Does the spatial arrangement of a group of structures or features on the ground “reflect” a pattern in the sky? In this article, we examine the Hermetic concept of what is below, the microcosm, is a reflection of what is above, the macrocosm.
Testing an Age-Old Idea
In 1989, Robert Bauval proposed that the three pyramids in Giza were arranged to mirror the pattern of three stars in Orion. With Bauval, Graham Hancock further expanded upon this idea claiming the layout of these and nearby pyramids along the Nile were a terrestrial representation of the constellation Orion and the Milky Way. Hancock and researcher John Grigsby later proposed a similar correlation between the spatial arrangement of temples at Angkor and stars in the constellation Draco.
Although these and other claims have been criticized by the archaeological community (see, for example, this article by Magli and Belmonte), there has been no attempt to test the correlations using quantitative methods. A recent paper describes a new method that maps stellar coordinates to corresponding ground locations for the purpose of measuring the similarity between the two patterns.
Ideally, a mapping of stars to the ground should be “conformal” — preserving shapes and angles. Attempting to match the three stars in “Orion’s Belt” to the corresponding pyramids in Giza stretches and distorts the pattern of the stars so that they match the corresponding pyramids (see figure below). However, forcing a match in this way skews the pattern. Mappings with a large amount of skew are not conformal and not accurate representations of the star patterns on the ground. The amount of skew can be measured by mapping a rectangular region in the sky to the ground. If the projected region is rectangular (corner angles close to 90°), the transform has minimal skew.
So while Orion-Giza is correlated, it is not conformal. If Menkaure were located approximately 45 meters northwest of its current location, the layout of the Giza pyramids would match the pattern of the three stars in Orion exactly. It would seem that had the architects of the Giza Necropolis intended the layout of these three pyramids to match the stars in Orion, they would have arranged them just as precisely as they were oriented to the cardinal directions.
In another proposed Orion correlation, also illustrated above, an even greater skew is introduced if we try to match these same three stars to the layout of the Temple of Quetzalcoatl and the pyramids of the Sun and Moon at Teotihuacan.
It seems unlikely that either Giza or Teotihuacan was intended to be terrestrial representations of Orion. But with only three stars/pyramids, it is difficult to say for sure.
In Heaven’s Mirror, Graham Hancock and John Grigsby claimed the layout of temples at Angkor were correlated with the pattern of stars in the constellation Draco. Although they identified more than three temples/stars, there was a methodological problem. According to Jason Colavito, “It looked like many of the stars of Draco were missing, and Angkor seemed to have temples where there were no stars.” In order to fill in some of the missing information, using Google Earth, seven temples can be identified that appear to be correlated with stars in Draco. Using our method to match this pattern of temples to the corresponding stars in Draco results in a mapping with much less skew. As mentioned above, a simple measure of skew is the amount the corner angles of the rectangles deviate from 90°. The corner angles for the Draco-Angkor correlation are 90±6°. This is much less than Orion-Giza (corner angles 90±18°) and Orion-Teotihuacan (corner angles 90±75°).
Wayne Herschel, proposed an alternative hypothesis – that the Angkor temples are correlated with stars in and around the constellation Perseus. Another measure of similarity is the average difference between the location of a temple and the projected location of its corresponding star. For Draco, the average difference is 950 meters, which based on a site extent of almost 12 km, gives a relative error of 8.1%. The Perseus correlation has comparable skew (corner angles 90±7°) but a smaller relative error of 6.2%.
Is there any basis for preferring one correlation over the other or rejecting both?
Perhaps the key question in evaluating a correlation hypothesis is whether or not the terrestrial pattern can be seen by an observer as a “reflection” of the corresponding stars. Viewed from the north, Orion would have reached its culmination along the meridian over the Giza pyramids circa 2450 BCE. Although there are mountains south and east of Teotihuacan, they are too far away for an observer to see the individual structures at the site, and looking north-northwest, Orion would not be in the field of view at any time. The terrain at Angkor is relatively flat. It would therefore be difficult to visualize the layout of Angkor Wat and the surrounding temples over an extended area. If the Angkor temples were arranged to match the Draco, how did they do it, and for what purpose was it done?
It, therefore, seems reasonable to require that:
- The spatial layout of a pattern on the ground matches the corresponding pattern in the sky at least to within the measurement limits of naked-eye astronomy
- The ground pattern can be viewed in its entirety from some vantage point
- The corresponding stars can be seen in relation to the pattern on the ground at some point in time.
Several sites in the Northeastern US contain linear patterns of cairns and other stone features that are thought to represent serpents and could therefore be considered terrestrial representations of Draco. Glenn Kreisberg describes one such site on Overlook Mountain in New York State that satisfies all three of the above requirements.
The skew is the least of all sites considered (corner angles 90±4°) with a relative error of 6.7%. As shown above, the stone features on Overlook Mountain can be seen as a “reflection” of the constellation Draco as it sets above the northwest horizon around the winter solstice when viewed from a vantage point to the southeast. If the stone features at the site can be dated, the degree to which the visual correlation could have been better/worse at that time can be assessed.
In the 1930s, Katherine Maltwood claimed that certain patterns in the English countryside were designed to mirror celestial zodiacs. Although the Glastonbury and other proposed landscape zodiacs have been disproven, evidence suggests the Native people might have attempted something similar at Poles Hill in Gloucester, Massachusetts.
Glacial erratics of various shapes and sizes are scattered atop Poles Hill. The arrangements of three boulders relative to a central sighting stone have been shown to be aligned in the directions of the summer solstice sunrise and sunset, and winter solstice sunrise. A previous paper explored the possibility that the central sighting stone and two other stone features matched the pattern of three stars, Rastaban, Etamin, and Thuban in Draco. Adding three additional stars in Draco and associated stone features reveals a sky-to-ground match with an average location error less than Overlook Mountain but with somewhat greater skew (corner angles 90±11°).
What is particularly interesting is that correlations around Draco may also exist at Poles Hill. Certain stones to the west appear to correspond to a group of stars in Hercules known as the Keystone Asterism. In the opposite direction, a large glacial erratic can be found at the projected ground location of Polaris. Given the large number of boulders present, it is statistically possible for such correlations to occur by chance. Still, the possibility remains that the Native people who are thought to have established the solar alignments at this site by moving and manipulating glacial boulders may have also represented an extended portion of the northern sky in the same way.
Featured image at the top of the article and imagery in other figures courtesy Stellarium and Google Earth.