The site itself is a relatively recent discovery as Thomas Y. Canby¹ explains in an article in the June 1990 National Geographic Magazine:

"The spiral and the sunlight pattern were discovered in 1977 by Anna Sofaer, a Washington D.C., artist. On the shortest day of the year, she found later, two vertical beams of light would bracket the spiral. The Anasazi, Sofaer believes, were demonstrating a sophisticated use of astronomy".

The arrangement apparently once delineated both pairs of Solstices and Equinoxes with great precision, employing a double set of spirals as an integral part of the scheme. Considered the work of the Anasazi (700 - 1600 BCE, Krupp 1983:152), it has apparently deteriorated in recent times, but in working order it must surely have ranked as one of the most impressive solar sites encountered anywhere. As can be seen, the Summer Solstice (B) "dagger" of light is exactly positioned in the center of the large spiral, while the Equinoxes on the other hand (A and C) also employ a secondary "dagger" of light on a smaller secondary spiral. In these two instances, however, although the secondary "daggers" of light are effectively centered, the larger indicators appear to be similarly offset from the centre of the main spiral. For more on Anna Sofaer's research, see the latter's Solstice Project.^.2  For details concerning the astronomical complexities of Fajada Butte and Figure 2 below see also The Mystery of Chaco Canyon and Sun Dagger video presentations.

    But all this to what end? Although an explanation for the use of a double spiral at the Equinoxes may be found below, it is not immediately helpful in so much as it occurs among the ancient Celts in an earlier period and on another continent into the bargain. It is usually accepted that agrarian societies necessarily require a good working knowledge of the seasons, but hardly to this degree of accuracy, surely. Moreover, what can be made of the technical competence and sustained intellectual effort involved in the construction of such a site? And why in such a remote and relatively difficult location? Even though the Anasazi have other impressive credentials, there still remains the major question of why the "Sun-Dagger" project was implemented in the first place. One cannot, of course, ignore the shamanistic and ritualistic sides of the matter, but this still does not necessarily account for the skill and competence inherent in the Site itself. Just how much competency was involved? Those unfamiliar with the indicated phenomena should realize that all four events fall very precisely on one special day in each instance - in simple terms, the Summer and Winter Sostices are the longest and shortest days of the year respectively while the two Equinoxes are the two days of the year when the lengths of daylight and night are equal in length. The reason for the differences in the lengths of daylight lies in the tilt of Earth's axis; simply stated again, in the Northern hemisphere the axis tilts directly towards the sun at the Summer Sostice, and directly away (i.e., tilts outwards) at the Winter Solstice. At both Equinoxes the tilt is to all intents and purposes along the direction of Earth's orbit around the Sun - see the diagrams in "Summer Solstice" by W.T.S. Thackara; for a more detailed exposition see "A Sky Watcher's Primer" by John B. Carlson ^{3, 4}  in "America's Ancient Skywatcher's" (National Geographic Magazine, Vol. 177, No.3 March 1990:76-107) and the Internet version of How the Shaman Stole the Moon by William H. Calvin.⁵  Additional information concerning Archaeoastronomy in general and the Americas in particular may be obtained from Introduction to Archaeoastronomy by The Center for Archaeoastronomy (University of Maryland) and the Archaeoastronomy Journal.

The larger spiral beneath the slabs at Fajada Butte is bisected by a descending dagger of sunlight for 18 minutes in the hour before local noon on the summer solstice. This is reminiscent of what goes on in some of the California Indian shrines and, for that matter, at Newgrange ⁶

As far as other solar sites in North America are concerned, related research carried out in Inyo County (California) provides the basis for Roderick Schmidt's Equinox Project while on a wider note it would seem reasonable to expect that similar examples of this kind of solar observatory could occur elsewhere, especially in the complex region encompassing the "Four Corners" of Utah, Colorado, Arizona and New Mexico. The inclusion of the Neolithic site at Newgrange (Ireland) on the other hand adds further complications to an already complex matter, for Newgrange is not only separated from Fajada Butte by an ocean and thousands of miles, it is again a much earlier construction (ca. 3500 BCE). But what of the Anasazi themselves in the present context? The National Geographic article of November 1982 ⁷ points out that north from Chaco Canyon and "From Mesa Verde west to Blanding, Utah, the Anasazi occupied the Great Sage Plain, a 4,000-square-mile area tilting slightly to the south. This tilt towards the sun creates a warm ' solar oasis ' that extends the growing season a few crucial weeks." Furthermore, the Anasazi tenancy of this unusual "solar oasis" is also accompanied by elements of mystery that include the suggestion of outside influences, as Thomas Y.Canby relates:

Sun Dagger, long-distance communications, mysterious roads, mammoth building, outliers,... What social system created these sophisticated ingredients of the Chaco phenomenon? Answers to this great riddle of archaeology run the gamut of speculation. Chaco's undoubted contact with Mexico, combined with architectural features common to the two areas, leads many scholars to embrace a hypothesis often referred to as the ' Mexican connection'.⁸

The same article adds further that:⁹

"Support for the Mexican connection came from Alden Hayes, a respected former Park Service archaelogist. ' Too much happened too fast to have been a local happening,' said Mr. Hayes. ' The jump from one- to five-story building, the roads and the astronomical observatory, the complex social organization they imply - it's too much to accept without outside influence.' "

Moreover, the roads in question are literally mind-boggling in their extent, as the following abstract for a recent article on the subject by Stephen H. Lekson ¹⁰ in "Archaeology" attests:

The ancient Southwest has long been viewed as a patchwork of boom-and-bust cultures. Pueblos were thought to have come and gone independently of one another, and archaeologists rarely looked beyond the areas immediately surrounding their excavations. But a new study of the Southwestern landscape has revealed that three of the region's largest and most important ancient centers were linked by a 450-mile meridian line--Chaco Canyon, in New Mexico; Aztec Ruins, 55 miles due north near the Colorado state line; and Casas Grandes, 390 miles due south in Chihuahua, Mexico. Chaco and Aztec were also connected along the meridian by a road known today as the Great North Road (see ARCHAEOLOGY, January/February 1994).
Tree-ring dates indicate that Chaco was occupied mainly from A.D. 850 to 1125 (after which its population was greatly diminished), Aztec from 1110 to 1275, and Casas Grandes from 1250 to 1500. As Chaco was dying out a new center was being created on the same meridian at Aztec. In commemoration of the earlier site, the new one was connected to it by the Great North Road. When Aztec collapsed and the Four Corners area was abandoned, Casas Grandes arose due south of Chaco. While no road has yet been found between Chaco and Casas Grandes (efforts are under way to survey the corridor by aerial and satellite photography), the alignment of the two centers no doubt reflects ideological and symbolic connections.
The area covered by the Chaco-Aztec-Casas Grandes meridian and adjacent sites is more than 100,000 square miles--1,000 times the typical survey area around a Southwestern archaeological site. The existence of a political system encompassing so great an area will require the review and revision of almost every aspect of Southwestern prehistory, but its full meaning is not yet clear.¹¹

Thus the mystery deepens, for although the Mexican component surfaces once again, a straight line 450 miles long running north-to-south to Mexico is hardly to be unexpected in Pre-Columbian North America. As for the technicalities involved in an extensive enterprise such as this, William H. Calvin suggests a practical method to the mark out the line in question utilizing gnomons and shadows, but it is nevertheless still a daunting undertaking ("Leapfrogging Gnomons" survey method for meridian lines). The line seems to have extended northwards and southwards along 107 degrees 57 minutes West, thus passing close to the longitude of Fajada Butte but whether this has any significance appears to be an open question at present. But even remaining with the line itself we still need to ask why there was so much expenditure of effort in its construction and whether the selected longitude has any significance. Perhaps if we had not already been alerted to the concept of "Geographical Astronomy" by Proclus in previous sections we might be able to dismiss the line as a communications and transportation path, its great length notwithstanding. But the question now arises as to whether the concept may have had broader applications beyond Egypt and the Old World. On the face of it this would appear highly unlikely in the present context. It would necessarily entail ocean voyages and definite diffusion before the time of Columbus, a possibility - Norse claims notwithstanding - that remains hotly disputed, if not outrightly denied in many modern academic circles. But still the enigmas remain and even contact limited to Mexico alone raises further complications, for where did the latter get their information and expertise in turn?

The universes we design reflect our perceptions of order. For the present-day Desana Indians of northwest Colombia, the principles of cosmic order are visible overhead. The same energy that animates life in the cyclical pattern of reproduction moves the stars and sets the seasons in sequence. Nearly everything of consequence follows the celestial cycles--the weather, the growth of plants, the availability of fish, the abundance of game--and so the sky is the key to the state of the world at any given time. The Desana are interested in the way the universe behaves as much as in what it looks like. They reside in a rain forest environment, and the survival and the continuity of their way of life depend on their ability to preserve a delicate balance between their needs and the resources available to them. Although they grow some food and obtain an adequate supply of fish from the rivers, the Desana must cope with alternating periods of scarcity and abundance. This is especially true of the availability of game. Hunting is the focus of the men's lives, and so the pursuit of game animals and their preparation into food define, to a great extent, what it means to be a Desana. The Indians are well aware they could--with little difficulty--deplete the forest of its game animals, and so strict rules of behavior, based upon the Desana concept of the world, help preserve the environmental balance....

There is a link between the sense the Desana have of the organization of their territory and the organization of the sky. To see this aspect of their cosmology, we have to look at their creation myth, as reported by Gerardo Reichel-Dolmatoff. The center of their homeland was determined, they say, by Sun Father, who, when time began, picked a place where his upright staff could cast no shadow. There, at a whirlpool entrance to the womb of the earth, Sun Father impregnated the earth, and from that spot the Desana and their neighbors emerged, transported by living anaconda canoes to the places they settled along the river. Figuratively, the shaft of light from the zenith sun fertilized the earth with the procreative energy. The place where this happened defined the center of the Indians' world. The boundaries of the Indians' territory were established by six mythically huge anacondas, each outstretched to form one side of a hexagon. Until we encountered the hexagonal border of six giant anacondas, the elements of this story were consistent with the idea that the world's structure is derived from the sky. But how does a sense of six-sided bounded space enter the picture? The answer is the shaman; the answer is quartz. In Gerardo Reichel-Dolmatoff's words, the shaman is an "ecological broker." Rituals designed to promote the fertility of the game and successful hunts are his responsibility, and he acts as an environmental protection agent for the Desana to make sure they don't consume themselves out of their habitat. Quartz crystals are essential tools in the shaman's kit of magical paraphernalia. Quartz, along with hallucinogenic drugs, permits him to communicate with the unseen world. Associated with Sun Father's creative energy, it sometimes is called crystallized semen. With it the Desana shaman diagnoses illnesses and effects cures. Recognizing an abiding principle of order in the hexagonal shape of a rock crystal, the Desana integrate its geometric regularity and symmetry into their system of cosmic order. For that reason, the hexagon defines the shape of their sacred space. All hexagonal shapes in nature have a special significance for them: the honeycomb, the spider's web, even the shell of a particular land tortoise. Each cell in the shell's pattern of hexagons symbolizes a character in the creation myth or an organizational principle of society--the family, for example, or marriage into another family. Desana rules for marriage exchange are visualized, in fact, in terms of a hexagon. Because of its importance as an organizing principle of thought, the hexagon metaphor reappears in one aspect of Desana tradition after another. A giant hexagon of stars, centered on the belt of Orion, is equated with a hexagon of landmarks on the earth that establishes the limits of the tribal territory. The corners of this terrestrial hexagon are marked by six waterfalls, each a place where the head of one of the six original giant anacondas meets another's tail. Each of these snakes stands for one of the six rivers that frame the traditional homelands. The center of the celestial hexagon corresponds to the intersection between the Pira-Paranfi River and the earth's equator. Here, where the sky is said to cohabit with the earth, is the place where Sun Father erected his shadowless staff and fertilized the world. The Desana time the arrivals and departures of the seasons by the stars. Orion's belt is one of their seasonal indicators, and as the center of the earth's celestial template, it occupies a key spot in the cosmic structure. It is nearly on the celestial equator, and so it can pass through the zenith just as the equinox sun does. The center of the world is associated with the vertical axis to the zenith. This explains why Orion's belt is the center of the celestial hexagon. These same three stars are also identified with an important figure in Desana mythology-the Master of Animals. He is the supernatural gamekeeper, and he helps maintain equilibrium in the flow of procreative energy by controlling the availability of the rain forest's game and by lathering the river's fishes. Both game and fish adhere to seasonal behavior, and the function of the belt of Orion as an announcer of seasons is consistent with its association with the Master of Animals. Also, because these stars are located very close to the celestial equator, they rise nearly due east and set nearly due west. Accordingly, they reinforce the importance of the east-west, or equinoctial line. In the Amazon, the equinoxes are important, for they signal the start of each rainy season. One begins in March, the other in September. At the equinoxes, when the rivers rise, fish head upstream to spawn and so become relatively scarce. Likewise, game is less available. The rainy seasons are regarded as periods of gestation. The Desana associate a pair of intertwined copulating anacondas with the celestial equator's intersections on the ecliptic, or annual path of the sun. These two intersections are, of course, the places occupied by the sun at the equinoxes, and at these times of the year, with the onset of the rains, anacondas swim upstream to mate. At night, when these great reptiles make their way upriver, they can be heard far from the banks. They lift two-thirds of their dark bodies high out of the current like poles and slap themselves down upon the water's surface with a thunderous crack. The Desana say the anacondas are lifting their heads from the water to watch the stars....

......Petroglyphs on the Rock of Nyl, a sacred site of Colombia's Barasana Indians, depict the myth of creation. The tradition is the same as that held by their Desana neighbors to the north. The large human figure portrays Sun Father at the moment he erected a perfectly vertical rod. It cast no shadow. The world was fertilized by Sun Father at this spot, and from it the first people emerged. In fact, the sacred Rock of Nyl is almost exactly on the equator. The sun, therefore, rises due east and passes through the zenith on the equinoxes. When, at equinox noon, the sun is straight overhead, an upright staff loses its shadow. In a sense, the zenith sun's rays penetrate directly into the earth, and when this happens the world is seasonally renewed. (G. Reichel Dolmatoff, U.C.L.A. Latin American Center Publications) [Krupp 1983:315-319, emphases supplied]




Map 1. Territories of the Desana, Yagua, and Shipibo-Conibo

But what has this to do with Pre-Columbian North America in our present context? Returning to the Anasazi, it seems that the hexagon may indeed play a role in astronomical contexts here also - for further on this aspect see Chris Hardacre's Native American Geometry - in particular the latter's research concerning the "Hexagon and Solstices" as applied to the impressive Kivas in Chaco Canyon. As for the purpose of the Fajada Butte solar observatory at the southern end of Chaco Canyon - apart from the purely calendaric value - the dual "Sun-Dagger" phenomena and the nagging question of the off-centered positioning on the main spiral at the Equinoxes still remains to be explained.

quite simply the finest decorated passage-grave of all, with Newgrange in Ireland its only rival. Twenty-three of the twenty-nine slabs which form the walls of Gav'inis are carved with intricate spirals, intersecting semicircles, and other whorled patterns. It is not yet known whether these patterns are purely decorative of whether they have some religious significance. A meaning or a symbolism seems likely, since the spiral forms occur so often in Neolithic carving, but the code remains hidden.¹²

Ornate spirals and patterns also adorn two large stones outside the entrance to Newgrange, perhaps pointing the way to what lies inside - further carvings of grouped spirals on the roof of side cells, and an enigmatic triple spiral illuminated by sunlight flooding down the passage at sunrise on the winter solstice. (Photo Credit: Light Years Ago by Tim O'Brien; shamrock and text added). The emphasis on snake-like spirals (triple or otherwise) in Neolithic Ireland is unusual, for the snake is not indigenous there, and furthermore, as legend would have it, the snake was driven out of Ireland by Saint Patrick in any case. Thus the predominance of such spirals provides a further enigma, solar symbology notwithstanding. Another surprising aspect of neolithic spirals (though not entirely surprising after what was covered in Section IVc) is that they are also found carved on numerous small stone balls in neighbouring Scotland dating from the same period. The latter appear to include all five "Platonic"solids(see Fig.3b below)
Moreover, Ralph H. Abraham notes that of the five solids represented in the group:

Fig. 3. Megalithic Spirals: Left: Newgrange; Center: Scottish tetrahedral sphere;
Right: Tarxian, Malta




Fig. 3b. All Five Platonic Solids.

Note: The above numbers have been added. The original seekers-net presentation (now defunt) was best viewed with its own related graphics.

In these contexts there are also single, triple and quadruple spirals with further intriguing symbols laboriously illustrated in the ornate celtic Book of Durrow ¹¹ and the Book of Kells,¹² but however one views these enigmatic objects and motifs initially, one should perhaps be aware of the ancient yet complex relationship between the triple serpent, the ouroborus and the caduceus, as H.P.Blavatsky explains in the Secret Doctrine (1-3-09):

Every one knows what the caduceus is, already modified by the Greeks. The original symbol -- with the triple head of the serpent -- became altered into a rod with a knob, and the two lower heads were separated, thus disfiguring somewhat the original meaning. Yet it is as good an illustration as can be for our purpose, this laya rod entwined by two serpents. Verily the wonderful powers of the magic caduceus were sung by all the ancient poets, with a very good reason for those who understood the secret meaning.

Secret meanings or not, what are we to make of the complex spirals carved in stone on Malta and those that occur in France, Ireland and Scotland so far back in time (broadly 3400-1600 BC), especially a megalithic triple spiral accorded a special place on the Winter Solstice at Newgrange. What is the overwhelming significance attached to this particular motif and/or the triskele form? And just how important are these passage sites, including Maeshowe (58;59 North, 3;11 West) in the Orkney Islands also oriented on the Winter Solstice, but here towards the setting sun?

    East of Newgrange across the Irish Sea lies the third largest stone circle in Britain - Long Meg in Cumbria, which in turn has a spiral engraved on its namesake (a 3.6 meter stone pillar) in consort with a design involving four concentric circles. A similar configuration is also to be found associated with its close neighbour, Little Meg. Further north, extending east and west, and beyond mainland Scotland as far as the Orkney Islands are numerous other luni-solar monuments. Many are in the form of standing stones similar to Long Meg (with or without recumbent markers) in addition to better known stone circles such as Callanish in the Outer Hebrides. Even further north lies one of the largest stone circles in Britain - Brodgar (59;00 N, 3;14 West) the near companion of Maeshowe in the Orkneys. For further information on the astronomical alignments of over 75 Scottish Megalithic sites see Robert Pollock's extensive analysis in Stones of Wonder ; see also the wide-ranging image collection by Leicester University archaeologist Clive Ruggles.

   Even granting religious and calendaric considerations there still appears to be no truly satisfactory explanation for the proliferation of luni-solar megalithic monuments in the British Isles and elsewhere. Nor are there immediate solutions to the oddities which attend many of them, e.g., the relatively large sizes of the stones employed, the great numbers of sites, and locations in often bleak and inhospitable environments. There are apparently some 900 luni-solar monuments still standing in Britain alone, and there is also the apparent use of a standard unit of measure throughout the length and breadth of the British Isles to contend with. The latter measure - the "megalithic yard" (MY) of 2.72 feet - was determined from statistical analyses carried out by the late Alexander Thom^15,16 as described in part in his Megalithic Sites in Britain¹⁷ based on the analysis of some 600 sites. There are, it seems, literally thousands of them.¹⁸ This is especially curious in a country that was not even unified by the time of the Roman Conquest some two millenia later. But there is more. In addition to the astronomical aspects of these sites Thom's careful analysis also included the mathematical and geometrical elements underlying the construction of the various types of stone circles. His research - reinforced by statistical analysis - indicated among other things the use of "pythagorean" triangles, although not necessarily the explicit understanding of the pythagorean theorem itself. Thom noted that with the hypotenuse limited to 40 that there were six such sets:


and that:

Megalithic man knew at least three of these. He may have known all six ... The remarkable thing is that the largest, the 12, 35, 37, was known and exploited more than any other with the exception of the 3, 4, 5 ¹⁹

A further surprise lies in the apparent use of a value for pi of 3.125, i.e., 25/8, or three and one eighth. Thom explained this in the context of the diameters and the circumferences of the Megalithic stone circles as follows:

there are concentrations at diameters 10, 20, 30 and 40 MY but only a few at 15, 25, and 35. The concentrations at 4, 8, 12, 16, 20, 24 and 28 are obvious. The reason for this last sequence becomes evident when we consider the circumferences.
The Circumferences
Perhaps the most striking feature is that large concentrations occur at 12.5, 25, 37.5, 50, 62.5, 75 and 87.5, all multiples of 12.5. If we accept the approximation = 3.125 then a circle with a diameter of 4 has a circumference of 12.5. So the above sequence of circumferences follows from a diameter sequence 4, 8, 12, etc. This immediately explains why there are so many circles with a diameter of 8 or 16, since these have circumferences very close to 25 and 50 MY.
For the larger circles the error in taking = 3+1/8 would begin to show up seriously. In fact with a diameter of 28 the approximation = 3 + 1/7 gives P = 88 and we may suppose that this rather than the poorer value of 3+1/8 x 28 or 87.5 was the reason for the four circles having this diameter. The reader may also have noticed the small groups at diameters 7, 14, and 21. Turning to the large holes beyond the range of Fig 5.1 we find:

Aubrey Holes, Stonehenge, D = 105 MY giving P = 329.87
Avebury (inner Ring), D = 125, P = 392.70
Brogar, D = 125, P = 392.70
Stanton Drew, D = 137, P = 430.39

If these circumference are all intended to be multiples of 2.5 we can write them 330, 392.5 and 430 giving the interesting approximations for pi of 3 +1/7, 3.1400, and 3.139.²⁰

Perhaps it is redundant, but in case it is not immediately apparent, the concentrations of the radii in the second set are in turn 2, 4, 6, 8, 10, 12 and 14; alchemists and others might also have noticed the sequence 7, 14, and 21 in terms of the motion of the moon. One further point that needs to be noted here is that there appears to have been an additional requirement on the part of the Neolithic constructors to emphasize and integrate the factor 2.5 into their methodology. As for their general competence, Thom states:

There is ample evidence that, when they wanted, these people could measure with an accuracy better than 1 in 500, so it is certain that they knew what they were doing when they made adjustments.²¹

How did they manage to measure to such accuracy? Thom's detailed statistical analysis applied to the determination of the Megalithic Yard led him to conclude that:

An estimate of the standard error can be made by the formulae given and so the data of the main table (Table 5.1) give finally:

1 MY = 2.720 +- 0.003 ft.

A further conclusion is that this unit was in use from one end of Britain to the other. It is evident from Table 5.5 that it is not possible to detect by statistical examination any difference between values determined from English and Scottish circles. There must have been a headquarters from which standard rods were sent out but whether this was in these islands or on the Continent the present investigation cannot determine. The lengths of the rods in Scotland cannot have differed from that in England by more than 0.03 in. or the difference would have shown up in Table 5.5. If each small community had obtained the length by copying the rod of its neighbour to the south the accumulated error would have been much greater than this.²²

Given the relatively small size of this land, its large population, numerous roads, railways, and many farms, the above information and the number of megalithic sites still extant is truly remarkable. The number itself poses serious problems, not only those associated with necessary support and social organization, but also the engineering competence and the mathematical/astronomical elements implicit in many of them. For how does one go about such work without mathematics and without record keeping? Then there is the apparent use of a standard unit of measure and temporal continuity, i.e., the better known site at Stonehenge in southern England dates from 2750 BC, but the structure nevertheless underwent a series of modifications which extended over a period of 1000 years, far, far beyond all requirements to establish calendaric norms etc. But apart from vague theorizings about primitive religions and primitive mathematics - which like almost all else associated with such monuments cannot be substantiated - no real explanation exists to account for the complexity of the sites, their enormous numbers and their wide-spread distribution throughout England, Scotland, Ireland and Wales.

Details from Alexander Thom's Megalithic Sites in Britain (1967, 1971) are provided below for those who might wish to judge this complex matter for themselves:

   We could certainly and safely remain with prevailing viewpoints, ignore much of Thom's careful mathematical and astronomical analysis, and assign these structures to the activities of little known inhabitants of Megalithic Britain. But if we do so we can go no further. Alternatively, we can seek external builders and sufficient purpose (if not due cause) for their being there. An external influence poses severe difficulties to be sure, but it might nevertheless furnish explanations and origins for some of the oddities described above. Not that they are necessarily that odd in any case, just a long way from home, perhaps. We do know from the mathematical cuneiform texts of the Old Babylonian Period [1900-1600 BC] that the use of "pythagorean" triangles is well attested both in general and in more complex contexts (i.e., Plimpton 322), and that the approximation for pi of three and one eighth (25/8 ) is also attested and applied to the circumferences of circles. One point of possible relevance here is the obvious convenience of the latter approximation over the more accurate ratio 22/7 in base-60, i.e., in sexagesimal notation 22/7 = 3 + 1/7 = 3;8,34,17,8,34,17,8,34,17,.. which is an inconvenient repeating sexagesimal number, as is its reciprocal. The more accurate 22/7 might still have been required, but as Thom suggests, it may have been reserved for the largest of the stones circles with the more convenient approximation 25/8 = 3 + 1/8 = 3;7,30 (reciprocal = 0;19,20) employed in less critical applications. In any event, for the latter estimate, four "pi" (25/2 ) is simply 12;30, i.e., the factor 12.5 mentioned above in the same context with the approximation 25/8. In addition, the other two working estimates determined by Thom - 3.1400 and 3.139 - are also convenient numbers in sexagesimal notation, i.e., 3;8,24 and 3;8,20,24 respectively. Lastly, the same convenience is again apparent in the conversion of the Megalithic Yard to base-60, i.e., 1 MY = 2.720 = 2;43,12 (for the curious, e in base-60 is 2;43,5,48,52,..)

   Unfortunately, even though considerable mathematical skill is attested in the texts of the Old Babylonian Period there are no astronomical texts of comparable quality to draw on. On the other hand, the details and methodologies provided in the Babylonian astronomical cuneiform texts of the much later Seleucid Era [310 BC - 75 AD] were entirely unknown and unsuspected until the latter half of the Nineteenth Century. Thus as far as the earlier period is concerned the adage "Absence of Evidence is not Evidence of Absence" is certainly applicable in our present context given that the mathematical expertise was already highly developed and indisputably in place.
   As for the significance of Britain in this context, one should bear in mind that although thousands of megalithic sites are scattered throughout Europe with standing stones erected "from Denmark to Corsica" ²³ the location of Stonehenge in England is critical in its own right, and that the further north luni-solar monuments lie, the better will be the delineation of the two major luminaries with respect to such phenomena as sunrise, sunset, moonrise, and major standstills etc. One further point to be made here is that from the south-west tip of England to the northernmost limit of mainland Scotland one can never be more than sixty miles from the sea, yet the region extends almost a thousand miles northwards with coastal-hopping/maritime access to the North, East, West and all the outlying Islands. The latter considerations apply to Northern Scotland and Ireland especially, but as elsewhere, we still need to find sufficient reason for the expenditure of so much energy and intellectual effort on the construction of astronomical monuments, not only those in Britain, France and the rest of Europe, but also the massive and more complex structures found in Egypt, Mexico, Peru, and Bolivia.

In general, certain features seem to present themselves more often than not. The first would appear to be a strong focus on the extremal movements of the sun and the moon, especially the former with further emphasis on solstitial events. In certain instances the constellation of Orion and its "belt" appear to take on some degree of importance, while the amount of time, effort, and resources expended implies both a sound reason and a definite purpose behind their construction. The enigmatic features of such structures have attracted attention for decades (if not centuries) but more recently a number of independent researchers have suggested that conventional wisdom concerning the relatively recent rise of civilization on Earth may be in need of revision. Although not in keeping with prevailing viewpoints, the works of Charles Hapgood ²³ (Maps of the ancient Sea-Kings), Colin Wilson²⁴ (From Atlantis to the Sphinx), Michael A. Cremo and Richard L.Thompson ²⁵ ( Forbidden Archeology), The Hidden History of the Human Race ²⁶ and the antarctic hypothesis of Rand and Rose Flem-Ath ²⁷ (When the Sky Fell: The Search for Atlantis) all reflect this concern. To which may also be added the further conclusions of John Anthony West  and Robert Schoch concerning the antiquity of the Sphinx, the astronomical theories concerning the purpose of the Pyramids proposed by Robert Bauval ²⁸ and Adrian Gilbert (The Orion Mystery), the latter's 1995 research with Maurice Cotterell ²⁹ (The Mayan Prophecies) and Graham Hancock's ³⁰ integration of the ancient and the modern in his 1996 publication, Fingerprints of the Gods.³² With respect to all such works, it is no doubt necessary to take heed of the opinions of archeologists on matters of archeology and likewise respect those of Egyptologists concerning Ancient Egypt. But by the same token, it is equally necessary (as in the age of the Sphinx) to defer matters pertaining to weathering and aging to climatologists and geologists respectively. This measured approach should, one would hope, also be extended to embrace the astronomical alignments of ancient monuments and further include the mathematical proportions provided by Schwaller de Lubricz and John Anthony West for the Temple of Luxor, both in the original work and in West's more recent Serpent in the Sky³¹
The questions posed by the latter, the Sphinx, the mathematical relationships inherent in the Great Pyramids and astronomical monuments scattered around the world have undoubtedly given rise to a bewildering variety of mathematical, astronomical and celestial hypotheses concerning origins and ultimate purposes. But to what extent any of them truly represent the intention of the builders has still yet to be established with any degree of certainty. In addition to the various theses proposed in support of earlier dates for such monuments as the Sphinx and the Pyramids there are writings that hint of even greater antiquity - as discussed by H.P.Blavatsky in the Secret Doctrine. Here is a source that provides numerous references and rare material that might aid the quest for understanding with or without the acceptance of hoary antiquity also evident in the work. But if we do reject the latter possibility out of hand, then we are still left with the uncomfortable conclusion that the ancients builders must have been motivated by something of unprecedented magnitude to have embarked on such massive enterprises. This problem underlies most (if not all) unconventional approaches to the enigmas of our past. It was also discussed at some length in Graham Hancock's recent Fingerprints of the Gods (1996). In fact, towards the end of the book the latter presented the following hypothetical scenario:

Suppose that we had calculated, on the basis of sound evidence and beyond any shadow of a doubt, that our civilization was soon to be obliterated by a titanic geological cataclysm - a 30 displacement of the earth's crust, for example, or a head-on collision with a ten-mile wide nickel-iron asteroid traveling towards us at cosmic speed.

Of course there would at first be much panic and despair. Nevertheless - if there were sufficient advance warning - steps would be taken to ensure that there would be some survivors and that some of what was most valuable in our scientific knowledge would be preserved for the benefit of future generations.

Strangely enough, the Jewish historian Josephus (who wrote during the first century AD) attributes this behaviour to the clever and prosperous inhabitants of the antediluvian world who lived before the Flood 'in a happy condition without any misfortunes falling upon them' 'They also were the inventors of that peculiar sort of wisdom which is concerned with the heavenly bodies, and their order. And that their inventions might not be lost - upon Adam's prediction that the world was to be destroyed at one time by the force of fire, and at another time by the violence and quantity of water - they made two pillars, one of brick, the other of stone: they inscribed their discoveries upon them both, that in case the pillar of brick should be destroyed by the Flood, the pillar of stone might remain and exhibit these discoveries to mankind; and also inform them that there was another pillar of brick erected by them.³³

PYRAMIDS OF STONE, BRICK, ROCK AND EARTH
Before expanding on the implications of the above it is worth digressing to consider the account of the pillars of brick and stone at its face value. Ideally, the scheme should work both ways with the structures located in two separate geographical regions. And if there were indeed real concerns that the pillar of brick might be destroyed by a flood, then it would also be reasonable to suppose that it might have been built on high ground, constructed inland, or both. Lastly, there would also be a reciprocal requirement for each monument to point to the location of the other. From this viewpoint the reference to Adam in the above passage supplies a vital clue which suggests that the pillar of bricks might still exist and even where it might be located, i.e., on the island of Sri Lanka. One of the themes that repeatedly surfaces throughout discussions concerning ancient wisdom is that a sound knowledge of geography is inherent in the locations of many of the ancient monuments. Given that the island of Sri Lanka (Ceylon) was in any case strategically located on the trading routes between the Middle and the Far East, knowledge of the latter in Ancient Egypt is not out of the question even from a conventional viewpoint. Now as it happens, in the heart of Sri Lanka lies "Adam's Peak," a 7,200 foot mountain. As the Sun rises in the East the mountain's shadow retreats to the West - a distinct, even shadow in the familiar shape of a pyramid. This renowned phenomenon has long been observed and honoured by Buddhists, Moslems, Christians and others alike, each within their own specific frames of reference. Further north, although still in the interior of Sri Lanka lies the ancient and sacred city of Anuraphapura with its buddhist temples and ancient monuments. Dr. Roland Silva discussed the restoration of three large towers there in a recent televison documentary ("Ancient Stones of Sri Lanka," Marathon Productions, 1996). Dr. Silva carefully and helpfully recounted that:

"When I walked around these sites ... my mind went back to the pyramids of Egypt. But when I compared the measured sizes of the monuments, they were only 25 meters short of the three pyramids of Egypt - with just one difference - that the pyramids were of stone, and that these were the largest monuments of brick of the World and Mankind."

Interestingly, part of the restoration of these monuments appears to have entailed the replacement of bricks to the exterior - made necessary, no doubt, by the latter's utility, availability and predictable disappearance. In the present context the use of bricks might be considered a necessity since it is central to the story, but it would perhaps be preferrable in the long term to employ large, heavy and/or customized components to ensure a degree of permanence.
The occurrence of a second major pyramid raises the intriguing possibility that there might be some substance to the following comment by H.P. Blavatsky in the Secret Doctrine (Vol. 2, p.351) even though the latter places little emphasis on the Egyptian component and the reference is itself most obscure:

"The GREAT DRAGON has respect but for the ' SERPENTS' of WISDOM, the Serpents whose holes are now under the triangular stones," i.e., "the Pyramids, at the four corners of the world."

Thus, taking our cues from the above we would expect to find at least two more major monuments, both in distant and separate settings. Should this pair of pyramids be constructed of the same materials as the others, or was there a concept of massive redundancy that included further diversity? Because if it did, then it makes the locations of the other two slightly less problematic. In other words, we might perhaps search for (a) a Pyramid of Rock and (b) a Pyramid of Earth. While not ignoring the structure at Teotihucan (Mexico) we might then tentatively associate the Pyramid of Rock with pyramid-shaped Mt Huyama, the adjacent companion to Machu Pichu (Peru) in South America. The Pyramid of Earth on the other hand raises some intriguing possibilities, for there are two major structures in the United States that might indeed fit the bill - Cahokia in Illinois, and the Emerald Mount along the Mississippi-Natchez Parkway. James Q.Jacobs states in a private communication that in terms of size the most obvious choice would be: "Monk's Mound at Cahokia, beyond a doubt. In volume it surpasses all," although he also cautions that there are other sites to be considered in the Americas, e.g., "... Saxsayhuaman in Cuzco. It is a terraced mound and has some of the greatest stones ever placed by humans. It was at the center of Tawantinsuyu, the land of the four directions, the Inca realm. It is truly immense....The Pyramid of the Sun in Mexico and Huaca del Sol in Peru, both adobe pyramids. Pachacamac is also worthy of consideration. It is a converted hill and very immense also." All of which no doubt need to be addressed, the marked temporal, cultural and geographical differences associated with the four "pyramids" notwithstanding. But if there was indeed some grand scheme, then who is to really know on what scale it was conceived, where it was to be carried out and how long it was intended to run.

Returning to the catastrophism thesis raised earlier by Hancock, the latter next recounted that:

... when the Oxford astronomer John Greaves visited Egypt in the seventeenth century he collected ancient local traditions which attributed the construction of the three Giza pyramids to a mythical antedeluvian king:The occasion of this was because he saw in his sleep that the whole earth was turned over, with the inhabitants of it lying upon their faces and stars falling down and striking one another with a terrible noise...And he awakened with great fear, and assembled the chief priests of all the provinces of Egypt ... He related the whole matter to them and they took the altitude of the stars, and made their prognostication, and they foretold of a deluge. The king said, will it come to our country? They answered yes, and will destroy it. And there remained a certain number of years to come, and he commanded in the mean space to build the pyramids ... And he engraved in these Pyramids all things that were told by wise men, as also all profound sciences - the science of astrology, and of Arithmecke, and of Geometry, and of Physicke. All this may be interpreted by him that knows their characters and language.³⁴

Hancock finally suggested:

Taken at their face value, the message of both of these mysteries seems crystal clear: certain mysterious structures scattered around the world were built to preserve and transmit knowledge of an advanced civilization of remote antiquity which was destroyed by a terrifying upheaval.

Could this be so? and what are we to make of other strange traditions that have come to us from the dark vault of prehistory.

What are we to make, for example, of the Popul Voh, which speaks in veiled language about a great secret of the human past; a long forgotten golden age when everything was possible - a magical time of scientific progress and enlightenment when the 'First Men' (who were 'endowed with intelligence') not only 'measured the round face of the earth' but 'examined the four points of the arch of the sky.'

... The secret of what happened was never entirely forgotten because a record of those distant First Times was preserved, until the coming of the Spaniards, in the sacred texts of the original Popol Vuh. The abuses of the conquests made it necessary for that primordial document to be concealed from all but the most highly-initiated sages and replaced by a watered-down substitute written 'under the law of christianity': 'No longer can be seen the book of Popol Vuh which the kings had in olden times ... The original book, written long ago, existed - but now its sight is hidden to the searcher and to the thinker...'

On the other side of the world, among the myths and traditions of the Indian subcontinent, there are further tantalizing suggestions of hidden secrets. In the Puranic version of the universal flood story, shortly before the deluge was unleashed, the fish god Vishnu warned his human protégé that he 'should conceal the Sacred Scriptures in a safe place' to preserve the knowledge of the antideluvian races from destruction. Likewise, in Mesopotamia, the Noah figure Utnapishtim was instructed by the god Ea, 'to take the beginning, the middle, and the end of whatever was consigned to writing and then bury it in the City of the Sun at Sippara' [emphases supplied]

.... After the waters of the flood had gone, survivors were instructed to make their way to the site of the City of the Sun 'to search for the writings', which would be found to contain knowledge of benefit to future generations of mankind.

Strangely enough, it was the City of the Sun in Egypt, Innu, known by the Greeks as Heliopolis - which was regarded throughout the dynastic period as the source and centre of high wisdom handed down to mortal men from the fabled First Time of the gods. It was at Heliopolis that the Pyramid Texts were collated, and it was the Heliopolitan priesthood, or rather Heliopolitan cult - that had custody of the monuments of the Giza necropolis.³⁵

Hancock's hypothesis, reached after more than 500 pages of discussion and a wealth of detailed references was that certain monuments might contain valuable information, if not the prevailing wisdom of the time, deliberately incorporated or buried in their structures. As a corollorary, the monuments might also provide the much needed reason for their actual construction in terms of the event itself. But having made this suggestion it is necessary to emphasize that it is not necessarily beneficial to defer the technical and mathematical knowledge inherent in the construction of such monuments to extra-terrestrial help and/or lost civilizations, even though such possibilities cannot be entirely discounted. On the other hand, if we consider that the monuments were largely the product of unthinkable toil, extremes of hardship and the very best that the minds of those times could muster, then we most assuredly need to determine exactly what it was that motivated them, how well the matter was understood, and how much of it they managed to pass down to us.
Thus we arrive back at the original question only to add three more. What could it have been that precipitated such an extreme response? Was it indeed the result of some major catastrophe - fire, flood, earthquakes, or all three, and did this generate an overall scheme to investigate the matter, to delineate it as best as possible, and also to pass the details on? And, covering all eventualities, what would have been the plan for the worst-case scenario?

If we are to pursue this last possibility at all, then we should first consider the enormity of the task, for how does one pass on a complex corpus of information and a specific, technical message if one allows that the parent organization, be it city-state, country, or civilization might be seriously diminished by floods, earthquakes and fire? Embracing all possible scenarios, it seems that whatever was to be done would have to meet a number of critical base requirements. First of all, the structures would have to be made earthquake proof; fireproof, and flood proof. And allowing that even this might not be sufficient at any one location, a strong measure of redundancy would also have to be factored into the scheme. Next, all structures and information-bearing media might in the worst case scenario have to last for centuries, if not millenia. Thus the scheme should exclude the use of materials that are perishable, portable, useful, or valuable, while rock, stone and clay are plentiful and for the most part also durable. As a rider it would also be advisable to utilize heavy or highly customized components to render them immovable, basically useless elsewhere and earthquake proof to boot. The massive, fitted irregular stone walls at Machu Pichu, Tiahuanaco, and Cuzco come to mind here, as do the huge stone blocks utilized in ancient Egypt and the enormous stones utilized in Neolithic monuments from the Mediterranean to Northern Europe. The same argument concerning longevity would also apply to the erection of luni-solar monuments in austere and inhospitable regions (e.g., the remote Scottish Isles) and unlikely locations such as the mountain-top placement of Machu Pichu in Peru. And if these construction projects could only be accomplished by prodigious effort, then this too might serve the vital purpose of generating the question that still concerns us today: why was it deemed necessary to go to so much trouble in the first place?
The above simply represent some of the physical requirements; far more complex would be the social organization, planning, and integral construction of the desired information, which would appear to require a strong focus on the Sun and the Moon, and hence relatively advanced knowledge of mathematics and astronomy. To cope with this kind of specialized information there would be a need for education, training, continuity, and yet perhaps allowances to offset a cataclysmic loss of information during the event itself. Which means that each structure might also have take on the function of a self-starter, i.e., just about where we are today. To facilitate this it might have been deemed necessary to provide alternative approaches allied to common themes, still redundancy per se, but with elements of connectivity nonetheless. The most obvious, it would seem, would be the emphasis on the extremal movements of the Sun, captured and delineated by stone structures, with parallels perhaps, in both written and oral traditions. In the former case this would obviate a need to provide multiple documentation and vital attendant keys. Although not necessarily for this precise reason, the Rosetta Stone and the triple texts carved on a precipitous rock-face copied by Rawlinson come to mind here, i.e., these were the keys that led to the eventual decipherment of Egyptian hieroglyphics and Mesopotamian cuneiform. Perhaps the worst case scenario would embrace the possibility of a near complete loss of previous knowledge, which would lead to an initial dependancy on oral traditions, both those that survived and those that included the event and whatever mythos grew up around it. Or alternatively, information-loaded myths and religious beliefs could be premanufactured to carry at least part of the message. This could be entrusted to specific groups to ensure that it was, but here one unfortunately enters the swampy grounds of organized religion and secret societies, which also historically appear to have played rôles in this matter. What exactly would be the overall purpose? This is hard to say, but remaining with the notion of a highly competent but not necessarily technologically advanced civilization, one could theorize that it might have been to preserve or pass as much as was known about the event to both warn and enable future generations to explore the matter more thoroughly. As for general education and training, this would represent another enormous task, which again might involve oral and written traditions, shielded perhaps by secrecy yet augmented by multiple redundancy. We have already remarked on the significance of "Homer's Golden Rope" in this context (see Section V ) and also the following quotations from Proclus and Plato on this particular aspect, i.e.,

Plato, for the sake of concealment, employed mathematical names, as veils of the truth of things, in the same manner as theologists employed fables, and the Pythagoreans symbols. For it is possible in images to survey paradigms, and through the former to pass to the latter. [Proclus]

[The Sophists]... fearing the odium which it brings, adopted a disguise and worked under cover. Some used poetry as a screen, for instance Homer and Hesiod and Simonides; others religious rites and prophecy, like Orpheus and Musæus and their school; some even ... physical training, ... [while] Music was used as a cover by ... many others [Plato: Protagoras (316d-317B) emphases supplied]

As for the scope of the scheme, in technical terms, to increase the odds of the message getting through it would be preferrable to make it global in extent to disperse the information as wide as possible. If such an expansion was to be carried out, then a sea-going capability would also become a necessity, but generally speaking, it is not thought that the Egyptians or indeed anyone possessed any highly developed maritime expertise in the earlier periods. On the other hand, it seems from recent discoveries in Egypt that the former apparently possessed a number of superb sea-going vessels and there is a growing diffusionist trend towards earlier contact in the Americas (for further edification, see Ann Harrison's Diffusionism Page). Reasons for such journeys might have included passing information on to as many cultures as possible - not only regarding the event, but also perhaps requisite layouts and building techniques (for an intriguing suggestion concerning this latter possibility and the origins of Freemasonry, see Hippolyto Joseph Da Costa's 1820 Sketch For The History of The Dionysian Artificers).

The which Scottish Nation, journeying from Greater Scythia by the Tyrrhene Sea and the Pillars of Hercules, could not in any place or time or manner be overcome by the barbarians, though long-dwelling in Spain among the fiercest of them.... [ translation by Agnes Muir McKenzie from the copy in the Register House at Edinburgh].

One further point to be borne in mind here is that the ready maritime and riverine access in Britain would undoubtedly facilitate the work in question since it would be both feasible and preferrable to ship/barge large blocks of stone upriver as far as possible by both tidal flow and towing etc., to minimise the task overland. Moreover, it cannot be denied that the Egyptians in particular were more than familiar with both practices, and on a far greater scale at that.

The Egyptian component runs inexorably below the surface of much of this inquiry and it also provides further insights concerning both origins and linkages. Ancient Hermes - of great importance to Alchemy -was many things, but not least of all, among his various names he was also the messenger of the Gods. Moreover, his "Emerald Green Tablet" is fortunately one of the better-known Alchemical and Hermetical works that have come down to us. As for Hermes himself, Jack Lindsay notes that:

"Diodoros sets out the general Hellenistic view:

'According to them [the Egyptians], it was by Hermes that the common language of mankind was first further articulated and many objects still nameless got an appellation; that the alphabet was first invented and ordinances dealing with the honors and offerings due to gods were properly established. He was the first also to observe the orderly arrangement of the stars and the harmony of musical sounds and their nature ...He also made a lyre and gave it 3 strings, imitating the seasons of the year; for he adopted 3 tones, a high, a low, and a medium: the high for the summer, the low for the winter, and the medium for the spring. ... The Greeks were also taught by him the expounding, hermenia, of their thoughts, and for this reason he was named Hermes. In a word, Osiris, taking him for his priestly scribe, communicated with him on every matter and used his counsel above that of all others. The olive tree also, they assert, was his discovery, not Athena's as the Greeks say. ..."The Souda says he was the discoverer of metals, especially gold, silver, and iron ... "

"Tertullian for the Christians cited Hermes Trismegistos as the master of all who concern themselves with nature (scientists of any kind). Iamblichos and Galen rationalized the legends. The first wrote, 'Our ancestors decanted to him the discoveries of their science, having agreed to attribute everything to Hermes.' The latter, 'In Egypt, all that has been discovered in the arts was submitted to the general approbation of the sages; then it was inscribed without its author's name on columns kept in the sanctuary. Hence the multitude of works ascribed to Hermes' Iamblichus put the total of his books at 20,000, according to Seleukos, Manethos made it 36,525. As the second number is divisible by 1461, the number of years in the Sothic period of the Egyptian calendar, it seems that some astronomic calculation intruded..." ³⁵

'There are those,' said Hermes, 'Who will thoroughly know all the secrets of my writings and interpret them, and even if they retain some of them for themselves alone, others among them that are for mankind's benefit they'll engrave on stelai and obelisks.

Iamblichos, dealing with Hermes' account of the universe, tells us of ' the most ancient principles of things - the self-born Father dwelling in the solitudes of his own unity - which are set above the ethereal and igneous gods and the celestial gods. Of the igneous gods Hermes has left a hundred works, of the etherial another hundred, and of the celestial a thousand. [italics supplied] ³⁶

But was there more to the scheme than simply the engraving of knowledge on stelai and obelisks? If there was, then who is to know on what scale it was conceived, how long it was meant to run, and whether it was indeed intended to be truly global in its extent. Such a plan is conceivable, surely, and from what we have already seen in the previous sections, "The Great Work" of the Alchemists might reasonably represent one of the principle components, carrying with it as it does much information, including vital elements of astronomy, mathematics and emphasis on both the Sun and the Moon.
Because of the above and the prominence given in alchemy to Hermes and his alleged Emerald Green Tablet it is worth examining the contents of the work in some detail. But it is also important to be aware from the outset that this is not a simple matter, nor is it one that can necessarily be finalized with any degree of certainty, as Cohn de Toraeke observes with due caution in his own introduction to the material:

This 13 stanza verse may be, to those who understand it, one of the most profound examples of wordmanship ever recorded. To this writer, these words hold within their scope the essence of all scripture, myth, and spiritual metaphor.
The following interpretation of the Emerald Tablet of Hermes is offered by this writer who has spent many years contemplating, and proving, its content. My intent is only to aid those whose inner being responds to the tablet's song. Please understand that there are as many interpretations as there are interpreters, but there is only one Tablet. Did Hermes write it? Was there such a person, after all? We cannot be sure, nevertheless, the words are before us and they resonate with the truth and power of their meaning.
Each person who is drawn to the Emerald Tablet will have their own ideas and understanding of it, as it should be. Hopefully, some of these ideas will be shared so that everyone may benefit. No one person, in my opinion, can comprehend all that these words contain. - Cohn de Toraeke. (for the latter's analysis see: A Commentary on the Emerald Tablet)

From our own viewpoint, however, the tablet's somewhat cryptic contents suggest that we might find a clue here, if not further guidance - an overview perhaps or a succinct summary. There are, it seems, a variety of versions of the Tablet (see Emerald Tablet of Hermes by Jon Marshall); that provided by Jack Lindsay in The Origins of Alchemy in Graeco-Roman Egypt (1970) is given below with line numbers added to aid the subsequent commentary.

The above lines may be examined from many viewpoints ranging from the Theological through the Biological to the Astronomical, or as some might have it, all three inclusively. From our present viewpoint we may add that it might also represent a compressed summary or an initial statement concerning the present inquiry. As a start, the first line establishes the veracity of the matter for any and all interpretations, but we suspect from the analysis of many megalithic monuments that the movements of the Sun (line 06) and Moon (line 07) are of major importance, and that Earth (lines 07, 09, 10, 11) and its various motions are integral factors in the same context. We can also see that the well-known adage: "What is above is like what is below, and what is below is like what is above" (lines 2 and 3) is in effect a definition of symmetry in addition to expressing the ratios between the reciprocal of Phi, Unity, and Phi itself, i.e., the ratios of any three successive periods of the phi-series based planetary framework. It is also, as we have seen in earlier sections, descriptive of the manner (utilizing fractional exponents, but still powers) in which the mean parameters of the superior planets may be seen to feed back into those of the inferior planets in the same series.
Line 10: "Separate Earth from Fire, the Subtle from the Gross, smoothly and with judgement" could be interpreted as the invocation of the heliocentric concept with its attendant complexities which are already implicit in the above-mentioned ratios in any case. Those who might object should at least recognize that if this is indeed a complex matter, then the attendant information is also likely to be complex.
If we backtrack slightly to recall that we suspect the astronomical monuments contain both useful information and also a "message," and this is indeed so, then we require two more parts to solve the puzzle - namely the instructions, and the understanding, i.e., we will require all "three parts of the wisdom" (line 16). And lastly, in case the point is not abundantly clear by now, we apparently also need to know that the matter concerns "the operation of the Sun" (line 17).
The meaning of line 6: "Its father is the Sun, its mother is the Moon" we will defer to a later time. Even so, one should nevertheless be aware that some alchemical interpretations equate four parts of Mercury with the Moon in this context (see The Glory of the World for this application). There are also similarities and differences in the various extant versions of the Tablet. The following selections are from material prepared by Jon Marshall (The Emerald Tablet of Hermes) which was sadly introduced with the following note: "Many years ago, a group of people decided to publish different translations of the Emerald Tablet and various commentaries upon it. The group broke up, the work was never finished.... Here is some of what remained. Verses have been numbered for comparison. - Jon Marshall."
The work itself includes a short historical overview of the Tablet and the complete variants from which the lines below have been chosen.

E: From Idres Shah
2 ) What is above is like what is below. What is below is like what is above. The miracle of unity is to be attained.
4) Its parents are the Sun and Moon.
13) I am Hermes the Threefold Sage, so named because I hold the three elements of all wisdom.
14) And thus ends the revelation of the work of the Sun.
[Shah 1964: 198]. [emphasis supplied]

AN ENIGMA OF THE SAGES.
In which the underlying substance of the Art, called the Phoenix of the Sages, is found to be thrice threefold.
If I tell you three parts of a thing you have no cause to complain. Seek one of three, and of the three one will be there: for where there is body and soul, there is also Spirit and there shine salt, sulphur, and mercury. Trust my word, seek the grass that is trefoil. Thou knowest the name, and art wise and cunning if thou findest it.

ANOTHER ENIGMA (Much easier.)
There is one thing in this world which is found occasionally. It is bluish-grey and green, and, wonderful to say, there is in this thing a red and white colour. It flows like water, yet it makes not wet ; it is of great weight, and of small. I might give it a thousand names, yet the thousand know it not. It is mean to look upon, yet to the Sage it is precious. He who solves it with the second and condenses it with the third, he has our glorious subject.

RIDDLE.
There are seven cities, seven metals, seven days, and the number seven; seven letters, seven words in order meet, seven times, and as many plates; seven herbs, seven arts, and seven stones. Divide seven by three, and thou shalt be wise. No one will then strive to precipitate the half. In brief, all will proceed favourably in this number. [emphases supplied]

The second enigma - purported to be "much easier" - would appear to be just that, since it is sensibly understood to pertain to the "Philosopher's Stone" itself. The first sentence of the Enigma of the Sages on the other hand is perhaps best understood in terms of the major superior planet Saturn, the triple interval [1,3,9,27] and the mathematical instructions provided in the last riddle. Neither need concern us at present, except to note the reference to herbs in this same context. Continuing with the Enigma of the Sages, we have already met the triadic set: "body," "soul," and "spirit" in Section VI in both alchemical and strictly quantified astronomical contexts, - Distance, Period and Velocity respectively - and true enough, if any one parameter is known the remaining pair are readily obtainable. The phrase: "seek the grass that is trefoil" is, however, both new and intriguing. We are already aware of the proliferation of names assigned to the Philosopher's Stone, the numerous allegories, and the multifarious divisions within additional groupings, i.e., animal, vegetable and mineral, etc. But here is something else pertaining to herbs that has apparently been accorded special significance. It is undoubtedly a clue, but what exactly might it mean?
We can see immediately that it could refer to Ireland in general and Newgrange in particular in so much as the well-known symbol of Ireland - the Shamrock - is undoubtedly trefoil, and so in a similar configuration and sense is the triple spiral illuminated at the Winter Solstice at that location. In this sense we are neither cunning nor wise in so much as we have in effect backed into the matter. The shamrock itself is apparently clover and also the herb sorrel according to The Sunset Book of Western Gardening ³⁷ - an aptly named reference that identifies the latter as:

Medicago lupulina (hop clover, yellow trefoil, black medick), an annual plant; Oxalis acetosella (wood sorrel) or Trifolium repens (white clover). The last is the most common. All have in common leaves divided into 3 leaflets (symbolic of the Trinity)³⁵ [italics supplied]

with Trifolium repens minus one of the varieties sold as shamrock.

This may or may not be sufficient for our present purposes, but in passing it must be observed that it is Oxalis regnelli (or the dark-leaved acetosella) that is by far the most remarkable of the trefoil shamrocks.

It is in fact a most unusual and impressive plant, especially for those acquainted with Plato's mathematics. Specifically, the plant is described as having an "Erect stem to nearly 1 ft.tall has many long-stemmed drooping leaves, each with 3-in.-long leaflets shaped like triangles attached by their points - three quarters of an iron cross." ³⁸  The latter description is somewhat misleading, odd though it is. The trefoil configuration appears to be more symmetrical, i.e., when open in essentially two dimensions it is more triadic with each leaf approximately 120 degrees from the other, while the configuration in three dimensions is also subject to remarkable variation according to the amount of daylight and darkness available. Moreover, there are two distinct "right" triangles for each leaf, triangles with sides that are also in approximate 1:1 ratios.
   But none of the above represent the most remarkable property of this plant, which is the fact that while the leaves maintain their open triadic form during daylight, instead of closing up at the onset of darkness, they fold outwards and downwards over ninety degrees to form what is in effect a six-sided indented pyramid.
   This is a most cunning allusion if it does indeed pertain to the matter at hand.

EXCURSUS: THE LOTUS FLOWER AND THE EGYPTIANS
With the above example still fresh in our minds, it is now perhaps useful to conside the place and similar significance of the Lotus flower among the ancient Egyptians.
Thus, as explained in Thomas Taylor's Iamblicus on The Mysteries of the Egyptians, Chaldeans, and Assyrians first published in 1821:

The lotus, before the rising of the sun, folds its leaves into itself, but gradually expands them on its rising: unfolding them in proportion to the sun's ascent to the zenith; but as gradually contracting them as that luminary  descends to the west. Hence this plant, by the expansion and contraction of its leaves, appears no less to honour the sun, than men by the gesture of their eyelids, and the motion of their lips. But this imitation and certain participation of supernal light is not only visible in plants, which possess nothing more than a vestige of life, but likewise in particular stones. Thus the sun-stone, by its golden rays, imitates those of the sun; but the stone called the eye of heaven, or of the sun, has a figure similar to the pupil of an eye, and a ray shines from the middle of the pupil. Thus, too, the lunar stone, which has a figure similar to the moon when horned, by a certain change of itself, follows the lunar motion. Lastly, the stone called helioselenus, i. e. of the sun and moon, imitates, after a manner, the congress of those luminaries, which it images by its colour. So that all things are full of divine natures; terrestrial natures receiving the plenitude of such as are celestial, but celestial of supercelestial essences; while every order of things proceeds gradually, in a beautiful descent, from the highest to the lowest. For whatever particulars are collected into one above the order of things, are afterwards dilated in descending, various souls being distributed under their various ruling divinities.”  (Thomas Taylor, Iamblicus on The Mysteries of the Egyptians, Chaldeans, and Assyrians, 3rd Ed., Stuart and Watkins, London, 1968: 344–345).⁴⁰

Continuing with our quest for understanding, we begin to realize that there is an overabundance of keys, hints and enigmas, that they have become inter-mixed, modified, and perhaps even changed drastically from the time of their inception. One could postulate that this may have been deliberate, but there is a alternate and perhaps more logical way of looking at the matter that needs no conspiratorial element whatsoever. The confused situation today may reflect a simple reality - that we are still pulling out of the last event, and this is why things are as they are, and why we are having so much trouble and difficulty getting to the root of the matter even now.

Why have so many symbols of British mythology and esoteric thought found their way into one single church? It is easy to explain why so many esoteric symbols - of the ouroborostime-serpent, of the green man, of zodiacal images, and so on - should be found at Kilpeck church as they are the work of one man. But time and time again one finds certain places attract many mysteries from different ages and sources. This is indeed one of the mysteries of Britain itself. The mysteries are found in the strangest of places, in sites as remote as the Hebridean islands, as accessible as the city of London, in museums, hillsides and in churches - the very places where one might expect miracles, but not mysteries. Indeed, the very number of British mysteries is almost a wonder in itself. Why have these islands been singled out as the repository for such a welter of mysterious remains? Was there something special in the British earth that the ancients should build so many stone circles ,... Whatever the reasons, there are so many centres in Britain where the mind is almost numbed by the weight of mythology and mystery associated with them that one is hardpressed to visit them all in the space of one lifetime.

If one spends time studying the British mysteries, one gradually becomes aware of the extent to which the calendar plays an important part in the secrets hidden behind their forms and symbols. In modern times, expert archaeologists have revealed that the huge stone circles of Stonehenge, Avebury and Callanish were used as complex (if primitive) calendrical machines for determining the cycles of the years in terms of eclipses, sun-settings, sun-risings, and similar lunar points - all phenomena of great importance to the rituals practice by the ancients. Additionally, many of the strange and mysterious customs which have survived, in a more or less garbled form, into modern times are also linked with the symbolism of the calendar - with the zodiacal points, with the four directions of space, with the solstices and the equinoxes, and the sequence of the zodiac. For this reason, if we wish to reach a little more deeply into the mysteries of Britain, it will be as well for us to glance at one or two of the calendrical traditions. When looked at from the point of view of mythology, the British calendar is revealed as a complex thing; some of the events it marks are derived from our first Christian civilizers those Romans who came as soldiers and stayed as monks - and some are distinctly pagan, being even older than the first recorded history of our land. The moment one begins to relate places, architectural forms and mythologies to the calendar, one is faced with the lore of astrology, which attempts to relate man to the cosmos and to the earth. It is the traditions attached to astrology, in regard to the pictorial imagery revealing the passing of the seasons, or the movement of the sun against the zodiacal belt, and the relationship these were believed to hold to the human being, which account for many of the secret symbols in the British Isles.³⁹ [emphases supplied]

With the above in mind, but with an emphasis on astronomy we seek next the second and third parts of the three wisdoms, specifically the instructions and the phenomenon itself - best approached, as it so happens, in reverse order.