Text Box: All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act their dream with open eyes, to make it possible…
T.E. Lawrence
It is clear the Ancestral Puebloan people dreamed of things much greater than themselves... 
In spite of over a full century of professional and academic archaeology, we are only now beginning to uncover the intricate shadow of a well-ordered scientific vision associated with a very ancient technical and astute imagination. Littering the troubled advance of human behavior, anthropologists, ethnologists and archaeologists alike have often included the specialization of tools, rock art, trade networks, ritual, sedentary custodianship and importantly, the application of engineering and mathematics to monumental architecture as principal manifestations of emerging social, intellectual and scientific consciousness; these are the halcyon characteristics of advancing civilizations. We now know the great San Juan culture of prehistory did all these things.
Significant changes in human, social and environmental conditions typically proceed somewhat oblivious to the frenetic, often sporadic and asynchronous pace of inspiration; the former repeatedly dragging its reactionary feet into the latter's future. However, here and there throughout the revelations of documented history, there appear sudden, dynamic and enormous leaps of cultural and/or technological advance resulting in profoundly rapid change in scale with enormous impact to the communities who engage them. The scale of architecture is particularly sensitive to these changes in the human condition. One such leap occurred during the first millennium AD in a rugged, remote corner of northern New Mexico called Chaco Canyon.
Architecturally, Chaco Canyon is unique in the rich Amerindian panorama of prehistoric cultures in North, Central and South America. Similarities in anthropological, archaeological and scientific data suggest a rough common experience beginning with the Paleo-Indian hunter/gatherers of the late Pleistocene Epoch, follow the seasonal farming cultures of the archaic Cochise and Oshara traditions, and include the entire experience of the resilient southwest Basketmaker culture (see Appendix A for temporal classifications). Similarity abruptly ends in Chaco Canyon with the sudden advent of the great pueblo-builders who introduced load-bearing masonry as a new technological medium to their traditionally pithouse-based society. Masonry was evident with Chacoan trading partners prior to the 9th century (i.e. Toltec and Maya). However, beginning with the initial planning and construction of Peñasco Blanco (c. ~AD850) and the careful inter-positioning of other Great Houses in the landscape, Chacoan Engineers began to construct a sweeping design of architecture and manipulated landscape based on a unique algebraic ratio of 1 to 1.618; a ratio which is by definition infinite.

Over the course of the next several hundred years, the Chacoan Engineers would extend this new architectural implementation into many outlier pueblos across tens of thousands of square miles in the American southwest. Often adhering to simple rectangular aspects of this ratio, its curvilinear form is based on this same ratio, a ratio when introduced into pueblo design frequently and incorrectly is referred to as D-shaped architecture (see Pueblo Bonito floorplan. These gently curving lines of sandstone masonry were in fact metaphorically designed walls intended to communicate their understanding not only of their landmark achievements in algebra, but of the infinite resonance they felt in their worldview, a view that even today remains largely veiled to the general public in an esoteric form of mathematics called fractal geometry—something not well understood nor clearly defined in our own contemporary understanding of geometry until the 1970's. Exactly how a prehistoric culture with no written language and possessing only stone tools accomplished this achievement has been one of the profound mysteries of the American southwest.
You will find in this research an ancient connection between a Chacoan reverence for algebra and geometry in architecture (in particular the fractal elements of infinity) and the personal and symbolic resonance Chacoan engineers perceived with the infinite and resonant nature of the universe. The architecture was testimony to both the reverence and the resonance of this metaphorical connection and it first emerged uniquely in the monumental Great House architecture of Chaco Canyon. This architecture reflected a cultural, political—and importantly—a scientific movement consisting of both physical relocation and political power re-centering (Lekson, 1999). This authority I believe was at least partly based on a body of knowledge united by arithmetically-based concepts of fractal geometry, mysticism and architecture constructed as a metaphor of indigenous knowledge. As such it became a scientific authority and coupled with mysticism was developed, inherited and passed on by generations of ancient tribal peoples. These enormous monuments in stone—while fundamentally fractal—are so visually elegant, so consistent and so dynamically graphic in appearance that no mathematical knowledge is necessary for identification beyond simple pattern recognition.  Substantiation via precise calculation with digital modeling adds only small incremental significance to what your eyes have already confirmed.
"You don't need a weatherman to tell which way the wind blows…"
Bob Dylan
This prehistoric tradition of implementing algebraic concepts into masonry I broadly label Chacoan Engineering. Referring to an architectural tradition in this way is (I hope) banal enough even for the most tortured of cultural linguists; Chacoan is a fairly well-accepted, non-contested term relative to the geographic location of the so-called Ancestral Puebloan (a.k.a. Anasazi) people in the southwest. For the group directly responsible for imagining and implementing the first advanced mathematics in the southwest and using this math to create metaphorical architecture I have chosen the moniker Shaman Architectural Engineer, a term much more likely to be the target of political and academic angst. However, it is important to start somewhere in proposing a metaphorical amalgamation between the normally disparate subjects of prehistoric Shamanism, architecture and science—no matter how tenuous the label. Problematically, even without the fractal design element, any suggested confederacy between mysticism and science has traditionally been eschewed by tribal, professional, political, religious and scientific scholars for decades and will be immediately suspect.  Shamanism, almost by definition, is a spiritual, a priori form of knowledge, an experiential act of faith normally considered free of the constraints of meta-cognitive fact, experience and scientific evidence. My definition necessarily encompasses (and clashes with) the idea that—occupationally at least—Shamans are the insular intermediaries and myopic messengers between normal physical reality and an asynchronous world of spiritual experience. This could be described as an occupational suspension of reality, and there is the rub. My assertion of spiritual, architectural and scientific collusion in southwestern prehistory is necessarily demanding, even when the hard architectural, mathematic and statistical evidence presented here suggests otherwise.
But, even if I can't prove collusion (nor do I need to do so in order to demonstrate the appearance of fractal architecture in prehistory), this doesn't mean collusion wasn't the case. It just means that in the context of a lost civilization that left no evidence of a written record, I cannot prove this supposition by holding up a Shaman resume itemizing participation in the fractal construction of Chaco Canyon. Suggesting that Shamans were doing algebra as part of a mystical or ritual exercise in metaphorical architecture at any level is going to be a stretch for those who are used to extant knowledge couched in warm, comfortable and familiar box-like interiors. The rest of us will have an easier time of it if we let go of traditional views of prehistory—biased views invariably tied to political agendas, cloistered tenure and the well-worn lecture notes of those heavily invested in a Chacoan past mired in a cultural ignorance that we now know never actually existed.
Yet, in embracing the growing and already overwhelming architectural and statistical evidence that something profound happened in or slightly before the 9th century AD that clearly and dramatically changed an entire Shaman-directed culture—from the privation of living in crudely constructed, jacal-covered holes in the ground—to a new, centuries-long tradition of massive, multi-storied Great House masonry based on algebraic constants, fractal geometry and metaphor, one tends to suspect the Shaman might have been in on a piece of that action.
Further, since engineering evidence and rigorous statistical analysis of Chacoan architecture already supports the presence of repetitive algebraically-based design rules used in and beyond the 9th century Chacoan architectural tradition, I think it is not unlikely the Shaman—in their role as a font of mystical wisdom and the 'go-to guy' for spiritual channeling, and therefore a defacto community leader)—would indeed have entailed some degree of influence, perhaps even outright control (if not actual inspiration and development) in engineering these leviathan projects.
Experience suggests that the technically inclined in any civilization are frequently a minority element within a larger population. A friend of mine used to say that what makes engineers different from the rest of society is engineers are willing to tackle complex technical problems for which there are no obvious and immediate solutions. The same might easily be said of Shaman motivation to embrace creative spiritual solutions to sickness, famine, poor hunting and bad weather, or an architect's penchant for combining architectural solutions to space, materials requirements, environmental challenges, politics and the fickle directions of mystically inclined or wealthy, powerful and frequently unstable and reactionary clients.
It is in this context I am specifically referring to a small sub-group in Chacoan society—an engineering moiety if you like, composed of a group of individual tribal leaders, mystically-driven mathematicians, spiritually-inspired Great House engineers and/or the technically inclined Shaman—who conceived and nurtured this knowledge, facilitated its metaphorical use in Chacoan architecture and passed it on to subsequent generations in what I refer to as the dawn of prehistoric science in the American southwest.  A critical element in this melting pot of arithmetically-based Ancestral Puebloan architecture is this unavoidable mixture of technical medium and metaphor.

Marshall McLuhan
I chanced some years ago to be part of a small group of journalists in Bloomington, Minnesota who interviewed the nascent Canadian philosopher of technology, author Marshall McLuhan. In September 1977, shortly before the stroke that would silence a great philosophical voice, McLuhan's audience at the Minnesota Society of the American Institute of Architects was arguably in awe of the critical mass that had coalesced around his original research regarding the impact of technology on the human condition. At its center was a theoretical construction stressing the enormous and ultimately personal and consequential impact a change in technological scale precipitated in human experience, a scale-change ultimately creating cultural consequences that result from the introduction of radically new, pervasive and deeply-resonant technology.
This change in scale he suggested is experienced as a significant agent of change in society—what McLuhan called the message contained in the context of any new technological medium.
...the medium is the message. This is merely to say that the personal and social consequences of any medium—that is, of any extension of ourselves—result from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology...For the message of any "medium" or technology is the change of scale...(editor's note: emphasis added)
Marshal McLuhan
It was one of McLuhan's principal premises that all cultures inevitably contain vulnerable technical breaking points (he called them break boundaries), and each boundary break produces predictable social impact and upheaval as a result of these changes in scale fostered by the introduction of new technology. These are Rubicon boundaries where culture and new technology intersect; transforming a given culture into something entirely different or, at a minimum, the society involved achieves a point of no return.
As I indicated earlier, architecture has always been particularly sensitive to expressing and recording this socio-technical collision in history. For instance, the introduction of Bessemer steel during the Industrial Revolution of the late 1800's led directly to the enormous skeletal steel skyscrapers that changed the visual and horizontal scale of every major city in the world (as well as the overpopulation, loss of personal identity, and cultural centralization inherent in wide-spread vertical scaling of architecture).  A cultural clash of what used to be with the radical introduction of "what's happening now" is ideological and political conflict by definition; conflict evokes rebellion and rebellion in its turn always becomes destructive. To make an omelet as they say, you have to break some eggs; the challenge to leadership is in limiting the rebellion and mitigating the destruction as the impact of a new scale permeates a changing society. Civilizations typically go through three phases of reactionary egg-breaking in response to these technological agents of change; social alarmism, cultural (typically reactionary) resistance coupled with rebellion and ultimately intellectual exhaustion associated with either voluntary or coerced acceptance.
In prehistoric Chaco, I believe the initial insight and inspiration of mathematics, algebra and fractal geometry produced—spiritually, intellectually and architecturally—an entirely new technology, a medium of load-bearing masonry which resulted in a massive reorganization of that society, a radically new definition of its ritual architecture and its ultimate perspective on lifeways and worldview. The reverberations of scale associated with this medium—inevitably realized in cultural alarm, rebellion and predictable exhaustion—probably also destroyed them.
McLuhan encapsulated this socio-technological upheaval succinctly;
All media work us over completely. They are so pervasive in their personal, political, economic, aesthetic, psychological, moral, ethical, and social consequences that they leave no part of us untouched, unaffected, unaltered.
Marshall McLuhan
The message carried in this new Chacoan medium was directly related to the profound consequences of the comparatively enormous new scale it produced; in this case, a fractal-based up-scaling of ritual architecture and landscape that spanned tens of thousands of square miles across the southwest by virtue of a deeply embraced and far-reaching metaphorical vision embedded in a new medium of algebraically shaped sandstone masonry.
Few events in southwestern prehistory present more substantial testimony to the effects of medium and message than those in Chacoan society where, in the short length of a few lifetimes, this ancient culture transformed itself from groveling in crudely covered holes in the ground to taking its place in the course of human events among the most advanced of civilizations; a transformation that produced monumental Great Houses on a scale to match or exceed everything in ancient Greece, Mesopotamia, Ur, Egypt, Islam and the Holy Roman Empire—by 1100AD Pueblo Bonito had reached four stories in height and contained over 600 rooms, one of the largest constructions of its era and larger than the Greek Parthenon. Pueblo Bonito's footprint was similar in scale to the enormous Roman Colosseum, considered for centuries to be the largest architectural construction on the face of the earth.
The Shaman Architectural Engineer added a unique element to this enormous arithmetically-inspired architecture. Using the medium of load-bearing stone masonry they introduced—as a kind of spiritual resonance embedded in the mortared design—the element of metaphor to Chacoan architecture. By this I mean the Shaman Architectural Engineers were clearly not satisfied with merely achieving arithmetic milestones and adopting new technology in order to create unparalleled upscale urban sub-divisions—they wanted a lasting record in hard rock architecture so the whole world could know about it.
Shaman Architectural Engineers intentionally incorporated a physical and symbolic vision of their mathematics into pueblo design and construction; a faith-based testament in stone of a prehistoric science that stood firmly behind their rapidly changing scale-free industrial revolution. They literally built an accurate analog of this knowledge into the actual shape of their plaza walls and pueblos; not merely an extraneous and vividly extricated three-dimensional form, but a repeatedly consistent, unequivocal and metaphorical statement of the universiality of mathematics and the infinite properties they recognized in algebra and fractal geometry. This was a message from the ancients that stated in stone, not merely what they thought might be true, but more significantly "…this is what we know".

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