In the 1970s the Dutch-Peruvian mathematician, Maria Sholten D’Ebneth wrote a book in which she claimed to have discovered, or rediscovered, an alignment of pre-Columbian sacred sites stretching from the ancient city of Tiwanaku (Tiahuanaco) in Bolivia to north of the city of Cajamarca in northern Peru. The alignment appeared to be incredibly accurate and covered a distance of around 1,000 miles (1,600 km), cutting across some of the highest mountains and steepest gradients in the entire world. The alignment had a precise orientation of exactly 45° West from true North, following the line of the Andes mountains.
Published only in Spanish, and now out of print even in that language, Sholten D’Ebneth’s, La Ruta de Wiracocha (The Route of Viracocha)[i] contains a wealth of information hardly known to the English speaking world. The alignment’s association with Viracocha, the great Andean creator god, teacher and civiliser of humankind, is a highly significant one. Many legends concerning the feats of Viracocha speak of his undertaking a journey, from the city of Tiwanaku towards the North West, eventually to leave the shores of South America’s Pacific coast just south of the present day border between Peru and Ecuador. Viracocha’s legendary journey, Sholten D’Ebneth revealed, corresponded with her own geometrical discovery of the alignment of many of the most ancient and sacred sites in the Andes, including the famous ones at Cusco (Cuzco), Ollantaytambo and, of course, the great and mysterious complex of Tiwanaku.
The many megalithic sites along Way of Viracocha have long given rise to theories and speculations about who built them and controversies about when they were built. At this juncture, it is perhaps worth pondering the sheer technical challenge of surveying this vast alignment across some of the most rugged, remote and mountainous terrain on earth. Indeed, my own research and that of others, indicate that the alignment could extend beyond Tiwanaku. The Peruvian architect Carlos Millena Villena has even suggested that it may form part of a great circle that girdles the entire globe. Whatever the length of the alignment is eventually determined to be, whoever surveyed it must have been aware of the curvature of the earth, as I hope to demonstrate.
When I plotted the Route of Viracocha, I had the benefit of using software such as Google Earth® and Marble. These programs enabled me to employ a spherical projection of the whole globe, rather than the “flat” Mercator Projection used in previous decades. As we will see later, using this map projection yielded rather different results from those of earlier researchers. This became evident when I extended Sholten D’Ebneth’s alignment beyond Tiwanaku towards the South East. If my findings are correct, it implies that whoever surveyed the Route of Viracocha, not only had an understanding of the earth’s curvature, but also understood the principles of spherical trigonometry.[ii] It is equally likely that those who undertook this work knew the dimensions of the Earth. The question then arose in my mind:
Could it be that Viracocha, the great teacher and restorer of civilization in the Andes, in some way embodied the scientific knowledge of a sophisticated, but long forgotten, high culture?
One clue to answering this question lies in Sholten D’Ebneth’s discovery of the connection between the Route of Viracocha and the geometry of an ancient South American sacred symbol, called the chakana.
Certain symbols seem to defy the changes brought about by time and ebb and flow of history. In South America, one such symbol is the chakana. Otherwise known as the Andean stepped cross, it has been found in the relics of so many of the varied pre-Columbian cultures of South America. In one form or another, you will find it in the Mapuche art work in the south, on the enigmatic stone blocks of Puma Punku, on the embroideries of the Incas, adorning the adobe walls of the city of Chan Chan and woven into the textiles of the war-like Huari culture. It has been found in the ancient pyramid city of Caral, which dates to around 4,000 BC, where it embellishes the joists of the Ceremonial Centre. Yet another name for it is the Inca Cross, but its provenance as a symbol is much more ancient. As with other symbols of great antiquity, the multiple meanings associated with chakana are the result of accretions over time.
Even today, you can see chakanas throughout South America, not just in the Andean region. I have even seen chakanas adorning the belt buckles of maté drinking gauchos in the Rio Grande do Sul in Brazil. In the Andes you will see the chakana everywhere: from rainbow coloured flags fluttering in the Plazas de Armas, to painted signs advertising restaurants and hotels. There is no space in a short article such as this to do justice to the multiplicity of interconnected meanings and correspondences associated with the chakana in contemporary Andean life and culture. These are usually summarized in the phrase Andean Cosmovision and readers interested in the manifold aspects of the chakana are encouraged to search the internet to learn more.
If we take the liberty for the moment of cutting through the complex of meanings associated with chakana, we find at its heart a code of number and geometry from which all of its later associations grew.
Astonishingly, these numbers appear to bear striking parallels with those found in ancient sacred texts from around the world. What is more, both the numbers and geometry of the chakana are found encoded in ancient architecture, much of it sacred, in many locations world-wide.
A still greater mystery is that certain numbers also seem to be encoded in the fabric of nature itself. Are we seeing here, not just the traces of an ancient, universal and sophisticated body of knowledge, but also a code that could tell us about the nature of the world in which we live? Perhaps there is something here that our current reductionist and materialist scientific consensus has missed, because it does not have the concepts to acknowledge its existence.
Let us now examine just a small part of the chakana’s number and geometry in order to provide some evidence of the above contentions. To draw the chakana geometrically, we start by dividing a square in two diagonally, and then circumscribing it (ie drawing a circle around the four corners of the square). The stepped cross of the chakana is then constructed within the space that has been outlined.
In classical Euclidean geometry, this process known as squaring the circle and was a fundamental task set for students of the discipline. In sacred geometry and alchemy, the square and the circle are thought to represent opposite principles; the square being masculine and the circle feminine. However, they are equal in that both consist of 360°. In esoteric terms, the act of squaring the circle equates with the unifying of masculine and feminine principles at work in the universe. Interestingly, a Peruvian researcher into the Route of Viracocha, Javier Lajo, found that many ancient sites and temples along its length had either square or circular geometry, depending on whether they were dedicated to male or female deities.[iii]
However, there is a little more to the process of drawing the chakana in the manner described above. It also involves drawing a 45° diagonal line across the square. The cutting of the square in this way produces a diagonal with a value equal to something called the Pythagorean Constant, which equates to the square root of two. The ancient Ancient Egyptians used exactly this geometric operation to derive the linear measurements of both the Royal Cubit and Remen.[iv] Interestingly, there appears to be a connection between this geometry, and not only ancient Egypt, but also the measurement system used at the Akapana Pyramid in Tiwanaku.[v] A further example of this geometry is seen in the traditional Andean flag, called the wiphala, which takes the form of a square divided diagonally.
The modern mind is accustomed to think of numbers solely as a means of defining quantities, but the ancients saw things differently. For them, particular numbers, and their multiples, also expressed certain qualities. Thus, odd numbers were considered masculine and even ones feminine, for example. There is one particular series of numbers that seems to recur in many sacred texts, which has been identified by several researchers in various fields of study. This set of numbers, or some of its members, occur in ancient systems for measuring time, in the dimensions of sacred buildings and numerous other contexts. They include the numbers 36, 72, 108, 144, 216, 288, 432, 504 and their multiples both by 2 and 10.
There is one particular number from this series that seems to be associated with the geometry of the chakana. In the form pictured in this article, the chakana contains 12 x 90° internal angles. Multiply these numbers together and we get a product of 1,080°. Multiples of this number occur frequently in the years, both human and divine, attributed to several of the Yugas in Vedic cosmology. In Gnosticism, 1,080 was said to represent the Divine Feminine and the Serpent of Wisdom.[vi] In Japan, Shinto priests strike the temple bell 108 times to herald the New Year, indicating the end of one cycle and the beginning of another. Even more than this, the number 108 seems to be encoded within certain measurements we use today to quantify the physical universe. The atomic weight of silver is 108 (traditionally considered a feminine metal) and the radius of the moon (alchemically and astrologically associated with silver) has been estimated to be 1,080 miles. (…)