The content of this section is primarily archaeological because it was in this context that the geometric system became clear to me. Though the geometry is evidenced worldwide, the site was entitled Native American Geometry in deference to the works of their ancestors that I had been researching for years. Generally, the archaeologist is restricted to the pure observation of the material remains of the behaviors of previous cultures that survive the ravages of time, whether on or beneath the surface. Rare is the opportunity to actually participate in those behaviors, and rarely still, to benefit from the wisdom associated with those behaviors. The few common exceptions would be approaches to lithic and ceramic technologies that archaeologists attempt to reconstruct and replicate through hands-on experimental applications and frameworks. It is in this same experimental spirit that the material on geometry is advanced in these pages.
Non-random geometry radiates throughout a wide range of cultures serving both religious and secular functions. Semitic cultures have employed it for millennia to celebrate the Creator in an art form that avoided the use of graven images in their representation of God. Hellenic cultures utilized this tradition in their architecture and also in their graven images and sculpted art; the sacred (natural, intrinsic) proportions were especially evident in their sculpted works that represented the human body. During the American Revolution,this tradition was securely instituted in America with the symbols chosen to decorate the colonial script, and later for the Great Seal of the United States. It has been located on all continents in the Old World, and now it is beginning to be recognized in Prehistoric America.
Problem is, there is hardly a word about this geometric paradigm in the New World archaeological and anthropological communities. Therefore, this web site is dedicated to introducing the concept, its methodology, and ways that it can provide quantitative information regarding New World built form and iconography. It is also dedicated to opening a channel of dialogue between Native Americans and the Immigrant American cultures in at least one critical area of mutual concern: it is a system of knowledge that may have an immediate impact on the way we teach our children.
Universal traditions are important in anthropology. The recognition of this widespread, multi-cultural tradition is relatively new. Currently, the best place to find associated elements of this geometry would be under the subject heading of symmetry studies. Elsewhere, in the math and science worlds, one finds many references covering this topic. However, they often require a fairly hefty background in math and science just to get through the first chapter.
My contribution is the attempt to provide the rules that scientifically ground this tradition in a way that is accessible to social scientists. The rules are quite simple, but they prevent the construction of shapes that fall outside the parameters of the built-in spatial and mathematical ramifications of the circle. Further, all geometry covered is restricted to the 2-dimensional planar variety which examines width and length, but forgoes height. This will be left for others to pursue.
This is a tradition of spatial investigation that knows no limits. It is flawless. And it seems to be part of the human legacy to rediscover it now and then, and to rediscover the hope and the optimism that accompanies the recognition of a deep, abiding, orderly structure that underlies the oft-perceived cacophony of everyday existence. Examples: the Mayan Civilization, the European Renaissance, the Prehistoric Southwest.
The focus here is with Southwestern Cultures of Native America, past and present. In time, the page could grow to include other cultures, such as the Moundbuilders of the Midwest and Southeast, the Maya and other cultures and civilizations in Mesoamerica and South America. The first order of business is to begin to recognize the forms and elements of non-random geometry. And the best way to achieve this recognition is to practice it, to find out for ourselves how it works and what it does.
Though my interests are obviously archaeological and anthropological, the non-random geometry explored here could have a much greater impact on studies related to cognition, the multiple intelligences theory (pioneered by Harvard's Howard Gardener), and neurophysiology.
Given the presence of non-random geometry in diverse cultures separated by thousands of miles and thousands of years, it would seem to be a tradition of knowledge and a system of application that is easily understood by every culture that comes in contact with it. The same cannot be said of other mathematical traditions, such as algebra. And this brings up a most question:
Does non-random geometry constitute a language in and of itself?
The question was posed in a letter to Noam Chomsky some years ago. His response was that the question had never been asked before. His suggestion to seek the opinions of educational psychologists was followed but equally fruitless. No one seems to know, or even to have framed the question before.
Under the spell of our Western cultural bias, where geometry is tightly defined as a subcategory of the larger field of mathematics, could it be that such a question is without an academic frame of reference? Is the idea a ridiculous proposition, one that grates against established parameters of the academic bifurcation of arts and sciences?
Not necessarily. Non-random geometry has its ultimate origin in the natural world. The proportions and shapes constructed with compass and straightedge are mirrored in nature, from the double helix of our DNA, the skeletons of diatoms, and hexagonal snowflakes to phi-spiral galaxies light years away. Could it be that this program of geometry is built into our neurophysiological framework? Would this explain the kaleidoscope of geometric images caused by the anoptic flashes that erupt when we rub our eyes or press our fingers against closed eyelids?
If non-random geometry can be qualified as a universal language, i.e. one that can be learned by anyone from any culture, then it would appear to be an example of a trans-cultural, trans-linguistic tradition that could provide a cross-cultural standard for researchers concerned with how the brain/mind learns and transmits information, perhaps even a standard for measuring intelligence itself. One advantage to this field of study should be attractive to researchers: The rules that govern this possible "language" are firmly grounded in an elegant scientific logic.
Time, and deeper questions asked by qualified researchers, will tell.
E-mail: Chris Hardaker
Copyright 1994-2000, Chris Hardaker