Stone monuments with no secular use continued to be built within the historical period and many of them appear to share the megalithic metrology and geometrical ideas then developed further into religious buildings. This section explores a few examples what came to be called sacred geometry based upon different cultural and sacred driving forces; including Gothic, Arabic and Greek temples.
- Category: Post Megalithic
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As Europe emerged from the Romanesque, undocumented Norman and Benedictine influences manifested a "Gothic" style of cathedral building, conflating church building with exotic cosmological ideas involving sacred geometry and astro-harmonic symbolism. The prime exemplar of Gothic is perhaps the Cathedral of Chartres, now shrouded in many mysteries including who could have built such a masterpiece. John James  reports that records concerning its construction were lost in the century following its completion.
Figure 1 The Western Towers of Chartres Cathedral
The ratio between the twin towers is the same as that between the 12 month to 13 month lunar years, the latter being the same astronomical period John James proposed as intended for the whole length of church (then in Std Geo Royal feet.)
Figure 2 John James interpretation of the overall design was
an embodiment of 12 and 13 month lunar years.
1. The Master Masons of Chartres. James, John. Routledge and Kegan Paul: London 1982.
"The most important astronomicial calculations undertaken in the middle ages were to compute accurately the dates for Easter. Though dependant on the moon, the dates still had to keep in step with the cycle of the solar year. This hey did through a simple formula, where for two years running they fixed Easter from the short year of thirteen [twelve]lunations, followed by one long or embolismic year of 384 days which, with suitable adjustments, brings the Easter cycle back into phase with the sun." 111.
Two times 12 (=24) plus 13 equals 37 lunar months, three of those 111 months and six such periods equal 235 months, the duration taken for the 19 year (Metonic) anniversary of sun, moon and stars. In the Julian calendar of that date, an extra month every three lunar years could keep Easter later than the Spring Equinox. Meanwhile, 37 lunar months equals three Saturnian years of 364 days thus synchronising Easter with the seven day week, since the rubric for Easter established by the synod of Whitby was "the first Sunday after the first full moon after the equinox." (see also our articles)
Another possible view, taken here, is that the heights of these towers, were in root geographical roman feet of 0.971003 ft since 344 ft (as quoted) is 354.367 x 0.971003=344.09142 ft. 
2.This view became possible due to Ernst Levy's appendix to Simson, Otto von. The Gothic Cathedral. Bollingen: Tennessee 1956. called On the Proportions of the South Tower of Chartres Cathedral. This was removed from later editions)
In a previous article, Chartres: Relation of Western Towers to Gothic Floor Plan, Keith Crichlow's ideas were explored: that the two towers were (a) symbolic of the sun and the moon (as per their popular naming) in their heights but that (b) these heights also figured a horizontal lengths in that the Rose Window equated to the Labyrinth and the aisle lengths might correspond to the linear development of the cathedral's floor space, from a common line at the base of the towers. Two key questions emerged:
- Do the Tower lengths correspond to features along the floor plan?
- And why would such a concept have been employed at Chartres?
Firstly one can see (figure 3 below) a correspondence between the façade and the floor plan: The single lunar month difference between 12-month and 13-month lunar years corresponds to the radius of the Rond. Though Critchlow thought the two towers were 365 and 354 feet high (the sun and moon towers in both name and measure) the ratio in their heights of ~1.08 is not the ratio between the solar and lunar years but (as stated) is 12:13, the ratio between the 12 (normal) and 13 month (embolismic) lunar years.
Figure 3 Identifying the 1.08 ratio in the floor plan
and locating the labyrinth as mirroring the Rose Window
Do the Tower lengths correspond to features along the floor plan?
If the metrology within the cathedral had a starting point on entry to the Nave one can reach the start of the Apse as delimiting one lunar year using a new measure, a cubit of 1.77 feet*** . One hundred of those cubits equals 354 half cubits whilst the diagonal across the Nave and Choir is then 360 half cubits eight times 45, the harmonic root of Adam (see figure 4 below).
[***Root version of the cubit of Al Mamun. NEAL. 2000. 92.]
Figure 4 Metrological Interpretation of Chartres Floor Plan,
organised according to astronomical time
The first pillar of the Ambulatory defines the 13 month year and before that lies the solar year (as red diagonal of a purple four-square rectangle) on an arc so as to touch the central ceiling boss, which boss then marks the solar year of 365.2422 days as central to the Apse/Rond (the sun central to the solar year and solar system.)
The embolismic year defines side length of a 24 by 7 rectangle (in blue) to the first pillars of the Rond, a proportion of chromatic semitone 25/24 to the lunar and a 25 unit diagonal of 400 days (see below). The width of this rectangle is 112 half cubits (16 times seven), the same as the number of cusps around the outside of the Labyrinth.
And why would such a concept have been employed at Chartres?
The answer lies in the diabolical functional approach to calculating Easter and why the Synod of Whitby should have fought the Celtic church so hard to have such a labyrinthine definition for Easter. I highlight the word functional because the method of calculation is just that and carries no understanding of the phenomena behind the two lunar years which the twin towers of Chartres represent also relating to the Easter of the western church.
Every solar year there are 12 and 7/19th lunar months and this means that after nineteen years there are 12 x 19 = 228 + 7 = 235 lunar months, the Metonic count. These seven extra months are being distributed so as to become 12 + 12 + 13 = 37 lunar months so that six of these are 222 lunar months. Add one month and one obtains the Saros eclipse period of 223 lunar months. Add thirteen months and one obtains the 235 lunar months of the Metonic. The Metonic has seven embolismic years of 13 months because of the 7/19th of a lunar month per year. Since the Embolismic is a normal lunar year plus one, then seven lunar years can be taken off the 12 x 19 leaving only twelve, used for the mixed counting scheme with seven longer years.
Whilst towers, aisles and their metrology can be symbolic, we saw in the earliest Greek temple (the Heraion of Samos) that its columns (thought merely symbolic or supportive) had an astronomical counting function. The twelve columns up to the rond seem to offer a counting function but instead it is the bosses of the gothic arches above each stall of the aisles that appears to have a celestial counting function as equalling a single lunar eclipse. There are twelve bosses/stalls in each side aisle and in the central nave/crossing/ choir able each to count twelve lunar months. If the central twelve are linked to the single boss of the Rund, then the central hall plus Rund add up to the Embolismic year of thirteen lunar months and, with the side aisles, a total of 37 lunar months can be counted, as shown in figure 5.
Figure 5 Chartres Cathedral as Device
for Counting Astronomical Time
Since a count of the Saros and Metonic requires a common basis of six such counts of 37 lunar months then the six columns of the Rund appear to give a mechanism for knowing where the count has reached. Having made six counts of 12 + 12 + 13 = 37 x 6 = 222 then counting the Rund gives the Saros of 223 lunar months whilst then counting the central twelve gives the Metonic period of 223 + 12 = 235 lunar months or nineteen years.
One can say that the arrangement above resembles an abacus in form and also that the notion of placing the lunar months in the highest point of each ribbed ceilings boss has considerable symbolic merit that might even point to how the boss functions to keep the ceiling from falling; like an ethereal equivalent of a column, the boss is connected to the sky.
Figure 6 The Bosses of Chartres Cathedral Choir and Rund
CCAS by Marianne Casamance
- Category: Post Megalithic
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The Kaaba appears to express a geometrical progression of adjacent odd numbers starting with one and three. This differs from the super-particular ratios findable within the right triangles of astronomical time periods in the Megalithic, ratio pairs separated by only one rather than two. However, the multiple-square rectangles, used by the megalithic as approximations to celestial ratios, made use of the three-square rectangle. One of the earliest of these rectangles, this rectangle approximates two pairs of ratios: The eclipse year (346.62 days) to the solar year (365.2422 days) and the solar year to the thirteen lunar month year (384 days)
Figure 1 The three-square approximations in a triple series of astronomical periods. Note that the diagonals relative to the base are the result of having three squares in a rectangle then one high and three along - and two different. Two such rectangles geometrically sum (their angles) to give that of the (First Pythagorean) 3-4-5 triangle, 36.8 degrees.
If one adopts a square of 36 inches side length and projects outwards from the triple-square, one generates succeeding "odd couples" 3:5, 5:7, 7:9 and then 9:11 inside the walls and then 11:13 as the normalised plan for the Kaaba.
Figure 2 The geometrical progression of odd sided rectangles leading to the Kaaba wall plan.
This suggests that the design was to include the building within an implicit progression of odd-sided rectangles for reasons connected to the monuments orientation to astronomical time (lunar maximum standstill) and the facility of the triple-square "origin point" for the geometrical progression and of the triple time periods relating to the lunar nodes, in figure 1.
When the unit side length for this architectural grid is the plain yard of three (English) feet and 36 inches, then
- The inner perimeter is 9 x 2 + 11 x 2 = 40 yards, 120 feet and 1440 inches, 1,440 being the number of Adam.
- The outer perimeter is then 11x 2 + 13 x 2 = 48 yards, 144 feet, or 1,728 inches, 1728 being 12 cubed (one possible meaning for the Kaaba name) associated then with Arks and Ages in the ancient traditions.
The 11 by 13 rectangle is therefore the perfect scheme for expressing Adam, (whose temple the Kaaba was said to originally be) in relation to the head number (sans zeros) of Krita Yuga number 1,728,000.
Figure 3 Numerically symbolic perimeters of the Kaaba walls
Since the Kaaba was aligned to the 18.618 years (6800 days) of the nodal period, then in those 6800 days, there are 19.618 eclipse years (of 346.62 days). And this is exactly the ratio generated at the centre of the rectangular progression of figure 2 where the three-square rectangle has a diagonal that stands in the ratio of 19.618 to 18.618. If the three-long base of the rectangle is 18.618 years then the diagonal is 19.618 eclipse years long because such right triangles (half the rectangle) represent the inverse relationship of periodic frequency (within the same period) as well as the (same) ratio between periods.
Figure 4 The ratio between eclipse and solar years will be inversely reflected in the number of each contained in the 18.618 nodal period of the Moon's orbit.
This reveals that the eclipse and solar year lengths express a rationic difference normalised to a unit of time equal to 18.618 days. There are 18.618 of these in the eclipse year and 19.618 of these in the solar year, but what is this 18.618 day period? It is the time taken for the moon's node to move one DAY in angle on the ecliptic, and this is the average angle traversed by the sun on the ecliptic in one solar day. It is therefore true that the movement of the lunar nodes are synchronised to the sun's motion per day according to the number 18.618. The nodes are slower and retrograde in their angular motion and so the nodes take 18.618 solar years to completely traverse the ecliptic.
For the Kaaba, it is profoundly significant that the two numbers (1440 and 1728) naturally emerge from the three-square geometry which encapsulated the meaning of the monument's orientation; only when 36 units (inches) is taken as the unit length, and both sides of the rectangle are repeatedly lengthened by two units. Most ancient temples employed grid designs and most ancient mythology seems to have found a use for 1440 and 1728 in some of their greatest stories, but the Kaaba links, in an original and probably unique way, mythological numbers to astronomical facts in the numerical geometry of its design and its orientation of the Moon's Maximum Standstill.
- Category: Post Megalithic
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The prophet Mohammad declared himself the last prophet of Allah, a name resembling the El Shaddai (trans. Lord God, KJV) of Abraham in the Bible. Mohammad galvanised the Arabs and nearby nations with an original religion, branching off from the start of the Patriarchs found in the Bible's first book, Genesis. His story follows Ishmael, the first son of Abraham, from whom the Arabs believe themselves descended.
Figure 0 "Reconstruction of the Ka'bah as it must have been (left) when Abraham built it" and
(right) "as it must have been rebuilt in Muhammad's lifetime" [Esin. 24. & 46.]
[Shaikh Tahir al-Kurdi of Mecca, after al-Sab'ai, A. Tarikh Makkah. 1952.]
Mohammad's religion of Islam ("salvation") started in Mecca where he received visions of angels and spontaneously recited suras (verses) which became the Quran and associated texts. An unknown history of Abraham and Ishmael emerged, intimate with Mecca, long a spiritual centre for the Arabs. Mecca's principle monument, the Kaaba or "cube", has taken a number of forms. Adam located it as a dolmen created by God when Adam was formed; Ishmael built the next design for his father, "open to the sky", using surface stones from nearby mountains; and Mohammad's dispensation adds ancient stories about cubic arks and located these as a renewed Kaaba, the prime centre, or Pole of redemption for the world.
The Kaaba as Ark
Within both myth and the historical period, the Kaaba has been restored or rebuilt many times. Mohammed himself was involved in one restoration effort after flood damage, and that version was probably not much different from the present form; which is not cubic. I believe the original Kaaba was referenced to a cubic relationship in time, which was then adapted into the harmonic number most favoured for arks, the cube of twelve or 1,728. These two references to a cube are anciently megalithic and (more recently) harmonically symbolic. Mohammed and his fellow rebuilders of the Kaaba appear to have demonstrated a contact with the harmonism of YHWH and hence with the Abrahamic tradition found in the Bible.
Figure 1 The symbolic use of numbers for Adam and Ark
in the interior and exterior perimeter of the present Kaaba, in inches.
The Prophet's Kaaba, if it involved 1440 inches as its interior circumference, placed Adam* at the heart of the monument whilst the outer perimeter appears to be 1728 inches in length**, referencing the Kaaba as an Ark. Such a simple integration is achievable in a rectilinear building by having a wall depth of 36 inches. The notion of using perimeters in a focal monument (as a simulacrum of the centre of the world***) is then enacted by perambulations of the faithful and the calling to prayer facing Mecca from around the world. Islam is a distinctly oral religion with its own sounds and of course the recitation of the Quran and other originally oral works, after Mohammed.
* this basis for Adam's name code was discovered by Ernest G. McClain (1975.) whose work I use extensively in my next book on planetary harmony, published later this year.
** the author has here used the plan, with thanks, provided by Bjank through Wikipedia
*** in Lords of Time, p178-180, the author demonstrated how the wall of Jerusalem's Temple Mount was a scale model of the Earth's Meridian referencing precession of the Equinoxes according to an ancient model of the celestial earth, in the sky.
The Kaaba as Pole
The older signification of the Kaaba as cube can be seen in its (continuing) orientation to the maximum northerly ("standstill") moonrise to the east, every 18.6 years. The monument was (always) located with Mount Hira in the east (frequented by Mohammed during key visions and recitations) whose northern limit is a valley enabling visibility of the maximum moonrise in the northeast. A further circumstance for Mohammed's time was that Canopus rose to the south-east, at right angles to the maximum moonrise. At that moment, the semi-circular Hatim would have pointed towards the axis of the moon's orbit within the circumpolar stars.
Figure 2 The alignment of Canopus to the axis of the lunar orbit in Mohammed's time
Canopus, a giant golden star, second brightest star in the sky, is emblematic of the Golden Age within the precessional cycle of 25,920 years since it is the bright southern pole of that Age, whilst the Babylonian ark of 1,728,000* is (numerically) the Hindu Krita Yuga or duration of the golden age in "years". As such, Canopus was shining into Mohammad's Kali Yuga Age and the star Canopus figures in the illuminist literature of Islamic Sufi orders, especially Persian, as Kutb (Pole), the teacher of the Age. These orientations of the Moon evidently go back to the Arab monument which, by Mohammed's time, had 360 stone monuments to worship, and we know the harmonic root of Adam, according to his Hebrew letter-numbers, is A.D.M. = 1 + 4 + 40 = 45, when summed, which times two cubed or 8 equals 360, a number rooted in Adam's 45.
* The thousands are not arbitary: being the cube of 10 x 10 x 10 but also the decimal base of 1440 = 360 x 4.
The Kaaba as Great Time
The original monument was described (see figure 3) as trapezoidal, involving four lengths of 20, 22, 32 and 37 ells, and from this one can make a trapezoidal shape which does not simply use these lengths as sides. One finds that the draconic period of 18.618 years, in which the moon's nodes travel around the ecliptic, can numerically appear when a base length of 32 ells and hypotenuse of 37 ells, are used to form a right triangle.
Figure 3 An interpretation of Ishmael's Kaaba as Code for the 32:37 right triangle
whose third side is closely 18.618, the years in the moon's nodal period.
(compare to first figure above of Abraham's Kaaba)
At this point one needs to know that the cube of 18.618 years is one quarter of 25,814 years, so that the 18.618 side of the triangle is the side length of a cube of time related to one quarter of a Great Year (to the extent that precession of the equinoxes could be established then or now.) The revision of the Kaaba in Mohammad's time appears to have placed the cube of Twelve in the outer perimeter of the monuments wall and then subtly located Adam's 1440* by having walls of suitable thickness.
* 4 x 360 = 1,440 and Adam's name using position notation of 1.4.40 (again after Ernest McClain 1975. 126-7: "now 8 is a cube number in both decimal and sexagesimal systems, and the cube plays a sacred role in many religions, including that of Mecca and Delphi.")
It remains to be seen whether the uniqueness of Islam as an Abrahamic religion comes from a fresh perspective on the Great Year connecting Abram, Adam and the Moon. It is certainly true that the rotation of the Earth, the length of its orbit and the motion of the moon's nodes are normalised with respect to each other, and that the tilt of the earth's axis would have been changed by the primordial collision with the moon, and thus the creation of the Moon is the reason for the separation of earth and heaven, then subject to precession.
Esin, Emel. MECCA the Blessed MADINAH the Radiant. London: Paul Elek, 1963.
McClain, Ernest G. (see http://ernestmcclain.net/ for pdf)
The Myth of Invariance. New York : Nicolas Hays, 1976.
Meditations on the Quran. New York: Nicolas Hays, 1981
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