Tag: Le Manio Quadrilateral

Shaping of Stones in Alignments

Megalithic sites are subject to strict evidence criteria regarding solar and lunar alignments. Studies show that stone configurations often indicate astronomical events, with specific shapes reflecting lunar cycles. Notably, the alignment of stones at sites like Le Manio and Carnasserie highlight ancient observation techniques, suggesting intentional design to mark celestial occurrences.

where the sun or moon rose or set at a site can allow a dating due to the tilt of the earth having varied over a very long term cyclicity. One can also see that alignment to such events was a major feature of megalithic monuments, of pointing to sun and moon events. This approach gets even more powerful when day or month counting between alignment events can be measured within the dimensions of a site, using units of length seen belonging to a megalithic culture, like the megalithic yard.

However, another feature of stones at megalithic sites is their shape. When tracking the tracking the moon in time, its phase is changing so that shapes could indicating lunar phase, according to some sort of code. Le Manio Quadrilateral near Carnac shows a great shape variation in the 36 stones of its southern curb of 36, marking the 36 lunar months in three lunar years alongside a day-inch count of 1063 days-inches. This count starts from the Sun Gate from which the summer (and winter) sunrise can be viewed (so that the curb is 14 degrees south of the summer sun line.)

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Counting the Moon: 32 in 945 days

One could ask “if I make a times table of 29.53059 days, what numbers of lunar months give a nearly whole number of days?”. In practice, the near anniversary of 37 lunar months and three solar years contains the number 32 which gives 945 days on a metrological photo study I made of Le Manio’s southern curb (kerb in UK) stones, where 32 lunar months in day-inches could be seen to be 944.97888 inches from the center of the sun gate. This finding would have allowed the lunar month to be approximated to high accuracy in the megalithic of 4000 BC as being 945/32 = 29.53125 days.

Silhouette of day-inch photo survey after 2010 Spring Equinox Quantification of the Quadrilateral.

One can see above that the stone numbered 32 from the Sun Gate is exactly 32/36 of the three lunar years of day-inch counting found indexed in the southern curb to the east (point X). The flat top of stone 36 hosts the end of 36 lunar months (point Q) while the end of stone 37 locates the end of three solar years (point Q’). If that point is the end of a rope fixed at point P, then arcing that point Q’ to the north will strike the dressed edge of point R, thus forming Robin Heath’s proposed Lunation Triangle within the quadrilateral as,

points P – Q – R !

In this way, the numerical signage of the Southern Curb matches the use of day-inch counting over three years while providing the geometrical form of the lunation triangle which is itself half of the simpler geometry of a 4 by 1 rectangle.

The key additional result shows that 32 lunar months were found to be, by the builders (and then myself), equal to 945 days (try searching this site for 945 and 32 to find more about this key discovery). Many important numerical results flow from this.

Origins of the Olmec/Maya Number Sciences

ABOVE: Stela C from Tres Zapotes roughly rebuilt by Ludovic Celle and based on a drawing by Miguel Covarrubias.

Introduction

The archaeological view regarding the Maya, and their root progenitor the Olmec (1500 BCE onwards), is that cultural innovations were made within Mexico alongside an agrarian revolution consisting the “three sisters“, squash, maize (“corn”), and climbing beans. This agriculture led to civilizing skills and it reads like the Neolithic revolution in Mesopotamia after 4000 BCE, where irrigation made the fertile loam able to realize agricultural innovations from the northern golden triangle, leading to writing, trade, city states, religion, arithmetic and so on, all in isolation from European or Asian civilizations. The notion of diffusion from the ancient near east, or from India, could have occurred through ocean conveyors, of ocean currents and trade winds, has been proposed but never accepted. Yet there are reasons to think that, the astronomy and monumentalism of the pre-Columbian Mexican civilizations has clear precedents in the ancient near east and Asia.

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Story of Three Similar Triangles

first published on 24 May 2012,

Figure 1 Robin Heath’s original set of three right angled triangles that exploited the 3:2 points to make intermediate hypotenuses so as to achieve numerically accurate time lengths in units of lunar or solar months and lunar orbits.

Interpreting Lochmariaquer in 2012, an early discovery was of a near-Pythagorean triangle with sides 18, 19 and 6. This year (2018) I found that triangle as between the start of the Erdevan Alignments near Carnac. But how did our work on cosmic N:N+1 triangles get started?

Robin Heath’s earliest work, A Key to Stonehenge (1993) placed his Lunation Triangle within a sequence of three right-angled triangles which could easily be constructed using one megalithic yard per lunar month. These would then have been useful in generating some key lengths proportional to the lunar year:  

  • the number of lunar months in the solar year,
  • the number of lunar orbits in the solar year and 
  • the length of the eclipse year in 30-day months. 

all in lunar months. These triangles are to be constructed using the number series 11, 12, 13, 14 so as to form N:N+1 triangles (see figure 1).

n.b. In the 1990s the primary geometry used to explore megalithic astronomy was N:N+1 triangles, where N could be non-integer, since the lunation triangle was just such whilst easily set out using the 12:13:5 Pythagorean triangle and forming the intermediate hypotenuse to the 3 point of the 5 side. In the 11:12 and 13:14 triangles, the short side is not equal to 5.

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Knowing Time in the Megalithic

The human viewpoint is from the day being lived through and, as weeks and months pass, the larger phenomenon of the year moves the sun in the sky causing seasons. Time to us is stored as a calendar or year diary, and the human present moment conceives of a whole week, a whole month or a whole year. Initially, the stone age had a very rudimentary calendar, the early megalith builders counting the moon over two months as taking around 59 days, giving them the beginning of an astronomy based upon time events on the horizon, at the rising or setting of the moon or sun. Having counted time, only then could formerly unnoticed facts start to emerge, for example the variation of (a) sun rise and setting in the year on the horizon (b) the similar variations in moon rise and set over many years, (c) the geocentric periods of the planets between oppositions to the sun, and (d) the regularity between the periods when eclipses take place. These were the major types of time measured by megalithic astronomy.

The categories of astronomical time most visible to the megalithic were also four-fold as: 1. the day, 2. the month, 3. the year, and 4. cycles longer than the year (long counts).

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Vectors in Prehistory 2

In early education of applied mathematics, there was a simple introduction to vector addition: It was observed that a distance and direction travelled followed by another (different) distance and direction, shown as a diagram as if on a map, as directly connected, revealed a different distance “as the crow would fly” and the direction from the start.

The question could then be posed as “How far would the plane (or ship) be, from the start, at the end”. This practical addition applies to any continuous medium, yet the reason why took centuries to fully understand using algebraic math, but the presence of vectors within megalithic counted structures did not require knowledge of why vectors within geometries like the right triangle, were able to apply vectors to their astronomical counts.

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