Architecture: Paradigm and Outline


[A book designed as a text for teaching the understanding of architecture, intended for a wide general readership and for use at the university level for instruction in Arts and Humanities courses.]


We know that constructions are technically arithmetics, which map the complete and con­sistent formal relations between axioms, which in (prior) turn derive from definition. Thus, constructions are "forms taken out of the form." (G. Spencer Brown, Laws of Form, Chapter 2, P. 3).

The definition of subject focuses first upon the keyword: ARCHITECTURE. It is composed of two roots as lexical elements, which can be traced back to Indo-European sources of the seventh millenium. In the Appendix to the Ameri­can Heritage Dictionary of the English Language, the root arkw- is defined as "Bow and arrow (uncertain which, perhaps both as a unit), "and is ramified in the group of words which includes ARROW, ARC, ARCH in its primary sense, ARCHER, ARCHIVOLT, ARCIFORM, ARCADE AID ARCUATE. The other part of the word "architecture," the -tech comes from teks- "To weave; also to fabricate, especially with an ax, also to make wicker or wattle fabric for (mud-covered) house walls."

"ARCHITECTURE" as a word, expresses the coming together of bow and arrow and basket weaving. Both of these technologies appear historically in the late paleolithic, old stone age, characteristically illustrating the division of labor between the complimentary male hunting and female gathering activities. We may imagine them coming together when the old way of life changed; as the campsites became more permanent, settled communities, hunting led to animal husbandry and gathering to agriculture. This change is recognized as the "Neolithic," or new stone age. Its name, from lithos, "stone," was invented by modern archaeologists who, in the interest of science sought to base their interpretations upon rock solid objective evidence, chose stone tools as primary artifacts, these having survived in material form from much earlier times. The "neo-" refers to a new way of working with stone, namely that of polishing and grinding. The principle of the mill wheel was invented, and the grinding of grain into flour led to an economy based upon the price of a loaf of bread. Evidence indicates that at first this was an economy of such abundance that most peoples whose myths of origin can be traced back so far accord some such title as the silver age to the period or stage of the process. The real Golden Age was of course the so-called Paleolithic: the Earth provided amply enough for human beings to wander freely about (more or less), there was plenty--and plenty of free time in which to enjoy it; human beings had more time not directly devoted to main­taining conservation, life and security than ever since.

With the neolithic appear collective large-scale building projects: walls to distin­guish between the forest and the garden, the open range and the stock breeding pen. With the whole earth as home, we domesticate plants and animals, and mark the boundaries of a much smaller, local house, concentrating the energy of life so that its critical processes occur in our presence. The intelligence of our species is fed back into the process of genetic selec­tion, so that it becomes us who do the choosing, for motives of our own. And we begin to arrange the stones around us as did our hominid forebearers for some two or three million years before.

Leaky (Origins) discovered a circle of stones east of Lake Turkana which he reckoned was one of the earliest sites evidencing the practice of architecture. There was a ring of stones, probably a wind break of branches long since crumbled to dust and blown away. But the stones remain, covered with volcanic ash and alluvial deposits sealed in the geology, and thus date-able through objective analysis of the stratification. No doubt Homo Habilis, now agreed to be Early Man, articulated his sense of place on the surface of the earth with care and deliberation. The stones just didn't happen, to be arranged that way. An order of symmetry was seen by the archaeological eye, and fragments of bone were found that had been cracked with a stone tool of a general category called AX, but which included the sophisticated func­tions of hammer, knife and guided missle.

"...Also to fabricate, especially with an ax." The fabric is the textile, that which is woven. And the ax is the edge that cuts the thread, as Clotho spins, the possibly later interpolation of Zeus as Lachesis who usurps control in the temporal domain as measurer (of lots), and Atropos who cuts the thread. Well, the weaving begins with the thread. As the stuff is called in San­skrit, sutram, which in the Arabic becomes the Surah, is the thread spun by the first lady of the Fates. The Greeks chose to refer to them euphemistically--as everyone has heard the advice "Don't tempt Fate," more properly the three Fates. These are the Mothers of Necessity, to whom even the gods pay dues: Our Lady of St. Trinion, the Triple goddess whether called Bridgit or Mary, three roots to the void, the Trikaya principle, Trialectics. As Ichazo writes, "Human Process  perception of the Unity comes from a recognition of the three roots and a realization of the void."

We have two complementary kinds of evidence to consider in our exploration of the roots of architecture. The first provides data about measurable manifestations in the material order of being. But there is an order of being prior to material existence: that of the formal relationships ob­taining in what may be technically labeled Eternity. These relationships have been precisely mapped by several cultures, and expressed in terms of mathematics, abstract philosophy and the practice of esoteric disciplines. One function of the Arica Institute is to transmit, directly and objectively, indications for exercises, through the practice of which real knowledge of the structure and function of the human psyche may be unveiled. In a formal mathematical notation, G. Spencer Brown has set a map of the Eternal Regions into the marked state. It is understood that Dante and St. Dionysus the Areopagite glimpsed the same central vision of Unity.

Conventional threads are space and time, or as Aldo van Eyck puts it, place and occasion. For the art historian this became school and period. When Anthropology and Ethnology revealed to Ernst Ludwig Kirchner, in 1904, in the Ethnological Museum at Dresden, that art too was to be found among the qualities of material objects collected for the curiosity of science, the ethnocentric bias of Central European culture was grandly subverted. Picasso, in Paris at the Demoiselles place on the Rue Avignon, or earlier with the donas of Cataluňa, showed the mirror to Western art of its own primitive eroticism. Maurice Vlaminck also started his collection of so-called primitive art. And then the Rockefeller, and the de Menils, together with their Objets de Klein, Duchamps, Magrittes and Warhols.

We now reckognize that certain human beings have historically demonstrated the capacity to produce "art" at many different coordinates of space and time, and the word "art" intrinsically means a linking together, a construction, a yoking, or formation from disparate elements of a paradigm of Unity. The idea of Unity provides a "z-axis" of reference for the x y of space and time, place and occasion. So we say, without the z, there are only abstract spaces and times; they become places and occasions with the transformation of the third abstract axis, Information, into consciousness. And consciousness may be understood as that which recognizes itself, the Unity.

As a reference point, let us take the Great Pyramid of Khufu (Cheops) at Giza: the first large‑scale monumental stone architecture, manifesting the image of Unity as worked out in durable form, objective evidence of which has survived. We know that the Pharoah, as god/king, realized the Unity within, the full potential of the Divine Human Pro­totype. The precise architectural form was achieved within a few hundred years of the appearance of the craft of stone masonry, under the jurisdiction of the Priesthood of Ptah. Not only is the Great Pyramid a paradigm of the simplest, most elegant form of the psychic Space; at the same time it is a true geodeisic monument, demonstrating the Egyptian knowledge of the shape and measure of the earth itself, with a degree of precision (accounting for the oblate­ness of the spheroid earth) not confirmed by "modern" scientific measurement and computation until the time of Sir Isaac Newton. We know now that the Great Pyramid models the northern hemisphere of the earth, and by extension, that of the celestial hemisphere as well. Embodied in the system of standard units of measure employed in its building are the formal re­lationships of geometry and trigonometry, the appli­cation of which, to cartography, implies a refined abstract understanding of latitudes and longitudes--that is, to a sophisticated system of geographical coordinates. This was confirmed in the IVth Dynasty, as a surviving papyrus record documents, when the expedition to discover the source of the Nile estab­lished the remarkable fact that the river rises, a few degrees below the equator, to the east of Lake Kivu, at precisely the degree of longitude of the westernmost delta, where the Nile empties into the Mediterranean, later marked by the city of Alexandria, and that it is crossed at the First Cataract by the Tropic of Cancer. That these processes were clearly understood is further established by the use of the three pyramids at Giza as a practical theodolite. A precise understanding of time and its reckoning through spatial constants is expressed in a physical construction executed with the precision of an optician.

The Great Pyramid thus embodies a perception of the Unity as an integral expression of the psyche, of material reality, and of the geophysical, mathe­matical and cosmological realms.

Perhaps we may search for clues for the histori­cal antecedents of this perception in other pyramidal forms. The pyramid, pile of rocks or cairn is a structure which, in Classical Greeee, is associated with Hermes, the god of trade, culture, dice and commerce. One of the earliest archaeological exam­ples is a pile of carefully stacked spheroidal stones discovered in a Mousterian site, El Quettar cave in North Africa. At the top of the pyramid are stones made out of flint, corresponding to the later refined expression as capstone--or, as on the back of the U.S. one-dollar bill as the Eye of Providence.

Kurt von Meier
May 13, 1979