Counting Perimeters

above: a slide from my lecture at Megalithomania in 2015

We know that some paleolithic marks counted in days the moon’s illuminations, which over two cycles equal 59 day-marks. This paved the way for the megalithic monuments that studied the stars by pointing to the sky on the horizon; at the sun and moon rising to the east and setting in the west. It was natural then to them to see the 12 lunar months (6 x 59 = 354 day-marks) within the seasonal year (about 1/3 of a month longer than 12) between successive high summers or high winters.

Lunar eclipses only occur between full moons and so they fitted perfectly the counting of the repetitions of the lunar eclipses as following a fixed pattern, around six months apart (actually 5.869 months, ideally 173.3 day-marks apart). The accuracy of successive eclipse seasons to the lunar month can then improve over longer counts so that, after 47 lunar months, one can expect an eclipse to have occurred about one and a half days earlier. This appears to be the reason for the distance between the megalithic monuments of Crucuno, its dolmen and and its rectangle, which enabled simultaneous counting of days as Iberian feet and months as 27 foot units, at the very end of the Stone Age.

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How Geometries transformed Time Counts into Circles

Above: example of the geometry that can generate one or more circles,
equal to a linear time count, in the counting units explained below.

It is clear, one so-called “sacred” geometry was in fact a completely pragmatic method in which the fourfold nature of astronomical day and month counts allowed the circularization of counts, once made, and also the transmission of radius ropes able to make metrological metrological circles in other places, without repeating the counting process. This “Equal Perimeter” geometry (see also this tag list) could be applied to any linear time count, through dividing it by pi = 22/7, using the geometry itself. This would lead to a square and a circle, each having a perimeter equal to the linear day count, in whatever units.

And in two previous posts (this one and that one) it was known that orbital cycles tend towards fourfold-ness. We now know this is because orbits are dynamic systems where potential and kinetic energy are cycled by deform the orbit from circular into an ellipse. Once an orbit is elliptical, the distance from the gravitational centre will express potential energy and the orbital speed of say, the Moon, will express the kinetic energy but the total amount of each energy combined will remain constant, unless disturbed from outside.

In the megalithic, the primary example of a fourfold geometry governs the duration of the lunar year and solar year, as found at Le Manio Quadrilateral survey (2010) and predicted (1998) by Robin Heath in his Lunation Triangle with base equal to 12 lunar months and the third side one quarter of that. Three divides into 12 to give 4 equal unit-squares and the triangle can then be seen as doubled within a four-square rectangle, as two contraflow triangles where the hypotenuse now a diagonal of the rectangle.

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The Octon of 4 Eclipse Years

Having seen, in the last post, that three eclipse years fitted into the three-year count at Le Manio, another eclipse fact has come to light, recorded within the nearby site of Crucuno, between its dolmen and rectangle. The coding of time at Crucuno was an evolution of a new metrology based upon the English foot in which, the right triangle of longest integer side lengths was replaced by fractions of a foot using the same two numbers as the sides would have had. This allowed the measurement of a time period to be simultaneously seen in both days and months. That this was possible can be seen at Le Manio, where it could be noticed that 32 lunar months equaled exactly 945 day-inches.

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Kerherzo Rectangle near Erdeven & Crucuno

first published in March 2018

In 1973, Alexander Thom found the Crucuno rectangle to have been “accurately placed east and west” by its megalithic builders, and “built round a rectangle 30 MY [megalithic yards] by 40 MY” and that “only at the latitude of Crucuno could the diagonals of a 3, 4, 5 rectangle indicate at both solstices the azimuth of the sun rising and setting when it appears to rest on the horizon.” In a recent article I found metrology was used between the Crucuno dolmen (within Crucuno) and the rectangle in the east to count 47 lunar months, since this closely approximates 4 eclipse years (of 346.62 days) which is the shortest eclipse prediction period available to early astronomers.


Figure 1 Two key features of Crucuno’s Rectangle

About 1.22 miles northwest lie the alignments sometimes called Erdeven, on the present D781 before the hamlet Kerzerho – after which hamlet they were named by Archaeology. These stone rows are a major complex monument but here we consider only the section beside the road to the east. Unlike the Le Manec Kermario and Kerlestan alignments which start north of Carnac, Erdevan’s alignments are, like the Crucuno rectangle accurately placed east and west. 


Figure 2 Two stones, angled to the diagonal of a 3-4-5 triangle 235 feet from north west stone and setting sun at summer solstice
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Lunar Counting from Crucuno Dolmen to its Rectangle

A fuller treatment of this article can now be found in
Sacred Geometry: Language of the Angels (2021).

Figure 1 The entrance of Crucuno’s cromlech, which opens to the south-east
[Summer Solstice, 2007]

It is not immediately obvious the Crucuno dolmen (figure 1) faces the Crucuno rectangle about 1100 feet to the east. The role of dolmen appears to be to mark the beginning of a count. At Carnac’s Alignments there are large cromlechs initiating and terminating the stone rows which, more explicitly, appear like counts. The only (surviving) intermediate stone lies 216 feet from the dolmen, within a garden and hard-up to another building, as with the dolmen (see figure 2). This length is interesting since it is twice the longest inner dimension of the Crucuno rectangle, implying that lessons learned in interpreting the rectangle might usefully apply when interpreting the distance at which this outlier was placed from the dolmen. Most obviously, the rectangle is 4 x 27 feet wide and so the outlier is 8 x 27 feet from the dolmen.

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Educating Megalith Builders at Crucuno rectangle

Around Carnac in Brittany the land is peppered with uniquely-formed megalithic designs. In contrast, Great Britain’s surviving monuments are largely standing stones and stone circles. One might explain this as early experimentation at Carnac followed by a well-organised set of methods and means in Britain. What these experiments near Carnac were concerned with is contentious, there being no appetite, in many parts of society, for a prehistory of high-achieving geometers and exact scientists. Part of the problem is that pioneers interpreting monuments are themselves hampered by their own preferences. Once Alexander Thom had found the megalithic yard as a likely building unit, he tended to use that measure to the exclusion of other known metrological systems (see A.E. Berriman’s Historical Metrology. Similarly, John Neal’s breakthrough in All Done With Mirrors, having found the foot we still use to be the cornerstone of ancient metrology, led to his ambivalent relationship to the megalithic yard. Neal’s interpretation of the Crucuno rectangle employs a highly variable set of megalithic yards, perhaps missing the simpler point, that his foot-based metrology is supported as present within the dimensions of the Crucuno rectangle; said by Thom to be a “symbolic observatory” of the sun: this monument was an educational device, in which Neal finds the geometry of “squaring the circle” which, as we see later, was probably the Rectangle’s main metrological meaning.


Figure 1 Alexander Thom’s survey of Crucuno Rectangle by Alexander Thom, see MRBB, 1978,   19   & 175-176
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