What stone L9 might teach us

image of stone L9, left of corridor of Gavrinis Cairn,
4Km east of Carnac complex. [image: neolithiqueblog]

This article was first published in 2012.

One test of validity for any interpretation of a megalithic monument, as an astronomically inspired work, is whether the act of interpretation has revealed something true but unknown about astronomical time periods. The Gavrinis stone L9, now digitally scanned, indicates a way of counting the 18 year Saros period using triangular counters  founded on the three solar year relationship of just over 37 lunar months, a major subject (around 4000 BC) of the Le Manio Quadrilateral, 4 Km west of Gavrinis. The Saros period is a whole number, 223, of lunar months because the moon must be in the same phase (full or new) as the earlier eclipse for an eclipse to be possible. 

On the roof with Anthony Blake (left) on the DuVersity Albion Tour, in August 2004.

Handling the Saros Period

223 is a prime number not divisible by any lower number of lunar months, such as 12 in the lunar year. 18 lunar years equates to 216 lunar months, requiring seven further months to reach the Saros condition where not only is the lunar phase the same but also, the sun is sitting upon the same lunar node, after 19 eclipse years of 346.62 days.

However, astronomers at Carnac already had a number of 37 lunar months (just less than three solar years) in their minds and, it appears, they could apply this as a length 37 units long, as if each unit was a lunar month. We also know that the unit they used for counting lunar months was originally 29.53 inches (3/4 metre) or later, the megalithic yard. Visualising a rope of length 37 megalithic yards, the length can be multiplied by repeating the rope end-to-end. After six lengths, 222 or 6*37 lunar months were represented, one lunar month less than the 223 lunar months which define the Saros period.

Figure 1 The near-integer Anniversary of Lunar Months over Three Years

This six-fold use of the number 37 appears to be used within the graphic design of Gavrinis stone L9 (see figure 2), as the triangular shape which has an apex angle of 14 degrees and which refers to the triangle formed at Le Manio between day-inch counts over three solar and three lunar years. It appears that this triangular shape was used to refer to the counting of solar years relative to a stone age lunar calendar (see 2nd register of stone R8) but it could also have the numerical meaning of 37 because three solar years contained 37 whole lunar months just as a single solar year contains 12 whole lunar months (the lunar year).

I believe this triangle, already symbolic of 37, appears in pairs within stone L9, as a single counter showing two axe heads, their points adjacent so that they have one side also adjacent. The two triangles are found to be held accurately within the apex angle of another triangle, known to be in use at Carnac, the triangle with side lengths 5-12-13, with apex angle 22.6 degrees. These pairs would then effect the notion of addition so that each is valued at 37 + 37 = 74 lunar months.

Figure 2. The use of two three-year triangles, made to fit within the 5-12-13 triangle to form a single counter worth 74 lunar months. (MegalithicScience.org eventually became this website)

All of the three pairs have this same apex angle, of the 5-12-13 triangle, chosen perhaps because 12+12+13 = 37 whilst the 14 degree triangle was known to be rationally held within it when the 12 side is seen as the lunar year of 12 months. The third side is then 3 lunar months long (¼ lunar year) forming an intermediate hypotenuse within a 5-12-13 triangle, which is equal to the 12.368 months of the solar year. Robin Heath first identified the smaller triangle when studying the properties of the 5 by 12 rectangle of Stonehenge’s Station Rectangle, arguably made up of two 5-12-13 triangles joined by their 13 sides. Three solar years then seems to have become associated with the pattern 12+12+13 (= 37) by the historical period, since Arab and medieval astronomers came to organize their intercalary months within the Callippic cycle of 4 Metonic periods (= 4 x 19 years equaling 76 solar years).

Figure 3. The quantification of the Saros as 18 solar years and 11 days equal to 223 lunar months. The language of days and years at Gavrinis might well have been the primary perception of light and dark periods.

The Saros period of 223 lunar months then also appears indicated on stone L9, below these triangles, within the main feature of this stone, a near-square Quadrilateral having one right angle. It has a rounded top, containing a wavy engraved design emanating from a central vertical, not unlike a menhir. The waves proceed upwards but then narrow to a vestigial extent after the 18th, which would be one way to symbolise the Saros period as 18 years and eleven days in duration. A different graphical allusion was used on stone R8, again showing lines as years but giving the 19th year as a shortened “hockey stick”.

Conclusions

In Gavrinis stone L9, a “primitive” numerical and phenomenological symbolism appears to have expressed a useful computational fact: that the Saros period was one lunar month more than six periods of 37 lunar months. These three periods of 37 months were shown as blade shapes, each symbolising three solar years, but shown as pairs within three 5-12-13 triangles above a quadrilateral shape indicating 18 wavy lines plus a smallest period, this symbolising the 11 days over 18 years of the Saros Period, defined by 223 lunar months. This allowed the Saros to be seen as six periods of 37 lunar months, equal to 222, plus one lunar month. Once the count reached 222, attention to the end of the next lunar month would be key. This enabled a pre-arithmetic culture to approach prime number 223 from another large prime (37) which was nearly expressed by 3 solar years, then repeated six times yo become 222 lunar months. This same counting regime appears to have been employed elsewhere:

  1. Astronomical Rock Art at Stoupe Brow, Fylingdales.
  2. Eleven Questions on Sacred Numbers.
  3. Counting lunar eclipses using the Phaistos Disk.

Many thanks to Laurent Lescop of Nantes University Architecture Dept,
for providing the scan on which this work is based.

pdf: Counting lunar eclipses using the Phaistos Disk

This paper* concerns itself with a unique fired-clay disk, found by Luigi Pernier in 1908 within the Minoan “palace” of Phaistos (aka Faistos), on the Greek island of Crete. Called the Phaistos Disk, its purpose or meaning has been interpreted many times, largely seen as either (a) a double-sided text in the repeated form of a spiral and outer circle written using an unknown pictographic language stamped in the clay or (b) as an astronomical device, record or handy reference. We provide a calendric interpretation based on the simplest lunar calendars known to apply in Minoan times, finding the Disk to be (a) an elegant solution to predicting repeated eclipses within the Saros period and (b) an observation that the Metonic is just one lunar year longer, and true to the context of the Minoan culture of that period.

*First Published on 26 May 2017
web page version

Cretan Calendar Disks

I have interpreted two objects from Phaistos (Faistos), both in the Heraklion Museum. Both would work well as calendar objects.

One would allow the prediction of eclipses:

The other for tracking eclipse seasons using the 16/15 relationship of the synod of Saturn (Chronos) and the Lunar Year:

Locmariaquer 1: Carnac’s Menhirs and Circumpolar Stars

Read 1458 times when last published on MatrixOfCreation.co.uk, Wednesday, 16 May 2012 14:22

At megalithic sites, the only alignment of note on the northern horizon has usually been the direction of the north pole or “true” North on the site plan. “Megalithic” cultures worldwide, both the later manifestations in the Americas or the old world cultures of Northwest Europe or Egypt, built structures oriented in a very accurate way to North. The builders of the Great Pyramid for example or of the geo-glyphs of the Amazon rainforest, seemed to have had an unexpectedly good method for determining North, no easy task when a pole star is never exactly north and, in many epochs, there is no star near to the pole.

Continue reading “Locmariaquer 1: Carnac’s Menhirs and Circumpolar Stars”

The Cult of Seven Days

Published in Nexus Magazine in 2004

When understanding the origins of human knowledge, we tend not to look into the everyday aspects of life such as the calendar, our numbering systems and how these could have developed. However, these components of everyday life hold surprising clues to the past.

An example is the seven day week which we all slavishly follow today. It has been said that seven makes a good number of days for a week and this convenience argument often given for the existence of weeks.

Having a week allows one to know what day of the week it is for the purposes of markets and religious observances. It is an informal method of counting based on names rather than numbers. Beyond this however, a useful week length should fit well with the organisation of the year (i.e. the Sun), or the month (i.e. the Moon) or other significant celestial or seasonal cycle. But the seven day week does not fit in with the Sun and the Moon.

The Week and the Year

Continue reading “The Cult of Seven Days”

Story of Three Similar Triangles

first published on 24 May 2012

Interpreting Lochmariaquer in 2012, an early discovery was of a near-Pythagorean triangle with sides 18, 19 and 6. This year I found that triangle as between the start of the Erdevan Alignments near Carnac. But how did this 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.


Figure 1 Robin Heath’s original set of three right angled triangles that exploit 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.
Continue reading “Story of Three Similar Triangles”