On Brown's Laws of Form

"Laws of Form" is the name of a calculus for logic in which we may see how it is that the generation of unchanging archetypes may be represented, and the notion of Time imagined. It operates through a series of injunctions, which, when performed, demonstrate the archetypes as consequences and theorems in the calculus.

An archetype is a constant pattern that appears no matter what state variables may take. In Laws of Form, Brown set out originally to investigate the arithmetic assumed to support Boolean algebra, an arithmetic that had never been written down before. An arithmetic, as Brown explains in the Esalen transcript (p. 40) considers constants by which an algebra may consider variables. Brown found that in the two-values Boolean algebra (on/off, yes/no, etc.), one either makes a distinction between states, in which case they are seen to differ in value, or one does not, in which case they are seen as equal, and may be confused. The act of distinction became the constant. (A distinction itself is not an archetype, since it is single, integral, has no parts to relate in a pattern. It does generate a pattern of two states and the boundary between them, a relationship reflected in the Christian Trinity, for example.)

An arithmetic demonstrates how its constants relate to each other. It is the relationship between distinctions, successive or simultaneous, that gives rise to the different archetypal patterns, which Brown calls "the eternal forms."

The value or beauty or fascination of the calculus lies not only in what one can do with it (yang, function), but in what it can be seen to be (yin, substance). Laws of Form is a self-referential model of the cosmos, like a Moebius strip. Since it is presented in written language, it may be read, and we may discover in it a great cyclical poem on the order of the religious 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, manifesting patterns as axioms, arithmetic, theorems, etc. Dante looks the other way, from diversity toward union with God, and sees the Eternal forms as angels and levels of Heaven. We can show how, formally, the structure of the calculus and the structure of Dante's Heaven are the same; and the calculus itself shows how and why this is so. "Laws of Form" formally bridges the world of science/logic and the world of religion/art. We can approach it from either side.

It is not a new notion to suggest that in experiencing a work of art, we allow ourselves to respond to its beauty, which is to say, the way in which it presents the vision. Of what constitutes "beauty," there have been a number of suggestions. "Truth," advanced by Keats, can be shown to be insufficient, though not actually wrong. Aquinas analyzed it in terms of "integritas, consonantia, claritas,” translated by Stephen Dedalus as "wholeness, harmony, radiance," and deriving from roots meaning "untouched" (therefore whole), "sounding together," and "called aloud." The invocation of the unity of the whole and its parts.

We see this unity in the light of two principles, exoteric and esoteric, the former operating by distinguishing what would otherwise be confused, and the latter by integrating that which is otherwise seen to be separate. Both processes transmit information. These principles appear in the calculus itself in the two axioms, the law of calling (exoteric) and the law of crossing (esoteric). Any interpretation of the principles, such as science/religion, male/female, comedy/tragedy, may be considered an algebra, a set of variations; the relation of the principle to the interpretation is shown in the calculus by the way in which the algebra, or study of variables, grows out of the arithmetic, or study of what is constant. Thus are consonantia and integritas satisfied. Claritas  appears in the calling of the names by which, out of necessity, the forms are invoked. This is the relation of mathematics to myth and magic, alluded to by Spencer Brown in Only Two Can Play This Game (p. 35); and it is the sense that underlies Joyce's description of God as "a voice in the street" (in Ulysses) and the concept of the Word made Flesh.

Laws of Form is then a map of Eternity, a curiosity, really, like the I Ching or the Tarot deck. Brown presents his model not as a private fancy, but as the record of a vision that has been reported by others and that is presumably the same for all humans, at least. The Trinity and the First Distinction become, in this view, metaphors for the same common, and so hidden, referent. The forms, being "eternal," manifest in just as many matrices as we choose to distinguish. The constant appears as the Form itself, the iconic likeness in which differences intersect. Brown writes about Dante's vision in the Commedia as though he were confirming a story in the morning paper. Yes, he says, "there is no doubt, in my mind, that Dante was privileged to be called to stand witness to the First Presence, and that his description, in the final canto, is a true account, in so far as any such accounts can be true, of his divine experience in respect of It." (Only Two, p. 107). And again, "When in my review of the Commedia I stated that I thought Dante's vision of God was genuine, this was not irresponsible guesswork on my part. It was the result of a careful checking of his account with the known holocosmic principles (ibid., p. 118). We are being told here that archetypal patterns exist and may be experienced directly. Dante himself supports this objective approach; we may take Beatrice's remark, in the first canto of the Paradiso, that

"All things, whatever their abode,
Have order among themselves; this Form it is
That makes the universe like unto God"

as the poet's initiation into the Laws of Form. Dante also concurs in the conception of the inward journey as toward a confusion of what the outward quest distinguishes. His vision, the one Brown validates, is described, in translation by Laurence Binyon, as

I beheld leaves within the unfathomed blaze
Into one volume bound by love, the same
That the universe holds scattered through its maze

Substance and accidents, and their modes became
As if together fused conflati, "blown together all in such wise
That what I speak of is one single flame

Verily, I think I saw with mine own eyes
The form that knits the whole world

(Paradiso, xxxiii, 85-92)

Similarly, Brown's statement (Laws of Form, p. 101) that "to experience the world clearly, we must abandon existence to truth, truth to indication, indication to form, and form to void," bears directly on the organization of the calculus into algebra, arithmetic, axioms, form (marked state) and void (unmarked state); and Brown is explicitly relating the notion of existence and the construction of an algebra, the notion of truth and the derivation of the arithmetic, etc.

The journey toward infinite distinction is a quest and a tragedy. The journey toward zero, the void, is a pilgrimage and a comedy. (That's why it's the Divine Comedy.) The search for the Grail was essentially a journey inward through existence, truth, indication, and form into the void; the etymology of "grail," which comes from a root meaning to mix," or "to confuse," reflects Dante's vision. We see in the form (distinction) the nexus of the meanings collapsed in it. In language we have the homonym and the pun; in number, the concept of cardinality. "Substance and accidents," which we may see as constants and variables, arithmetic and algebras, in "one single flame."

The knight who did win the Grail, Parsifal ("pierce-the-middle"), did so only when he proceeded with awareness. The first time he saw the Grail, not recognizing it, he lost it again. Brown's great achievement in Laws of Form is to show us how the whole journey may be traced, from an original intention to cross or create a boundary. Using injunctive language, which joins ("injunction", has the same root as “yoga,” Indo-Europea “yeug,” to join) we create any cosmos we please--taking care that our commands do not conflict, and confuse what they intend to distinguish. Brown has written, in Laws of Form, a system of proven consistency (theorems 3, 4) and completeness (theorem 17); and he has done it so precisely and elegantly that the form the calculus. describes may be seen in the form of the calculus itself. We may then suspect that T. S. Eliot had someone like Brown in mind when he wrote:

...to apprehend
The point of intersection. of the timeless
With time, is an occupation for the saint--
No occupation either, but something given
And taken, in a lifetime's death in love,
Ardour and selflessness and self-surrender.
     (The Dry Salvages)

Saint or not, Brown is clearly a major poet in Laws of Form. His comments on the calculus, in the form of the Esalen transcript, relating the calculus to science, religion, and culture generally, in a manner that manages to be precise, profound, witty, and at times hilariously funny, are a rare treasure themselves, and a key to the treasure of the calculus. That is why we devote time and effort to provide a setting for publication of the transcript.

Clifford Barney
Kurt von Meier

Here are links to the AUM Conference transcripts and an introduction to them by Kurt and Clifford

Introduction to the transcripts
Session One
Session Two
Session Three
Session Four