The Root of Omasters: Laws of Form:
Any systematic study of whole systems must by definition be self-referential, and the study thus reflects or represents that which it analyzes. Much scientific investigation, however, has been undertaken as if the scientist were separate from his field of investigation. Godel's Theorem in mathematics and the uncertainty principle in physics have shown the limit of this approach, and have led to increased interest in the nature of self-referential, or feedback, systems (which previously had been barred from formal analysis on the authority of the Russell/Whitehead Theory of Types). Not until G. Spencer Brown undertook to find the constant arithmetical aspects of an algebra designed for a particular system of variables, formal logic, and codified his findings in Laws of Form (Julian Press, 1072) did a model for self-referential systems exist. Laws of Form enjoys something of an underground vogue as a powerful poetic vision. It is also considered mysterious, opaque, and impractical. It is a purpose of our book to show how, by examining the structure of Spencer Brown's calculus, which is to say its language and symbols and/formal relations of its parts, we may, by uncovering the form of the form, see and intuit the relation of form to content and the way in which all systems reflect themselves in each other.
We are aided in this discussion by a 121-page transcript of remarks by G. Spencer Brown in which he describes Laws of Form as a mathematical representation of the "eternal" realms described elsewhere by poets and religious visionaries. This is startling news from a 20th Century mathematician, and yet we can see its precursors in the archetypal forms represented in mythology and rediscovered for moderns by Jung and his colleagues. Archetypes are constant patterns that emerge from variable systems. The linear contribution of Laws of Form is to demonstrate how archetypal patterns are generated; this process has not been shown before. Beyond that, however, the calculus may be read as a great cyclical religious poem on the order of regeneration myths, the Divine Comedy, or Finnegans Wake. In the calculus, Brown indicates the void at the center and works outward through the form of distinction; the relationship of successive distinctions gives rise to the different archetypal patterns, which Brown calls "the Eternal forms," and which manifest as axioms, arithmetic, theorems, consequences, etc. Dante, in contrast, looks inward from diversity toward union with God, and sees the Eternal forms as angels and levels of Heaven. We can show how, formally, these structures are the same.
Since the calculus proves, mathematically, its own completeness and consistency, it is a bridge from the world of logic, mathematics, and science to the world of art and religion, which have often imagined themselves to be opposed, or at least separate. The practical value of such a bridge, long sought after as a link between the finite and the infinite, is obvious. In seeing how their work manifests a universal vision, investigators in a particular discipline can tap the strength of that vision. However it is a peculiarity of this bridge that to cross it we must also understand it, that is, "stand under" it, and we cannot understand it without crossing it; and so in fact we must build the bridge as we go along. The process of building this bridge is the theme of our book.
Since what is eternal is timeless and changeless, we cannot act upon it, but only contemplate its beauty, which is the source of its strength. Aquinas suggests that the quality of beauty requires "integritas, consonantia, claritas," which is translated by Joyce as "wholeness, harmony, radiance." The Latin words derive from roots meaning "untouched" (therefore whole), "sounding together," and "called aloud"; the invocation of the unity of the whole and its parts. We invoke this unity in an essay on the Laws of Form, in the light of two principles, exoteric and esoteric, by which information may be seen to be transmitted--the former operating in the mode of distinguishing that which could otherwise be confused, and the latter in the mode of integrating that which is otherwise seen to be separate. We see the diversity of these traditions in as many different matrices as we choose to distinguish: science/ religion, male/female, comedy/tragedy, etc. Any of these interpretations may be considered an algebra, a set of variations, which may be related to what is constant, or archetypal, just as Spencer Brown shows how the algebra, or study of variables, in Laws of Form grows out of the arithmetic, or study of what is constant. Thus are consonantia and integritas satisfied. Claritas lies in the calling of the names by which, out of necessity, the forms are imagined to appear.
Essentially, the essay is a breadth-first search of areas mapped individually by depth-first disciplines. To Place Laws of Form in the context of its own discipline, we will include in the book a chapter by a professional mathematician. And to demonstrate other responses to the calculus, we can present transcripts of remarks by other participants at the Esalen AUM conference that produced Brown's comments.
Following Whitehead's postulate that the first aim of education is to delight (the discipline then following naturally), we recognize that whatever the practical value of the book we propose, it is to be written and read for the joy of it. By contemplating the a beauty of the principles it embodies, we can come to feel the power of the calculus, which may be experienced before one undertakes to learn the mathematics. The value of the calculus is then limited only by the imagination of the reader.
[The Introduction to the AUM Conference Transcripts further elucidates the link between Laws of Form and Omasters]
I. Introduction. 20-25 pp.
Announcement of the intent of the book: to show how archetypal forms are generated, and how we may see in these forms the marriage of the elements of duality variously represented as yang and yin, male/female, science/religion, logic/art, etc. Presentation of the paradigm to be investigated, Laws of Form, with exposition of its general principles and definition of terms. Some historical and biographical material on G. Spencer Brown, the authors of the present book, and how the book came to be written.
II. Conference and transcript. 150-200 pp.
Brief description of the AUM conference convened by John Lilly and Alan Watts, at Esalen, March 18-25, 1973, and of who was present. Transcript of Brown's remarks, fully annotated. Precise, profound; and most elegant in its argument, the text shows Brown's polished wit in a discussion of the formal relationships of science and culture,
III. Commentary. 100-150 DD.
An essay on Laws of Form, analyzing its structure, language, and symbols to show how the calculus integrates dualities by being that which it distinguishes. With Brown's transcript as a point of departure, we explore other aspects of form in the areas of:
- Logic and mathematics (number theory, group theory, algebra)
- Exact sciences (wave and particle physics, astronomy, neurophysiology)
- Psychology (Jungian analysis, Gestalt therapy)
- Religion (Vajrayana Buddhism, the early Celtic Christian esoteric tradition and its suppression at the Synod Of Whitby)
- Literature and the arts (Dante's Commedia, the Grail legends, Ezra Pound, Marcel Duchamp, the Dada movement, pop art)
- Myth and folklore (the labyrinth, early astronomy, Celtic legends, fairy tales, Greek and Eastern mythology)
- Language (nature of injunctive and descriptive language and the exoteric and esoteric traditions' relation of roots and meaning.
- Cosmology (Brown's five-layered model of Eternity)
- Synchronicity (The I Ching, the Tarot deck)
- Government & politics (The Constitution of the United States, the history of freemasonry)
- Cognitive structures (cybernetics, process architecture)
IV. Other Views. 50-100 pp.
Annotated Transcripts of remarks by other participants at the AUM conference. Karl Pribram, professor of neurophysiology at Stanford, on how the brain generates models from sensory data. Heinz von Foerster, cyberneticist, on cognitive processing. John Lilly on simula and belief systems.
V. LOF and mathematics. 50 pp.
Contribution from a professional mathematician placing Laws of Form in the context of its own discipline.
VI. Bibliography. 50 pp.
A descriptive listing of some 200 books that we have found useful, together with a discussion of how it is that they constitute a reference net.