomplete without the viewer’s participation. If the film is indeed a model for the general category of film-viewing, that fact has broad implications. What does it mean for an event to be “complete”? Does not each interaction of each viewer with each event (or object) produce a unique situation? Is not experience (and therefore knowledge) of every sort finally subjective, and personal, and beyond a certain point, in communicable?

These questions underlie the very existence of Zorns Lemma, and it is to the film’s iconography that we must turn for a clearer understanding of their considerable ramifications.

Now then, you say, it has been established that Zorns Lemma is a movie, albeit strange. But what is the reason for its being like that? Why was it made? Upon closer inspection it becomes clear quite soon that the film is ultimately concerned with a kind of cosmology, that is, the theory of the universe as an ordered whole, governed by a set of general laws. The opening section has a biblical text, one interpretation of that order and its laws. Earth, Air, Fire, and Water as “primary structures” of the universe (as in the pre-Socratic philosophers and in Plato’s Timaeus) pervade Sections II and III—another order, other laws.

In Section II the first four alphabet-substitution images occur as follows:

(fire) for X—a raging bonfire at night
(water) for Z—sea waves advancing and receding
(earth) for Y—slow trucking shot of cattails
(air) for Q—steam escaping from a street vent

The remaining substitution images are a catalog of deliberately banal events, changing a tire, cutting cookies, bouncing a ball, etc., which fall into the rhythmic classes mentioned previously. This sequence of replacements, the four basic elements first with the rest following, is picked up and elaborated upon in the sound track for Section III.

A medieval Latin text by Robert Grosseteste (translated and edited by the filmmaker) forms the entire sound track for this last section. Entitled On Light, or the ingression of Forms, it begins by positing Light as “the first bodily form” which “drew out matter along with itself into a mass as great as the fabric of the world.” (A more apt description of the way film works would be hard to find.) Next, Earth, Air, Fire, and Water, the basic elements of the universe, were “brought forth” from Light.

That “fabric of the world” falls into four categories: Form, Matter, Composition and Entirety, in that order. Further, these categories equal the numbers 1, 2, 3, and 4, the ratios among which constitute the stabilizing harmony of the universe. Thus they appear in “dances and rhythmic times.”

From darkness to light, and thence to life (matter) and order—the metaphysical sequence both Greek and Christian. Indeed the cosmological imagery of Zorns Lemma seems to summarize a cycle—that man perceives order in the universe, has cataloged it before, and will attempt to do so again, in current terms for current needs. Darkness, the original mystery, the beginning of everything, turns out to be inside the mind. The overall order and general laws which are the cosmos have finally been located inside the human brain.

IT IS BY MEANS OF THIS cosmological metaphor that Zorns Lemma signals its most fundamental and complex concern. Having posited the act of knowing as the ultimate measure of what is, the film leads us through increasingly complex kinds of knowledge. On the simplest level, verbal meaning is replaced by visual meaning as the alphabet turns into a set of images. It is significant that Frampton began as a man of letters, as he puts it, studying languages both living and dead while fancying himself a poet.3 Over a period of thirteen years in New York his interests evolved from verbal to visual modes. Zorns Lemma details that conversion in compacted time.

To begin with words, with language, is to begin with symbolic meaning. Language encapsulates experience in order to communicate it to another person or persons. In that process the experience is necessarily deformed. Its essential characteristic is distilled out, thereby discarding as residue the infinite variety surrounding that core. Nouns are to the things they name as notation to live music; they schematize their subject matter. The effect of symbolizing must be a diminishing of the object or person or event. It must involve as well an emotional distancing for both writer (or speaker) and audience from their own as well as from each other’s experience. Spoken language was the first step and written language the final one away from the immediacy of “real” experience.

Zorns Lemma thus begins with spoken language, progresses to written language (the relief alphabet in gilt letters) and arrives in Section II at the central problem, of linguistic (representing symbolic) versus visual (representing immediate) experience. The shots of words making up this section are hand-held, as many as possible containing movement of some sort. They strive for maximum variety of space, surface, texture, color, etc., almost all being drawn from the urban environment. There are, in fact, conscious references to painting, drawing, and photographic styles, perceptible only after extensive viewing of the film. We do not, however, need such references to perceive the tension between the richness and restlessness of the images, and the static, one-dimensional quality of the words. That tension arises from the juxtaposition of flat versus illusionistic graphic elements, and thus refers to only half the realm of possible visual experience, that is, to representation. Visual representation is a symbolic system like language, equivalent in function to words and to written language. The “actual” or “real” experience reflected by such a system is also available to us, and as Zorns Lemma wears on, we are increasingly offered the latter in place of the former.

The replacement images in Section II attempt to be “sculptural” or “tactile” by referring to experiential aspects of objects and events rather than to their appearances. In contrast to the word images they are almost all carefully framed tripod shots, deliberately banal in content, and share some quality, however oblique, with cinema.

Since the distinguishing characteristic of cinema has been earlier identified as having to do with the articulation of time, these replacement images must all in some way contribute to that process. Time and space in our experience are measured by movement of various sorts. In the film every replacement image but one (a single winter tree replacing the letter “F”) has movement of some kind. That may be directional, in depth, repetitive, or imposed by the camera. Additionally there is the development of convergent acts throughout Section II. Those are:

A—turning pages of a book
B—frying an egg
D—cutting cookies
G—hands washing themselves
H—a man walking one block and turning the corner
I/J—grinding hamburger
K—a man painting a wall white
M–three men digging a hole
N—dried beans filling the frame
P—hands tying shoes
T—changing a tire
U/V—peeling and eating a tangerine
X—a raging bonfire

In that we cannot know the outcome of these events and must “live through” them, they’re equivalent to “real” experience. Similarly we must “live through” the whole of Section II and discern its overall patterning to notice that it progresses (though not in a straight line) from big close-ups in the opening images to long shots in the final ones. A certain amount of work is required to get at the experience offered by the film as its “meaning” becomes less and less schematized and encoded within the symbolic systems of language or representation. We are being asked increasingly to process “raw data,” as we do from moment to moment all of our lives.

Since the film develops toward “reality,” Frampton decided to deliberately incorporate within it a number of kinds of errors. His reasoning was that misfortunes are bound to occur in any “ambitious” work of art which functions within time and itself requires much time to make.4 These included metric errors (12 shots in Section II are 23 or 25 frames long instead of 24), omissions (typed-out words, superimposed rather than “found” in the urban environment), errors (shots made as though the cinematographe; used the wrong color filter), lapses of taste (overt phoniness or artiness, like the hand unwriting “xylophone” backwards), faking (color collages pasted-up for backgrounds instead of images from the urban environment), and breaches of decorum (black and white still photographs with “real” objects lying on them, for instance a green toothbrush on “wig,” etc.).

To detect these errors is hard work and in so doing the viewer is forced to recognize all of the film’s organizing principles. That fact constitutes a kind of corollary to the basic epistemological position of Zorns Lemma, that knowledge is finally subjective and personal and possibly incommunicable. As some restraint upon the floodgates of subjective fantasy, we may recall that until we perceive the errors or lapses in a given situation we have not fully grasped its ground rules.

The final section of the film, predictably, approaches the limit between “cinema” and “real life.” Its spoken text is manipulated so that it functions only rhythmically, not symbolically. Simultaneously the long-held image of a snowy field, empty of symbolic content and barely illusionistic, comes as close to an experience of “real” space and “real” time as is possible on film. Finally even that image fades to a rectangle of white light, the minimum definition of cinema.

Zorns Lemma ends by thrusting us back upon ourselves. If knowledge is ultimately personal and incommunicable, we are left to contemplate the ineffable solitude of that conclusion.

Wanda Bershen



1. P. Adams Sitney, “Structural Cinema,” Film Culture, #47, Summer, 1969, pp. 1–10.

2. Hollis Frampton, from his unpublished notes on Zorns Lemma.

3. Ibid.

4. Ibid.