Laws of Form
An experimental course Art 296 for the Spring Semester, 1975
by/through Kurt von Meier, Ph. D.
Department of Art
California State University, Sacramento
Adamantine Research Community
Diamond Sufi Ranch, Oakville, CA 94562
November 10, 1974
What are "Laws of Form?"
Laws of form govern how parts of a system relate. "Laws of Form" is a calculus expressing this relation symbolically. It is a Glass Bead Game.
What is Meant by "Form?"
The root of the word means "sparkle" or "gleam." It came to mean "outward appearance," "shape," or "beauty," and it turns up in Greek in the name of Morpheus, god of dreams. The form is what we imagine to be the structure of "content," which, in turn, is what we imagine to be contained in the form.
The university distinguishes the forms of teachers-students-administrators, courses of study, departments, classes, examinations, etc. English, biology, mathematics are examples of the content studied. When we attend to the form, we see how English and biology are representations of the same energy.
The calculus, "Laws of Form," unites the two orders as both form and content of this course. ("The key to the treasure is the treasure"--John Barth, Chimera.)
Our hypothesis is that "Laws of Form" is a useful tool for integrating academic disciplines. The calculus is the mathematics of form. (It is non-numerical--no messy numbers to add up wrong.) It may be applied in any discipline, since it is the unifying principle behind the various disciplines. It transcends the form of many distinctions by taking distinction itself as the form. This is one way to recombine the multiversity into a university.
If the biology student sees this course in terms of cells, nuclei, DNA, RNA, he can give the rest of us a window into biology through the calculus. The English student operates with nouns, verbs, syntax, rhyme, myth, the painter with color, and so forth. The mathematician works with the form itself. The course is structured so that the student continues to explore his own field of interest as he explores the calculus.
A frequent question arises in the mind of the hyperprogrammed student as academic pharmakos: "What will be expected of me should I enroll in this course?" The strategic alternative for an experimental course is to suspend expectations, on both sides. "Teachers" and "learners" enter a complementary process. (Cf. German Lehrer = teacher.) We can, however, offer a structural model to those who might wish to join in a cooperative exploration of the laws of form.
Twenty-eight (28) MEETINGS organized into four sections of seven meetings each. The course assumes paleolithic, lunar, female rhythms. The form is yin, receptive to yang energy brought to it by teachers and students.
Reference is made to the preliminary abstract Neurolinguistic Information Processing, Christopher Wells, Institute for Information Systems, University of California at San Diego. Data in each quadrant (section) of the course will be presented in accordance with its corresponding "grammar" in wells's Process Architecture.
A grammar is an analysis of structure--for example, the structure of language. Wells describes four orders of grammar, in which fields are structured according to guiding principles ("metagrammars"), iconic projections ("web" grammars), symbolic representations ("tree" grammars), or matrices ("array" grammars). The rules of chess are the metagrammar of chess. The iconic aspect of the game is the pieces on the board. These may be symbolically represented by the notation for a game. As each piece moves on the checkerboard matrix, it changes the message of the total array.
THE FIRST SEVEN MEETINGS introduce the calculus of indications presented by G. Spencer Brown. Material for this section derives mainly from Brown, and consists of the basic text, Laws of Form (Julian Press, New York, 1971, $9.00 hardbound edition required), plus:
Only Two Can Play This Game, published by Brown under the name of James Keys;
Probability and Scientific Inference, early Brown text on scientific induction;
Transcripts of Brown's remarks during Spring 1973 Esalen conference on "Laws of Form" organized by John Lilly and Alan Watts and attended by Prof. von Meier;
"Who Is G. Spencer Brown and Where Is That Marvelous Music Coming From," W. Barney, Pacific Sun, September 6-12, 1973 (report on Esalen conference);
Tapes of other contributors to the conference (Heinz von Foerster, Ram Dass, Karl Pribram).
This section is structured by a metagrammar, which maps the other three grammars onto each other. The mathematical mode is arithmetic.
THE SECOND SECTION of the course concerns itself with iconic expressions of form, and is structured by a web (or net) grammar. An icon is a likeness. The net grammar maps images onto directed graphs, as a halftone screen maps shades of grey into black dots and white dots. The grammar reflects the aspect of form that can be caught in a net.
The function of this grammar is perceptual, and its locus is in the right cortical hemisphere of the brain. Its mathematical mode is geometry.
The Tarot deck, I Ching hexagrams, Chinese characters, letters of the alphabet, flags, business logos, crosses, calendar stones, mandala, and yantras exemplify the kind of material we will focus on during this quarter. It may be imagined that these examples reflect our own current interests. Students are encouraged to discover and offer resonant iconic examples from their own fields.
IN THE THIRD SECTION we depart from the form a second time, into a third order, and consider symbolic representations of form. Where in the second quarter we considered likenesses of form, we may now make a description of a likeness. The icon expresses form as unity; when we analyze it, we have to present our analysis in some order. The vehicle is a tree grammar, which maps (iconic descriptions) onto hierarchical directed graphs or (symbolic descriptions). The branches of the tree determine the relationship of the parts; the tree is a hierarchy, the net is a heterarchy.
Locus of this cognitive/symbolic activity is the left cortical hemisphere. The mathematical mode is algebra.
Typical material for section 3:
Literature: Blake, America, Milton, The Marriage of Heaven and Hell, Songs of Innocence and of Experience; Joyce, Finnegans Wake; Pound, Cantos; Arthurian legends, Dante's Paradiso and the distinction between quests and pilgrimages, Tibetan sutras (Heart, Vajra, Maha-Ati), Taoist and Confucian texts: Chuang Tsu, I Ching.
Mathematics: Mathematics of the I Ching, arrangements of Earlier Heaven (0-63) and of Later Heaven (1-64); Leibniz and the binomial theorem; the calculus interpreted for logic.
"Science": Stonehenge as computer, astronomy and astrology, scientific method.
Language: Use of American Heritage Dictionary; injunctive and descriptive language (regeneration of the icon through injunctive language).
Sex: Relation of space and time, as expressed in yin and yang energies.
IN THE FOURTH SECTION we enter the imaginary state in which the students present their own work as a formal order of feedback to the instructors, thus effecting a figure/ground reversal as teachers and students inter‑change roles.
The information processing model is Wells's array grammar; these grammars map matrices of point terminals onto transformed matrices or images. Brain locus is posterior sensory/motor cortex. Mathematical mode is calculus.
The students themselves constitute an array, a matrix (root = mother) similar to the lights on the Astrodome scoreboard. Each student is a terminal for data received; classwork reflects the transformation of that data into a new image from which we can derive the metagrammar for the next trip around. This is the result of our experiment.
Feedback may be of two types, "positive" or "negative"; that is, the output may be fed directly to the input, or it may be fed back with the sign changed. In the first case, a circuit remembers; in the second, it oscillates. These two possibilities are manifested in a final exam (memory) and a special term project (oscillation); the student may choose which type of feedback he wishes to provide, or he may do both.
Though the course is presented serially in four sections, form and content for all four sections taken together can be represented as nesting inside one another like seven Chinese boxes, with the outside box, laws of form, being contained in the innermost, "Laws of Form" (Cf. Einstein's curved space). The model for this mapping is consequence 7 of the calculus, named "Echelon" (step). The model may also be seen in the musical octave, which is divided into seven steps and finally reenters itself at a higher level.
"At this point, before we have gone so far as to forget it, we may return to what it is we are deliberating." (Laws of Form, p. 68)
We are, and have been all along, deliberating the form of an experimental course to be presented in the spring semester, 1975, to graduate students and advanced undergraduates at the California State University, Sacramento, through Kurt von Meier, Ph.D., Professor of Art. The matter of this form is elsewhere expressed in the sources cited in the bibliography, which follows.
Books by G. Spencer Brown: Laws of Form, Julian Press, 1972; Only Two Can Play This Game, Julian Press, 1972 (Published as by James Keys); Probability and Scientific Inference, Longmans Green, 1957; Twenty-three Degrees of Paradise, Annie,
"Other Books" is the title of a section beginning on page 87 of Only Two Can Play This Game, in which twenty books are introduced to the reader, with critical commentaries. Brown (as Keys) writes:
"You may look at the world any way you please, through any window you choose. Nor does it always have to be the same window. Naturally how the world appears, what you see and what you miss, and the angle on what you see, depends on which window you are using, but how can a window be right or wrong? A window is a window. I elaborate on what can be seen through various windows, not to say that you should look through them, more to point out that there are other windows that sane, sensible, responsible amiable, and otherwise normal people can and do look through, and it is perfectly OK to try another window if what you see through yours seems meaningless or inadequate...The number of different windows is endless. The unbridled conceit of the western nexus is to say that only certain windows are 'sound,' and that others are wrong, misleading, hallucinatory, etc." (p. 98-99)
Carlos Castaneda describes the window as the "crack between two worlds." The relationship between male "tonal" and female "nagual" in his fourth book, Tales of Power, Simon and Shuster, 1974, suggests that one passes through the window, like Alice through the looking glass. Castaneda presents the crossing as a "real" experience, Lewis Carroll as a fantasy. Most of the books cited below, Dante's Paradiso, for instance, are reports from the other side of the window. Others are descriptions of what can be seen without actually crossing.
We list Brown's score as a frame for other books which may be used as source material for the course. (One of the most important documents, for us, which Brown does not consider is the Constitution of the United States of America. Brown is British, and the British Constitution is in the unmarked state.)
A. H. Chapman, Put-offs and Come-ons, Putnam
Students may be more familiar with Eric Berne, Games People Play; the Journal of Transpersonal Psychology.
Allan Watts, This is It, Pantheon
The numerous publications of Watts provide a rich personal frame of reference for the bridge between East and West. Watts was one of the co-sponsors of Brown's visit to America.
Khalil Gibran, The Prophet, Knopf.
Taste may lead one rather to Jorge Luis Borges, Franz Kafka or James Thurber as fabulists. But for the 'one-level' of writing we prefer Sufi stories in the tradition of Mullah Nasir al-Din as collected by Idris Shah. And in our own tradition we have Mother Goose.
Shelly, A Defense of Poetry
For general concern with the fine arts, Oscar Wilde, "The Critic as Artist" and The Importance of Being Earnest, which is very much more than being a mere pun, as Brown's taped comments on "importance" assures us.
Paul Foster Case, The Tarot, Macoy
We are aware of the current wave of occult interests particularly among members of the western counter-culture. Victorian exhuberance notwithstanding, Aliester Crowley's approach to the tarot deserves examination by art historians in the context of Pre-Raphaelitism, also with its socialist and Symbolist ramifications (Arts and Crafts Movement, Order of the Golden Dawn). The Tarot tradition extends to or parallels that of the Qabala (Kabbalah): a systematic relationship of letters of a written alphabet to numerical values. These values were historically first determined by "chance" (oracles, divination, especially of Hermes--the 'angel' or messenger-- who is credited with the invention of dice). Associated imagery was created by Mantegna, Durer, and may be discovered through out medieval culture, especially in the forms of popular arts.
Wu Ch'eng En, Monkey, Grove
This is Arthur Waley's translation, a Chinese folk novel belonging to a category of Oriental literature called "monster stories". In our own cultural frame of reference we may discover parallels in the genres of comic books, drive-in movies and late night television. Waley's translations also provide access to Taoist and Zen writings, and to the literature of less well-known cultures: The Secret History of the Mongols, and The Nine Songs: a study of shamanism in ancient China. The Complete Grimm's Fairy Tales, published by Pantheon provides some depth also through philological investigation.
C. G. Jung, Answer to Job
We use the Bollingen edition of Jung's Collected Works.
R. D. Laing, The Politics of Experience, Penguin
G. Spencer Brown has worked with Laing as a psychotherapist. Laing's works include: The Divided Self, Knots, Self and Others. Among recent publications in the area: Fritz Perls, Ego, Hunger and Aggression, Gestalt Therapy Verbatim; Thomas Szasz, Ceremonial Chemistry, The Myth of Mental Illness; Norman 0. Brown, Closing Time, Love's Body; Art Kleps, The Boo-Hoo Bible,
D. H. Lawrence, Fantasies of the Unconscious, Viking
"The theme is that one's deep unconscious is not, as Freud made out, a mere cesspool of unacceptable memories and repressed desires, but rather (as Jung later began to discover, the very life-spring of one's corporate being and reality."
In different styles, all the great works of a culture present the great truths, which are known to be simple. St. John of the Cross, The Ascent of Mount Carmel, also presents states of the soul with mathematical precision. Ezra Pound drew attention to this tradition with Cavalcanti and the troubadors preceding Dante; his own Cantos are of rather a different sort again, yet of such substance as to encourage analysis mindful of the laws of form. In addition, Joyce, Eliot, and Yeats; and Joseph Campbell's Skeleton Key to Finnegan's Wake. Shakespeare is interlaced with precise logic and good grammar, as well as poetic sentiment and dramatic expression. English and American literature is wealthy with mirror imagery and "yin/yang" sensibility: Marlowe, Milton, Bunyan, Blake, Melville, Chaucer and the Arthurian romances.
John Jocelyn, Meditations on the Signs of the Zodiac, Naylor
As Brown writes, "this is not a book about astrology...but about the deeper meaning of the twelve signs...divinity...humanity...it mentions the total love experience." Avon publishes a fine series, "Art and Cosmos," with well-illustrated short volumes on Astrology, Alchemy, Tantra, The Magic Spiral, Sacred Dance and Tao.
Beethoven, Piano Sonatas 28, 39, 31
Exemplifying Beethoven's infrequent use of the fugue, these intense, late sonatas were written when the composer was deaf. His earlier German dances are binary, or "Boolean" in form, as are many of the hundreds of harpsichord sonatas by the 18th century Neapolitan, Domenico Scarlatti. Recent 20th century musicians have greatly expanded our musical "formal" languages; John Cage, Notations, Something Else Press; works by Karl-Heinz Stockhausen, Pierre Boulez, Morton Feldman, La Monte Young, Jerry Garcia, John Lennon.
The Gospel According to Thomas
The secret sayings of Jesus of Nazareth, giving "an exact recipe, in fact, (for) what you actually have to do to enter eternity." The translation published by Collins is suggested.
Tao Te Ching
An edition by Dr. John C.H. Wu presents Chinese and English texts en face, published by St. John's University Press, New York. A new translation by Gia-Fu Feng and Joan English is published by Vintage Books; by the same translators also, Chuang Tsu, Inner Chapters. Richard Wilhelm, translator, The Secret of the Golden Flower.
Robert Graves, The White Goddess, Noonday
This Sufi scholar's appraoch to poetics may be augmented by R.B. Onions, The Origins of European Thought, Cambridge, 1954; and the AmericanHeritage Dictionary with its invaluable key to proto-IndoEuropean roots and word grouping.
Dionysius the Areopagite, The Divine Names, translated by C.E. Rolt, Macmillan.
Brown calls Rolt's Introduction "spectacular...without which I find the text almost unreadable." We may note Carlos Suraez, The Cipher of Genesis, Song of Songs, Shambala. Then Brown lists his own book, Laws of Form (as No. 17).
The Graphic Works of M. C. Escher, Meredith Press, New York.
We do not propose, here, to enter even a token bibliography for the visual arts. However, we observe that sometimes the greatest of graphic or plastic artists have also expressed themselves most eloquently in writing. For Michelangelo, Paul Klee, van Gogh, William Blake and Marcel Duchamp there are substantial bibliographies, frequently facsimile editions, and of course full treatment from the traditional, kunstwissenschaftliche approach. New expressive media generate instructive manifestations of the laws of form, for example Sergei Eisenstein, The Film Form and The Film Sense, Grove Press.
The Tibetan Book of the Dead
With the proclamation of the Dharma in the west in this, the year of the Male Wood Tiger (1975) by the Sixteenth Gwalya Karmapa, the spiritual head of the Kagyud Order of Tibetan Buddhism, we now receive an admirable opportunity to participate in extensive cooperative projects of translation. Our way has been prepared by the translations of the late W.Y. Evans-Wentz. Currently the activities under direction of Chögyam Trungpa, Rinpoche, and Tarthang Tulku, Rinpoche, are of consequence. Native to North America is the lineal, oral, "esoteric" traditional teaching of the Hopi Nation so harmonious with the Tibetan way. We may discover somewhere in the laws of form precisely that conceptual focus which enables us and the forthcoming cultural generation to embrace the wisdom of these traditions with dignity and clarity.
New translations of Tibetan classics by Herbert V. Guenther, such as: sGam.Po.Pa., The Jewel Ornament of Liberation; The Royal Song of Saraha; The Life of Milarepa; and The Teachings of Naropa, are excellent and apt. The Heart Sutra and The Diamond Sutra provide illuminating correspondences with Laws of Form. For guidance, The Opening of the Wisdom Eye by His Holiness Tenzin Gyatsho, the XIVth Dalai Lama.
The I Ching, tr. Wilhelm and Baynes, Princeton
We find this the most useful translation, along with the younger Wilhelm's analytical essays. Also, Z.D. Sung, The Symbols of the Yi King, Ch'eng Wen, Taipei, provides stimulating mathematical interpretations.
By way of "re-entering the form" we conclude With the mention of some few additional references in which the authors, from their respective approaches, provide access to the sense of the laws of form.
L.E. Dickson, Theory of Numbers (3 vols.), Chelsea.
D'Arcy Thompson, On Growth and Form, Cambridge
Warren S. McCulloch, Embodiments of Mind, MIT.
Thomas S. Kuhn, The Structure of Scientific Revolutions, Chicago.
Berlin and Kay, Basic Color Terms, University of California.
Robert E. Ornstein, The Psychology of Consciousness, Freeman.
John Lilly, Programming and Metaprogramming the Human Biocomputer, Portola Inst.; Mind of the Dolphin.
Charles Muses and A.R. Young, Consciousness and Reality.