The Eternal Present and the Forty-Eight Laws of Cosmic Objectivity
Suppose we were going to write a book and to call its title by the same name as that already used by another author for his book. Let us call our book THE ETERNAL PRESENT: THE BEGINNINGS OF ARCHITECTURE with the subtitle: A Contribution on Constancy and Change. That is the title of S. Giedion's Bollingen Series XXXV . 6 . II, published in 1964 but delivered as the A.W. Mellon Lectures at Harvard in 1957. No matter. Russell and Whitehead wrote the Principia Mathematica using Sir Isaac Newton's title from a much earlier and far greater book. The Giedion book nowhere reveals the mathematical justifications for concepts of space and time, no more than does his earlier and widely popular book, Space, Time and Architecture. However, more is known now than when these books were written.
Since Brown's Laws of Form, we have a published illustration of a notational system which maps with great precision and mathematical rigor the domain of the Eternal realms. The number of necessary crossings, counting from the "void," can be counted. We see that the first order of time comes into being at the fifth crossing, at a level of complexity other wise described as a Boolean algebra (such as that of switching logic or any other binary system is an illustration) of the second order, or an algebra containing an imaginary value and self-referential equations, such as an oscillation is now recognized to be. The oscillation, or change of value of states, appears in the first order algebra only as a variable with respect to the deeper, prior arithmetical constants. The necessities come from the constants, the invention born of them come from the world of variables; change we notice from the outside. Look deeper within and there is Unity in Eternity, fewer and fewer distinctions, until at the origin, there is utter confusion: any Unity is equal to (is confused with) any other way to see the Unity, and "then," the primordial distinction between the Unity and the Void dissolves. This is the content of the Heart Sutra, and of Laws of Form. It is also illustrated in the principle of Trialectics, and in the mystery of the Blessed Trinity.
The roots of the Void are three. The Holy Ghost (the inside edge of the first line tokening the first distinction), the Father (the first line), and the Son (the outside edge of the first line). This is also the subject matter of the Jordan Curve Theorem.
The Void =
The Form = ᒣ, or any other token of a mark, such as: 0.
Axioms = ᒣᒣ = ᒣ.
Arithmetic = The set of complete and consistent rules governing formal relationships of marked and unmarked states, expressable as constants.
Algebra = Introduction of a variable function for the constants of the arithmetic.
Second order Algebra = Introduction of variables that refer to the equation itself, creating an oscillation of the whole.
What it was before, it is not. What it is it isn't and what it isn't, it is. And as Chogyam Trungpa, Rinpoche said, there isn't any "it."
It is architecture, understanding the organizing principles of space. Emergence of a systems architecture; structure and function, product and process, noun and verb. The verb, the ordinal, the first, the action or Karma, the calling of the name; then the name.
The word "history" comes from a root related to the word "tissue." It is concerned with connectedness, and is analogous to anatomy. The word "evolution" in its current modern sense (as illustrated by the Scientific American 1978 issue of the idea of Evolution in the sciences) carries with it continuity of some wholistic quality. James Joyce makes the distinction in German, Nebeneinander and Nacheinander--side by side when the whole evolves, one after another as in the lineal flow of time when events in history connect like cells in tissue. If art and architecture have eternal qualities, it is surely these, the constants, the root, intrinsic sense of what art and architecture mean.
Art comes from a Proto-Indoeuropean root ar, with cognates in HARMONY, ORDER, ARMY, and with the sense of linking up, yoking, joining to make whole. Art is what makes it whole, closure in the Theory of Groups--Russell and Whitehead's forbidden but essential self-reference. The work of art is whole as man sees himself whole, and a part of the whole as man is a part of the whole; but, a part that is capable of perceiving or imagining no distinction between the part and the whole, hence capable of imagining at one with the whole, voiding any sense of separateness or distinction, and hence capable of imagining the Void. This has long been thought a capacity of consciousness limited to human beings—although in primitive form it can be demonstrated in a system as simple as a hard-wired electrical circuit--say one such as that illustrated on the paperback edition of Laws of Form on the cover. You can't always tell a book by its cover, but sometimes we can. It depends upon the author and his injunctions to the printer. It depends, in a practical sense, upon the publisher. In Tibet, volumes of gTerma, or sacred writings revealed to the Guru, Padmasambhava, and rediscovered by Tertons, or incarnations of certain aspects of the Guru, are published on yellow paper. Of course, any publisher can put any cover he wants on any book, all well within the First Amendment provisions respecting rights of Freedom of Speech and Expression.
In the emergence of a process architecture, we study the intrinsic sense of the principal word. ARCHITECTURE is composed of two Proto-Indoeuropean roots, arkw from which the arc, arch, and the bow and arrow, both the arc of the bow and the arrow itself, and the two of them together as a unit; and teks from which we see the texture derived from making baskets, weaving textiles. Architecture appears in conventional histories when the division of labor of hunters and gatherers, the male bow and arrow hunters (with technology developed rather late in the paleolithic) come together with the female gatherers of firewood, plants, grasses with which to weave baskets for gathering. In the first settled communities architecture appears. From the tradition of windbreaks for fire, shelter from rain, and thornbush kraals for protection from beasts of the wild, when humanity realized equality with all that lives (and in particular, through technology, had achieved a standoff with great beasts), the intrinsic elements of architecture are demonstrated by the objective record of material manifestation as interpreted by the science of archaeology.
Architecture is a social art, as is the ritual dance. The society may be of stars and other celestial bodies, or of life on earth, or of the cells within one's own body--in the ancient way of cosmologies (macro-, meso- or mero-, and micro-). An ordinary citizen understands architecture as being built of sticks and stones, or bricks and bones, possibly. Historians see the form of the first public monumental architecture evolving from that of the house. The house Above, as it were, the abode of God or the gods, like the great night sky and that of sun-bright day, becomes the inspiration for the temple. Each Hopi kiva is also an astronomical observatory.
The architecture of memory is the model for imaginary architecture within. In its most elegant and precise form, this "house of the mind" is like a pyramid; just like a pyramid, but without the stones, just the essential form of the pyramid, the psychic space. The clearer this internal vision, the more it is the same for all human beings. Dante saw it; so did William Blake and Dionysius the Areopagite, and the Egyptian architects following Sen Mut, who designed and built the Great Pyramid at Giza. The objective exercise has been published by Oscar Ichazo, and is illustrated in The Human Process for Enlightenment and Freedom, published by the Arica Institute.
Any person capable of reading, understanding and following injunctions can now practice the exercise of constructing this psychic space with the disciplined imagination. Although this is a very ancient exercise, traditionally it has been a part of the esoteric teaching, distinguished from the exoteric tradition that concerns itself with outward manifestations rather than with the interior imagination. Therefore, published indications for performing the exercise, if any, have appeared in symbolic guise, as in the literature of Western alchemy.
The scholar Frances Yates documents the tradition surrounding Giordano Bruno's Art of Memory. The central feature of Bruno's mnemonic method involves the imaginary construction of a house--the art of memory then being practiced by placing that which is to be remembered in this or that part of the imaginary house. The technique probably worked better when a person might live in the same house for an entire lifetime. If high social mobility and the experience of living in many different houses complicates our interior imaginary house, however, it also adds to possibilities of richness. Remembering all the houses in which we have lived, we know more of the many ways a house may be. But for all of us there is an essential form of house. Current research in the emergence of process neuro-architecture promises to articulate reasons why this imaginary space appears as it does — obviously, since we all have fronts and backs, right hand sides and left hand sides, with heads on top and the base of the spine below, legs and feet touching the earth toward the center of the strongest local gravitational field.
Our space has three dimensional axes, six vectors. This is exactly how it is characterized by Hopi tradition: And there are six different colors of corn, one for each direction: north, east, south, west, up and down. Other systems add the dimensions or directions of inside and outside which we have already introduced. Inside the Gates of Eden, all distinctions of formal spaces exist (if that be the proper verb-perhaps we should say "insist") simultaneously at the same time, which is to say at No-time, because there is not yet enough complexity in the formal nature of Eternity for time to be counted. Strictly considered, we should not even imagine these deep eternal spaces to be any more than analogies with the "dimensions" and "vector fields" of an architecture of sticks and stones, or of the world with one horizon over which the sun appears to rise and another over which it appears to set. They do not yet have the qualities of our conventional four-dimensional space/time continuum. Yet the physical structure of the human brain (and perhaps also of the cetacean and other higher mammals) permits an order of complexity in processing information that enables us to imagine such simple spaces with clarity and precision.
The Enlightenment and its children among the Western sciences demonstrate a profound bias toward right-handedness in the domain that could be described as working with duality. In Islam, where the affirmation of the Unity is essential, in the language of Al Qur’an, the sacred scripture revealed to the Prophet Muhammad, May Peace be upon His Name! in the Arabic language, the formation of plurals is fraught with subtleties and presents great difficulties for students of the language. And there is a special verb form for duals. In Western scientific belief we treat the world as though it were real and objective, "out there." The dichotomies of science and Western culture are justified at the level of Boolean algebra, and are illustrated by all systems based upon binary logic.
The Western sciences evolved until, within the several sciences, there arose the need for a deeper theoretical justification showing how it could be that a two-element system is based upon a system containing only one element, and showing the formal set of relationships between that one element and no elements, the void. G. Spencer Brown's text, Laws of Form provides instruction, showing one way in which these distinctions may be indicated. In the modern history of science there are many other rich stories about paradox, self-reference and the crisis of the so-called objective observer. Transcending the limitations of rigid dualism actually enabled a deeper perception of the abstract, formal spaces we have called Eternity. Historical consequences are seen in the flowering of cybernetics and the information sciences, quantum mechanics, art and architecture, psychology and the neurosciences.
If we imagine the Form to be equal to the Void, then that relationship, that equation, symbolized by the equal sign: =, is the form of distinction. This is a verb, a process, in which the equal sign functions as though it were a little bridge, linking both sides of the equation as it distinguishes them--a bridge crossing over the imaginary line of distinction. By articulating this process, we hope to remember what it is we are doing, making imaginary distinctions, and so we hope to avoid believing deeply in one or another side of any distinctions we make. In particular, we transcend duality and the habit of mind characterized by dichotomies. Then it is a matter of seeing where it is we choose to draw a given set of distinctions, at what level of complexity. For example--an important example--we know that the set of natural numbers can be generated by a simpler binary logic; and since we know that binary logics are technically algebras, the natural numbers (and linear algebras and infinite series) are at the level of complexity of five crossings from the void. We cannot have an oscillation before we have a variable, and we must generate a wave train before we can count.
In several esoteric or mystical traditions the number forty-eight (48) is associated with the idea of cosmic law. From Gurdjieff and Ouspensky we get the idea that 48 represents cosmic structure such as would be true for any universe we can imagine, not just this one in which we imagine ourselves to be, that there is an order of objectivity deeper than and prior to the way in which individual human beings see themselves as separate organisms, with personalities, unique and hence only as parts of a whole system.
The Arica Institute develops a closely parallel symbolic numerical notation. First the idea of Unity is expressed by the number one (1), just as in the monotheistic religious traditions. And recapitulating a statement of the Mystery of the Trinity, the active Karmic or functional nature of this original Unity is represented, not by duality and the number two (2), but by the number three (3). So the sequence proceeds, counting from the Void: zero, one, three. Buddhist doctrine also contains this triple representation of the unity of creation in the principle of the Trikaya, or Three Bodies of the Buddha.
Mapping these esoteric and traditional expressions to the current belief system of science, we find cognates in preliminary assumptions for the calculus of indications, Laws of Form by G. Spencer Brown. He states these assumptions in the Introduction (p. xv): "I have assumed on the part of the reader no more than a knowledge of the English language, of counting, and of how numbers are represented." The English language is thus the principal form in which the content of the book is presented, and as such we understand it as a wholistic system. But Brown also uses and invents symbols in the more formal sense of a mathematical language. "A major aspect of the language of mathematics is the degree of its formality. Although it is true that we are concerned, in mathematics, to provide a shorthand for what is actually said, that is only half the story. What we aim to do, in addition, is to provide a more general form in which the ordinary language of experience is seen to rest." (p. xxiii). And, "The fact that, in a book, we have to use words and other symbols in an attempt to express what the use of words and symbols has hitherto obscured, tends to make demands of an extraordinary nature on both writer and reader...." (p. xxiv). "Some of the difficulties apparent 'in...the earlier part of the text (in which Brown details the construction of the Primary Arithmetic, the rigorous foundation upon which Boolean algebra, and formal logic as well as all switching systems and binary logics are seen to rest) "come from the fact that...we are extending the analysis through and beyond the point of simplicity where language ceases to act normally as a currency for communication." (p. xxiv).
It is because these primary assumptions are necessarily three in number that the esoteric tradition continues its count of the objective laws through a process of doubling, or some might say through reflexions of the Trinity. Thus we may construct a series of "harmonic" orders, which can be represented as:
1 "Void" The first order of being, the unnameable name of God, Zero, Ultimate Reality, THE Unity, etc.
3 The Trinity, the triune aspect of Unity, the three roots of the Void
6 The first perfect number, Atomic number of carbon, upon which all life is based
48 Cosmic law
96 The deepest level at which we may continuously experience the self, integrated and intact.
The system goes on to characterize "levels of consciousness characteristic of submission to the contrived and multiplied "laws" that we generate for ourselves as expressed by belief systems, psychological, social and legal, and imaginary (such as superstition and fear).
192 Death of the ego
"1500" Actually 1536, Leaders of society
"3000" Ordinary citizens, believers in the system
"6000" Masses, proletariat, governed by fears & desires
"12000” Psychotic, incapacitated
The higher the number, the more "laws" to which one submits. At level "96" and higher, we must deal with analysis of the ego or disintegrated personality of the individual human being, whether projected as fantasy or as social convention, no matter how it has assumed shape as belief, custom, postulate, logical proposition or work of art. At level "48" and below, we should be able to discover statements of "cosmic law," that are the same for all human beings, no matter which way the true statements are expressed--that is, irrespective of the system of notation. employed.
In our ordinary language of experience, all of us may, and many of us frequently do observe illustrations of the cosmic laws: in the self-aware operations of our own minds, in the expressions of art--music, architecture, theater, watching television, in meditation, or, through what has been called Divine Grace, at any time and in any way whatsoever. There are, of course, ways in which we characterize such experiences when we describe them to ourselves or to others--we use terms such as insight, inspiration, vision and imagination, creativity, flash, gleam, idea, and so forth. These words do share common attributes in the English and American language; linguistic analysis on the bases of the sound of the words, the lexical form of the words and their histories in relation to older word groups, the visual appearance of the ways in which the words are represented, and the subtle distinctions and over-lappings of semantic significance reveal the depth and importance of the concepts indicated. But such an analysis within the form of language is grounded upon the cultural function of language, depending upon the relative nature of spoken and written tongues, and thus upon the algebraic relation we know as translation. They indicate a content somewhat deeper than that on which language itself conventionally functions.
Human culture has, however, developed a special use of language in order to indicate formal properties of psychological and theoretical realities, distinguished from ordinary descriptive language. This is called the injunctive use of language. We make such a distinction when we decide the Convention of intention, introduced as such by G. Spencer Brown in his calculus of indications, Laws of Form (p.3), where it is presented as the First canon of the calculus.
Let the intent of a signal be limited to the use allowed to it.
Call this the convention of intention. In general, what is not allowed is forbidden.
We may, of course, and frequently do decide not to follow this convention. Then, we do not require that something (a rule, a principle, an assumption) be specifically acknowledged, indicated, allowed into the particular system in use in order to be able to use it. This other way characterizes descriptive language, which works precisely because of its associations--the associative function between that which has been acknowledged and that which has not been allowed into the system yet. It works just like an algebra with the introduction of variables. The intent of a signal (word) is not limited to the use (understanding, meaning) only previously allowed, otherwise poetry and literature would be spare indeed.
Whenever we want to give indications, however, we find that the clearest way to proceed is to state assumptions, then to articulate, in an orderly fashion, and as simply as possible, the steps to be followed. This step-wise function is characteristic of a demonstration of consequences in an algebra. It is, in fact, a key to the way in which we enter the eternal realm of mathematics, a way in which we use language to reenter an order of being in which there is no time. This is to say, we depart from a temporal consciousness, conditioned by the perceptual forms of material being, and the appearance of reality, and enter a deeper, prior, internal order of being or state of consciousness. Many find themselves imagining their being in the Eternal realm without necessarily intending to be there; this is the source of comedy and tragedy, depending upon whether one comes back again and all is well (whole, healthy), or whether one does not return--which is why the Quest is always eternal.
With injunctive language we must recognize and obey orders. Thus are the formal spaces ordered. As we cannot expect to climb a ladder choosing the rungs in any sequence we want, if we expect to follow any set of injunctions--mathematical proof, cookbook recipe, doctor's diet, or body of law--the only thing that counts is what is in the specific indications. This discreet self-reference is made in the U.S. Constitution, indicating the rights of citizens (and the limitation of law) by stating a converse principle, what is not forbidden by law is allowed. But within these rights the body of law, based upon the Constitution, proceeds injunctively: words are entered into the marked state which either specifically allow or forbid, and one's actions and their consequences cannot be judged under the law unless a law has already been allowed (legislation passed). That is why America calls itself a free country.
The most generally stated injunctions appear in mathematics, in which we characteristically concern ourselves with the deeper formal relationships of the universe, rather than with their transient appearances and coincidences. Therefore we should expect to find the forty-eight cosmic laws most deeply expressed in mathematical form. But this is merely a technical convenience, a convention, for truly the Unity may be perceived, known, in all of us and in everything. But it is not true that we can keep track of where we are in relation to the Void, or to the Unity, or to the Trinity, in all systems, as we may in systems such as mathematics that utilize injunctive language.
In chapter 1, on page 1, Brown begins (in the English language), "We take as given the idea of distinction and the idea of indication, and that we cannot make an indication without drawing a distinction." What we have here is another way to show the three assumptions, which may be understood as the first three of the forty-eight laws of cosmic objectivity. The first in order is that of the language in which itself and subsequent laws are to be expressed. In order to retain a sense of self-referential clarity, we might here modify that assumption to mean the American language. Then the idea of distinction, which is seen as a precise analog to what we know in ordinary communication as counting, although technically the system is not yet complex enough to enable us to count until we have constructed a Primary Algebra because counting involves the function of a variable, hence an algebra, while arithmetic concerns itself only with the formal relationships of constants. And then, as the third of our trinity of assumptions, that we understand "how numbers are represented," which is to say that numerals are indications of number, tokens of the mark by which we have counted.
We may count these as the first three of forty-eight laws, humbly recognizing that any way we choose to describe any such system depends upon these or similar assumptions, no matter how we may express them. This is always the case, whether the system is mathematics, language, religion and metaphysics, or psychology, provided the order of analysis is genuinely profound. In Buddhism, according to the Heart Sutra, the first order of being is the Void. From our way of looking at or imagining this, come the ideas of the world of Name and Form, with the Form (process, function or verb) intermediate between the (nameless) Void and the Name. In ordinary language (the assumed context which maps to the Void), we recognize verb and noun, the act of calling a name, then the name first called. There are always three elements, it being merely a relatively superficial logical or semantic paradox that one of these three elements (in order of being the First) is known as the Void, or the Nameless State, in which no distinctions have been made. In our conventional way of counting we symbolize this as zero; the act of counting, or of "calling names" as the drawing of the first distinction; and the number one (1) as the first whole prime number. In Arica's system of Trialectics, these formal elements become, respectively, the Active, the Function, and the Attractive. Vajrayana Buddhism recognizes them as the Dharmakaya, Sambhogakaya, and Nirmanakaya. In Footnote 1, Only Two Can Play This Game (written as James Keyes), they are identified as the Holy Spirit, or Holy Ghost, God the Father, and God the Son, as presented in traditional Christian terms.
As it turns out, G.Spencer Brown lists, in the Index of Forms (p. 138) forty-five elements of his calculus. We propose to describe the forty-eight cosmic laws with reference to the mathematical properties illustrated by Brown's Laws of Form.
The first three prior formal assumptions we have already noted. These assumptions are set into the marked state by the first three elements of the calculus. Numbers one refers to assumptions of language, two of counting, and three of the way in which numbers are represented. These assumptions correspond to the mystical trinity only as illustrations, for the explicit purpose of writing a book about it all. In terms of cosmic law, they are otherwise described as the Void, the first act of creation. Let us then continue our count, summarizing all that might be said about the mystical Trinity as: 1,2 (first cross) and 3 (3 in 1, the FORM as VOID).
4. DEFINITION: Distinction is perfect continence.
5. AXIOM I: Law of Calling. (Two AXIOMS)
6. AXIOM II: Law of crossing.
(The ARITHMETIC which depends upon the above is composed of six canons, comprises a total of seventeen elements, nos. 4-15.)
7. Convention of intention.
8. Contraction of reference.
9. Convention of substitution.
10. Hypothesis of simplification.
11. Expansion of reference.
12. Rule of dominance.
13. Principle of relevance.
14. Principle of transmission.
15, Rule of demonstration.
(The ALGEBRA contains twenty four elements, nos. 16-39. They are comprised of two arithmetic, and two algebraic initials, eighteen theorems characterized as follows: four representative, four procedural, two connective, six algebraic, two mixed, and one algebraic theorem of independence, also the two rules of substitution and replacement.
16. ARITHMETICAL INITIAL I: Number (condense/confirm)
17. ARITHMETICAL INITIAL II: Order (cancel/compensate)
18. ALGEBRAIC INITIAL I: Position (take out/put in)
19. ALGEBRAIC INITIAL II: Transposition (collect/distribute)
20. T1 Form
21. T2 Content
22. T3 Agreement
23. T4 Distinction (Procedural)
24. T5 Identity
25. T6 Value
26. T7 Consequence (Connective)
27. T8 Invariance
28-. T9 Variance
(Algebraic--Theorems of the second order)
29. T10 Extension of 19. Transposition
30. Tll Extension of 47. Modified transposition
31. T12 Extension of 48. Crosstransposition
32. T13 Extension of 41. Generation
33. T14 Canon with respect to the constant
34. T15 Canon with respect to a variable
35. T16 The bridge
36. T17 Completeness
37. T18 Independence
38. RULE I: Substitution
39. RULE II: Replacement
40. Cl Reflection (Reflect/reflect)
41. C2 Generation (Degenerate/Regenenerate)
42. C3 Integration (Reduce/Augment)
43. C4 Occultation (Conceal/Reveal)
44. C5 Iteration (Iterate/Reiterate)
45. C6 Extension (Contract/Expand)
46. C7 Echelon (Break/Make)
47. C8 Modified transposition (Collect/Distribute)
48. C9 Crosstransposition (Crosstranspose, collect) / (Crosstranspose, distribute)
The classes of Consequences are not properly distinct, as larger numbers of steps are included by a single indication. "This is the dual form of contraction of a reference, notably the expansion of its content." (p. 36)
Theorems T1 through T9 (20.-28.) belong in the Arithmetic, T10 - T18 (29-37) belong in the Algebra. The Arithmetical Initials belong in the Arithmetic (18-19). The Consequences belong in the Algebra (40-48). Tabulating the above pages, this leaves 20 elements in the Arithmetic and 22 in the Algebra. Together with the one definition and two axioms and three assumptions the total is 48.
Kurt von Meier